If tan thita= 1/(root3) , then sin thita =? answer should be 1/2 according to book. please give solve​

Answer:

14

Step-by-step explanation:

ac/b - (a + d) = (-2)(-12)/3 - ((-2) + (-4)) = (-2)(-12)/3 - (-6) = 24/3 + 6 = 8 + 6 = 14

Answer:

  x = 25

Step-by-step explanation:

The given angles, x° and (6x+5)° form a linear pair. You want the value of x.

Two angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.

  x° +(6x +5)° = 180°

  7x +5 = 180 . . . . . . . . . divide by °, collect terms

  7x = 175 . . . . . . . . . . subtract 5

  x = 25 . . . . . . . . . . divide by 7

The value of x is 25.

The linear function g which has a rate of change of -16 and initial value 600 is; g = -16x + 600.

It follows from the task content that the linear expression which is as described by the given verbal description is to be determined.

Since the standard slope-intercept form of a linear function is as given; f(x) = ax + b.

Where, a = slope (rate of change) and b = y-intercept (initial value).

Therefore, the required linear function which is as described is;

g = -16x + 600

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Answer:

C. -3

Step-by-step explanation:

Subtract 6 from 27 and then divide 21 (27-6) by -7 to get -3

Answer:

A and B

Step-by-step explanation:

Vertical angles are angles that are opposite of each other on two crossing lines.

They have equal angle measure.

When we look at the image, we can tell that, from the given options:

A. <LRA and <FRA and

B. <TRF and <NRL are vertical angles.

Answer:

\(MO = 4.92\)

Step-by-step explanation:

Given

See attachment for triangles

Required

Find MO

To do this, we make use of triangle 2 because it is similar to MNO.

To calculate MNO, we make use of the following equivalent ratios.

\(MN : MO = 10:8.2\)

Express as fraction

\(\frac{MO}{MN} = \frac{8,2}{10}\)

\(\frac{MO}{MN} = 0.82\)

Substitute \(MN =8\)

\(\frac{MO}{8} = 0.82\)

Solve for MO

\(MO = 8 * 0.82\)

\(MO = 4.92\)

Answer: 6.6

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

300 - 240 = 60  ÷  300 = 20% mangoes.

Answer:

y=1

Step-by-step explanation:

Answer:

SEESH thanks for the points

Step-by-step explanation:

Answer:

2.50 dollars                                          

Answer:

2.50

Step-by-step explanation:

Answer:

We can assure the Ann Arbor officials that after look the information we conclude that the mean is 8 h

Step-by-step explanation:

From CI ( 95 % )  = ( 6,7 ; 9,3 )

And the information "large random size sample" we conclude that the population has a normal distribution; a normal distribution has a bell shape curve, and data must spread symmetrically with respect to the mean, therefore the mean is:

6,7 + 9,3 = 16

16/2 = 8

If we need t check we can use the other CI

CI ( 99 % ) = (6,257 , 9,743 )

6,257 + 9,743 = 16

16/2 = 8

We are sure the mean is 8 h  

Answer: B

Step-by-step explanation: Hope this helps:)

The values of the variables in number 3, in simplest radical form, are:

f = 6;  o = 3.

The simplest radical form, also known as simplified radical form or simplified surd, refers to expressing a square root (√) or other roots in the simplest possible way without any perfect square factors in the root. In other words, it involves reducing the radical expression to its simplest form.

Solving problem 3, we would apply the necessary Trigonometric ratios to find the variables:

sin 60 = opp/hyp

sin 60 = 9√3 / f

f = 9√3 / sin 60

f = 9√3 / √3/2 [sin 60 = √3/2]

f = 9√3 * 2/√3

f = 18/3

f = 6

tan 60 = opp/adj

tan 60 = 9√3 / o

o = 9√3 / tan 60

o = 9√3 / √3 [sin 60 = √3]

o = 9√3 * 1 / √3

o = 9/3

o = 3

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Answer:

o = 9

f = 18

Step-by-step explanation:

Triangle #3 is a right triangle with two of its interior angles measuring 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, this triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #3, the longest leg is 9√3 units.

As "a√3" is the shortest leg, the scale factor "a" is 9.

The side labelled "o" is the shortest leg opposite the 30° angle. Therefore:

\(o = a=9\)

The side labelled "f" is the hypotenuse of the triangle. Therefore:

\(f= 2a = 2 \cdot 9=18\)

Therefore:

..

SOLUTION

Mode is/are the most occurring value/values in a given data.

That means we could have more than one mode.

Answer:

4.3 *10^3

Step-by-step explanation:

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

The given data are: \(22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7\)

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: \(\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8\)

= \(\sqrt{128.3336}\)

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = \(11.3284 ^2\)

Variance = 128.33264656

Variance = 128.33.

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well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

\(~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}\)

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

b

Step-by-step explanation:

Answer:

8 boxes

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Let's define what we have:

We need to find the amount of boxes needed for his entire amount of action figures.

Since we can only fit 7 per box, we need to divide 50 by 7 to find the amount of boxes needed for the total 50:

50 action figures ÷ 7 action figures per box = 7.14286 boxes.

Now, here is the tricky part: we can't have 7 point something of a box, right? There is no such thing as a tenth of a box in the real world.

Therefore, since we need more than 7 boxes, we will have to round up to the nearest whole number, as we can only have 1 box:

7.14286 boxes ≈ 8 boxes.

∴ Rodrigo will need 8 boxes to ship all 50 of his action figures to his friend.

Answer:

4.75 = 475/100 = 19/4 = 4 3/4

Approximate value(s):

4.75 =~ 4 (error = -15.789473%)

\( - 4.74\)

\( = - 4 + 0.74\)

\( = - 4 + \frac{74}{100} \)

\( = - 4 + \frac{37}{50} \)

\( - 4 \frac{37}{50} \)

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

\(\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}\)

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.  

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

\(\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}\)

Therefore:

\(\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}\)

\(\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}\)

Answer:

The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

We have the point (-6,8) and a slope of -5/3.

Step 1: Use the point-slope formula to find the equation of the line in point-slope form.

y - y1 = m(x - x1)

where x1 and y1 are the coordinates of the given point.

y - 8 = (-5/3)(x - (-6))

Simplify this equation:

y - 8 = (-5/3)(x + 6)

Step 2: Convert the equation to slope-intercept form.

Distribute (-5/3) to get:

y - 8 = (-5/3)x - 10

Add 8 to both sides:

y = (-5/3)x - 2

This is the equation of the line in slope-intercept form. Therefore, the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.

Answer:

y= 8

Step-by-step explanation:

y= k/x

-8= k/4

k= -8×4= -32

y= k/x

y= -32/-4

y= 8

hope it helps!

Answer:

the answer is 8 if y= -8 when x is 4 amd

We reject the Null Hypothesis and conclude that the individual is likely to have embezzled.

Given a Goodness of Fit test is a statistical test used to assess how likely it is that an observed data set fits a theoretical distribution, in this case Benford's Law. This test should be applied in this situation, as it can be used to determine if a data set follows the expected pattern of the theoretical distribution. The Null Hypothesis is that the observed data set follows Benford's Law, while the Alternative Hypothesis is that the observed data set does not follow Benford's Law. The P-Value for this test is 0.0116, which suggests that there is a 1.16% chance of observing a distribution this far from the expected one if the Null Hypothesis is true. Therefore, we reject the Null Hypothesis and conclude that the individual is likely to have embezzled. Based on this evidence, law enforcement officials should pursue the case further.  

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The value of the angle B from the trigonometric ratios is 53.13 degrees

The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.

We have that;

TanB = 4/3

B= Tan-1(4/3)

B = 53.13 degrees

Hence we are going to have by the use of tan that the angle is 53.1 degrees

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Answer:

Area of ΔQRS = 2.3 square inches

Step-by-step explanation:

From the given information,

<S + <Q + <R = \(180^{o}\)

51 + 44 + <R = \(180^{o}\)

95 + <R = \(180^{o}\)

<R = \(180^{o}\) - 95

    = \(85^{o}\)

<R = \(85^{o}\)

Applying the Sine rule, we have;

\(\frac{q}{SinQ}\) = \(\frac{r}{SinR}\) = \(\frac{s}{SinS}\)

Using \(\frac{r}{SinR}\) = \(\frac{s}{SinS}\)

\(\frac{r}{Sin 85}\) = \(\frac{2.3}{Sin51}\)

r = \(\frac{2.3*Sin85}{sin51}\)

  = 2.9483

r = 2.9 inches

Also, \(\frac{q}{SinQ}\) = \(\frac{s}{SinS}\)

\(\frac{q}{Sin44}\) = \(\frac{2.3}{Sin51}\)

q = \(\frac{2.3*Sin44}{Sin51}\)

  = 2.0559

q = 2.0 inches

From Herons formula,

Area of a triangle = \(\sqrt{s(s-q)(s-r)(s-s)}\)

s = \(\frac{2.3 + 2.0 + 2.9}{2}\)

  = 3.6

Area of ΔQRS = \(\sqrt{3.6(3.6-2.0(3.6-2.9)(3.6-2.3)}\)

                        = 2.2895

Area of ΔQRS = 2.3 square inches

Answer:

2.4

Step-by-step explanation: