state the extrema of the given function

Absolute minimum y= ____
x-intercept? ____
Continuous or discontinuous?
PLS HELP YALL I HAVE FINALS TMR AND IM STRESSED!!!

The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

We can start by using the trigonometric identities:

cos(-θ) = cos(θ)

tan(-θ) = -tan(θ)

csc(θ) = 1/sin(θ)

Substituting these identities into the original expression, we get:

cos(θ) * (-tan(θ)) * (1/sin(θ))

Simplifying this expression, we can cancel out the cos(θ) and the sin(θ) terms:

-1 * cos(θ) * (1/(cos(θ))) The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

In other words, the original expression simplifies to -1 for all values of θ where it is defined (i.e. θ ≠ (2n + 1)π/2, where n is an integer). This means that as θ varies, the value of the expression will always be -1 when it is defined. Trigonometric identities are mathematical equations that involve trigonometric functions and are true for every possible value of the variables involved. There are various types of trigonometric identities, including:

Pythagorean Identities:

\(sin^2a + cos^2a= 1\\tan^2a + 1 = sec^2a\\1 + cot^2a = csc^2a\)

Angle Sum and Difference Identities:

sin(α±β) = sin α cos β ± cos α sin β

cos(α±β) = cos α cos β ∓ sin α sin β

tan(α±β) = (tan α ± tan β) / (1 ∓ tan α tan β)

Double Angle Identities:

sin 2θ = 2 sin θ cos θ

cos 2θ =\(cos^2\)θ - \(sin^2\)θ = 2 \(cos^2\)θ - 1 = 1 - 2\(sin^2\)θ

tan 2θ = (2 tan θ) / (1 - \(tan^2\)θ)

Half Angle Identities:

sin (θ/2) = ± √[(1 - cos θ) / 2]

cos (θ/2) = ± √[(1 + cos θ) / 2]

tan (θ/2) = ± √[(1 - cos θ) / (1 + cos θ)]

Product-to-Sum Identities:

sin α sin β = (1/2) [cos (α-β) - cos (α+β)]

cos α cos β = (1/2) [cos (α-β) + cos (α+β)]

sin α cos β = (1/2) [sin (α+β) + sin (α-β)]

Sum-to-Product Identities:

sin α + sin β = 2 sin [(α+β)/2] cos [(α-β)/2]

sin α - sin β = 2 cos [(α+β)/2] sin [(α-β)/2]

cos α + cos β = 2 cos [(α+β)/2] cos [(α-β)/2]

cos α - cos β = -2 sin [(α+β)/2] sin [(α-β)/2]

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The planes that are parallel in the cube shown would be C. NOR and LMP.

Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.

From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.

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The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

X= -1

Y= -4

That's the answer I believe

5x - 3y = 7

First, Add 3y to both sides

5x - 3y + 3y = 7 + 3y

5x = 3y + 7

Then, Divide both sides by 5

\(\frac{5x}{5}\) = \(\frac{3y + 7}{5}\)

\(x = \frac{3}{5} y\) + \(\frac{7}{5}\) (Answer to #1)

-3x - 3x - 5 = 23

First, we will simplify both sides of the equation

-3x + -3x + -5 = 23

Next, We will combine like terms

(-3x + -3x) + (-5) = 23

-6x + -5 = 23

-6x - 5 =23

Then, we will Add 5 to both sides

\(\frac{-6x}{-6}\) = \(\frac{28}{-6}\)

x = \(\frac{-14}{3}\) (Answer to #2)

Answer:

A,E

Step-by-step explanation:

Operation: Minus

To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.

6.8 km - 2.3 km = 4.5 km

Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.

Answer:

a and e

Step-by-step explanation:

got it right on homework

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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The key features of the dashed graph are

A graph is a pictorial representation of a function

To describe the key features of the dashed graph, we proceed as follows.

So, the key features of the dashed graph are

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The type of transformation must the line segment have undergone if Sandra transforms a line segment such that the new image is longer than the original line segment, is dilation, so option A is correct.

The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.

Given:

Sandra transforms a line segment such that the new image is longer than the original line segment,

The above transformation is an example of dilation, as in dilation the image can be transformed into a large image or a small image,

Thus, the given transformation is an example of dilation.

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TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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The ratio of chocolate bars More Preferred: (9 chocolate bars, 3 glasses of milk); Equally Preferred: (6 chocolate bars, 3 glasses of milk); Less Preferred: (3 chocolate bars, 2 glasses of milk) and (9 chocolate bars, 2 glasses of milk).

The ratio of chocolate bars to glasses of milk that Isabel consumes is 3-to-1. This means that whenever she has 3 chocolate bars, she also has 1 glass of milk. Currently, Isabel has 6 chocolate bars and 2 glasses of milk. The bundles listed above are compared to Isabel's current consumption. Out of the five bundles, the one with 9 chocolate bars and 3 glasses of milk is more preferred than what Isabel currently has because it has more of the ratio than Isabel's current consumption. The bundle with 6 chocolate bars and 3 glasses of milk is equally preferred because it holds the same ratio as Isabel's current consumption. The bundles with 3 chocolate bars and 2 glasses of milk and 9 chocolate bars and 2 glasses of milk are less preferred because they both have less of the ratio than Isabel's current consumption.

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The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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An order-preserving function refers to a function that preserves the order between elements of the partially ordered sets it operates on. In other words, if two elements have a certain order in the first set, the function ensures that the images of those elements in the second set maintain the same order. This concept is denoted as f(x) < f(y) whenever x < y in the original set.

If both sets, P and Q, are linearly ordered, meaning that there is a total order relation among their elements, then an order-preserving function is also referred to as an increasing function.

An increasing function in this context means that it strictly preserves the order of elements, where if x is less than y, then the image of x is strictly less than the image of y.

In summary, an order-preserving function maintains the order between elements of partially ordered sets, while an increasing function specifically applies to order-preserving functions in linearly ordered sets, indicating that the function strictly preserves the order relation.

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Answer:

Domain: set of possible input values (x-values)

Range: set of output values (y-values)

The range for the function \(f(x)=-2|x-5|+8\) is:

\(f(x)\leq 8\)

(5, 8) is the vertex of the line

Because |x - 5| is absolute (so always positive) and it is multiplied by -2,

-2|x - 5| will always be negative unless x = 5 (when it will be zero).  Therefore, the max y-value is 8.

However, your question actually asked what the function is when x = -5:

\(f(-5)=-2|x-5|+8\\\\= -2|-5-5|+8\\\\= -12\)

Step-by-step explanation:

Thats the all rhe answers step by step

The  APR on the loan will be $13. The APR is found by the standard formula. It is calculated annually.

APR is an annualized cost indication for a loan that includes all costs.

Suppose there is an initial amount as P. The interest, or say charge on it, is applied annually as 'C' amount.

The given data in the problem is;

Loan payment = $400

Fees  = $52

APR=?

The value of the APR is found as;

\(APR = \dfrac{C}{P} \times 100 \\\\\ APR = \dfrac{52}{400} \times 100 \\\\\ APR = \$ \ 13\)

Hence, the  APR on the loan will be $13.

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The solution to the question is mathematically given as

1)

H0: M \(\geqslant\) 300

H0: M \(\geqslant\) 300

2)

Z distribution.

3)

z=-2.4

4)

P=0.0082

5)

"H0" is rejected as a hypothesis with a level of significance of 0.05.

Generally, the equation for is mathematically given as

Solutions

we have, \($u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}\)

(1):

H0: M \(\geqslant\) 300 dollars;  customers save at least 300 dollars per year by switching to them.

H0: M \(\geqslant\) 300 dollars:

(This is a left-tailed test)

(2):

when \(\sigma\) is known, we use the Z test. we use Z distribution.

(3):

\(\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}\)

(4):

\(Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082\)

(5):

In conclusion, Since p-value = 0·0082 <0.05

This is statistically significant at the 0.05 level.

We thus "Refect H0" using a threshold of significance of 0.05.

"H0" is rejected as a hypothesis with a level of significance of 0.05.

There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.

Therefore, we would not consider making the transition to this firm.

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Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.

Divide the numerator (11) by the denominator (4).

11 ÷ 4 = 2 remainder 3

The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.

Write the mixed numeral using the whole number part and the fractional part.

The mixed numeral for 11/4 is:

2 and 3/4

Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

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(a) Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39
(b) The function is y = 3  (1.1)ˣ.

(c) It would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) It would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

(a)

Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39

(b) Let x be the number of clicks and y be the width of the door on the screen. Then, we can write the algebraic rule as:

y = 3  (1.1)ˣ

(c) To make the door approximately 3 feet wide on screen, we need to convert 3 feet to inches, which is 36 inches. Then, we need to solve for x in the equation:

3 (1.1)ˣ = 36

Dividing both sides by 3, we get:

(1.1)ˣ = 12

Taking the logarithm of both sides (with base 1.1), we get:

x = log(12) / log(1.1) ≈ 14.7

So, it would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) To transform the display of the door from 3 feet wide back to a width of approximately 3 inches, we need to find the number of clicks of the zoom-out button that will result in a width of approximately 3 inches. We can use the same formula as before, but with the initial width of 36 inches (since we are zooming out):

36 (0.9)ˣ = 3

Dividing both sides by 36, we get:

(0.9)ˣ = 1/12

Taking the logarithm of both sides (with base 0.9), we get:

x = log(1/12) / log(0.9) ≈ 11.5

So, it would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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Answer:

123321

Step-by-step explanation:

Answer:

Option 2 (N= 27 )

Hope it helps!

Please mark as brainliest :D

Answer:

B. 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Angle = 37°

Adjacent Leg = x

Hypotenuse = 10

Step 2: Solve for x

Step-by-step explanation:

please it my steps to work on paper whorksheet

Point located at each location: 1) A  2) I 3) W 4) H 5) X 6) G 7) J 8) N 9) U 10) M 11). Ordered pairs are:  B(2,8) 12) E(0,0) 13) T(3,3) 14) Q(8,7)  15) Y(7,6) 16) R( 9,8) 17)  F(9,0) 18) S(3,6) 19) C(6,7)

Describe Ordered pair?

An ordered pair is a pair of mathematical object elements, such as numbers or other mathematical elements, where the order in which the object elements are listed is important. The ordered pair is usually written in the form (a, b), where 'a' represents the first element or coordinate, and 'b' represents the second element or coordinate.

In the context of the Cartesian coordinate system, an ordered pair represents a point in two-dimensional space, where the first element or coordinate represents the horizontal position on the x-axis and the second element or coordinate represents the vertical position on the y-axis. The order of the elements in an ordered pair is crucial because (a, b) is different from (b, a) and represents a different point in two-dimensional space.

Point located at each location is:

1) A

2) I

3) W

4) H

5) X

6) G

7) J

8) N

9) U

10) M

The ordered pair for given points is:

11) B(2,8)

12) E(0,0)

13) T(3,3)

14) Q(8,7)

15) Y(7,6)

16) R( 9,8)

17)  F(9,0)

18) S(3,6)

19) C(6,7)

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This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

\(\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} \)

Now, check the triangle, sin 37° = 3/5

therefore,

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) \)

[ convert degrees on right side to radians ]

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) \)

There are three more possible values as :

\(\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} \)

or in decimals :

\(\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167\)

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

\(\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 2.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = -5.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 8.385\)

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

Answer:

D

Step-by-step explanation:

Answer:

\( \sf \: 4 \frac{4}{8} \)

Step-by-step explanation:

Given problem,

\( \sf \rightarrow \: 2 \frac{3}{8} + 2 \frac{1}{8} \)

Let's solve the problem,

\( \sf \rightarrow \: 2 \frac{3}{8} + 2\frac{1}{8} \)

\( \sf \rightarrow \: \frac{19}{8} + \frac{17}{8} \)

\( \sf \rightarrow \: \frac{(19 + 17)}{8} \)

\( \sf \rightarrow \: \frac{36}{8} \)

\( \sf \rightarrow \: 4 \frac{4}{8} \)

Hence, the answer is 4 4/8.

Answer:

the probability of rolling a sum of 6 with these dice is 1/6.

Step-by-step explanation:

To find the probability of rolling a sum of 6 with the given pair of dice, we can first list all possible pairs of outcomes that add up to 6:

(2,4)

(3,3)

(4,2)

For each of these pairs, we need to find the probability of rolling each number on its respective die and then multiply those probabilities together. The probability of rolling a particular number on one die is the number of times that number appears on that die divided by the total number of outcomes on that die.

For the first pair (2,4), the probability is:

(2 appears twice on one die out of six possible outcomes) × (4 appears once on the other die out of six possible outcomes) = (2/6) × (1/6) = 1/18

For the second pair (3,3), the probability is:

(3 appears twice on one die out of six possible outcomes) × (3 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

For the third pair (4,2), the probability is:

(4 appears twice on one die out of six possible outcomes) × (2 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

The total probability of rolling a sum of 6 is the sum of the probabilities of each possible pair:

1/18 + 4/36 + 4/36 = 1/6

Therefore, the probability of rolling a sum of 6 with these dice is 1/6.

Answer:

look at the screenshot!

Step-by-step explanation:

Here you go, hope that helps!