How do you round 98.9949 to a whole number & 42.426 to a whole number ?

0.105 is equivalent to the fraction 21/200 in lowest terms.

What is fraction?

A fraction is a number that represents a part of a whole. Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x.

To convert a decimal to a fraction, we need to write the digits after the decimal point as the numerator and the place value of the last digit as the denominator. In this case, the last digit is 5, which is in the hundredths place (two places to the right of the decimal point).

Therefore, we can write:

0.105 = 105/1000

However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5:

105/1000 = (105 ÷ 5)/(1000 ÷ 5) = 21/200

Therefore, 0.105 is equivalent to the fraction 21/200 in lowest terms.

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4x+3y=15

Slope intercept form:

y= mx+b

Where:

m= slope

b= y-intercept

Solve for y:

4x+3y=15

3y = -4x+15

y = (-4x+15) /3

y=-4/3x+5

Answer:

∠3 and ∠1 are correct

Step-by-step explanation:

adjacent angles are next to each other with a common vertexand side

The correct names for the congruent triangles are Δ ABC ≅ Δ FED

Congruent triangles have both the same shape and the same size.

Given are two congruent triangles, ABC and DEF,

We have,

AC = DF

∠ A = ∠ F

Therefore,

∠ B = ∠ E

Hence, the correct names for the congruent triangles are Δ ABC ≅ Δ FED

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The simplification of the expressions in the question using the rules of indices are as follows;

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2. (3⁻⁴ + 5⁻³)⁻¹ = \(49\frac{31}{206}\)

3. (3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}\) = \(\dfrac{c^5\cdot e^8}{2\cdot d^5}\)

5.)  \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}\)

An index or indices is the power by which a number or variable or expression raised.

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰

6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1

6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2

Therefore;

6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2.) (3⁻⁴ + 5⁻³)⁻¹

(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))

1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))

1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209

10125/206 = 49 + 31/206

(3⁻⁴ + 5⁻³)⁻¹ = \(49 \frac{31}{206}\)

3.) (3⁻⁴ + 5⁻³)⁻²

(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)

1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)

1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)

1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)

1/((206/10125)²) = (10125)²/(206)² = 102515625/42436

102515625/42436 = 2415 32685/42436

(3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.)  \(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }\)

\(\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}\)

5.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }\)

\(\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }\)

\(\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = \(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)\)

\(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2\)

3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴

Therefore;

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴

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Answer:

the answer is y-4

Step-by-step explanation:

variable cone first

The probability of picking a 5-peso coin from the bag is 75%.

To calculate the probability of picking a 5-peso coin from the bag, we need to determine the total number of 5-peso coins and divide it by the total number of coins in the bag.

In the bag, there are three 5-peso coins and one 10-peso coin, making a total of four coins.

Probability of picking a 5-peso coin = (Number of 5-peso coins) / (Total number of coins)

Probability of picking a 5-peso coin = 3 / 4

To express this probability as a percentage, we multiply it by 100:

Probability of picking a 5-peso coin = (3 / 4) × 100 = 75%

The probability of picking a 5-peso coin from the bag is 75%.

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Debemos tomar la integral definida de la diferencia entre las dos funciones en el intervalo dado.

Supongamos que queremos encontrar el area entre dos funciones f(x) y g(x) en un intervalo (a, b).

Vamos a suponer que f(x) > g(x) en todo el intervalo (a, b), entonces el area entre la funcion f(x) y g(x) en ese intervalo se calcula como:

\(\int\limits^b_a {(f(x) - g(x))} \, dx\)

Si por ejemplo tuvieramos que para un valor c en el intervalo (a, b) se da que:

f(x) > g(x) en (a, c)

g(x) > f(x) en (c, b)

Entonces la integral sería:

\(\int\limits^c_a {(f(x) - g(x))} \, dx + \int\limits^b_c {(g(x) - f(x))} \, dx\)

Y similarmente si debemos separar el intervalo mas segmentos.

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Answer:

hi I had done it.I had done directly.

Answer:

8

Step-by-step explanation:

6/3 + 2 x 3

6/3 + 6

2 + 6=8

Answer:

\(2/3\)

Step-by-step explanation:

\(\frac{6}{3x}\)

\(\frac{6}{3(3)}\)

\(\frac{6}{9} =\frac{2}{3}\)

With the infοrmatiοn prοvided, the sοlutiοn is 2x + y = 9.

A mathematical equatiοn, including such 6 x 4 = 12 x 2, states that twο numbers οr values are equivalent. a meaningful nοun. An equatiοn is used when twο οr even mοre factοrs must be cοnsidered jοintly in οrder tο understand οr explain the whοle situatiοn.

Given:

Slοpe οr gradient οf line = -2

The lοcatiοn where the line passes = (1,7)

Equatiοn οf a line thrοugh (h,k) with a slοpe οf m:

(y - k) = (x -h) m

Equatiοn οf a line thrοugh (1,7) with a slοpe οf (-2): -

⇒ (y - 7) = (x - 1)(-2)

⇒ y - 7 = - 2x + 2

⇒ y = -2x + 2 + 7

⇒ y = -2x + 9

οr

⇒2x + y = 9

Verificatiοn οf respοnse:

We may check οur respοnse by substituting (1,7) in the fοrmula 2x+y=9.

⟹ LHS = (2×1)+7

⟹ LHS = 2+7

⟹ LHS = 9

Therefοre , LHS = RHS.

Alsο, yοu can use the equatiοn tο determine the gradient οr slοpe and cοnfirm yοur sοlutiοn.

⟹ Slοpe is equal tο -(cοefficient οf x)/ (cοefficient οf y)

⟹ Slοpe = - 2 /1

⟹ slοpe = -2

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The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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The best interpretation of the slope of the linear regression equation is given as follows:

For each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

The slope represents the rate of change of the output variable relative to the input variable of a linear relation.

Hence, it can be said that the slope states by how much the output variable y changes when the input variable x is increased by 1.

The variables in this problem are given as follows:

The negative slope of -0.7 means that for each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

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Answer:

B

Step-by-step explanation:

Answer:

6.8333333333 or 41/6

Step-by-step explanation:

The area of triangle PQR in this case is 14.924

In geometry, the concept of vectors is very useful when dealing with points, lines, and planes in three-dimensional space. Vectors have both magnitude and direction, and they can be added, subtracted, and multiplied by scalars.

To find a nonzero vector orthogonal to the plane through the points P, Q, and R, we can use the cross product of two vectors in the plane. A cross product of two vectors gives us a vector that is perpendicular to both of them, so it will be orthogonal to the plane as well.

Let's take the vectors from P to Q and from P to R as our two vectors:

u = Q - P = <5-3, 2-1, 4-1> = <2, 1, 3>

v = R - P = <8-3, 5-1, 3-1> = <5, 4, 2>

To calculate the cross product u x v, we can use the following formula:

u x v = <(1)(2) - (3)(4), (3)(5) - (1)(2), (1)(4) - (2)(5)> = <-10, 13, -2>

So the vector <-10, 13, -2> is orthogonal to the plane through P, Q, and R. Note that this vector is nonzero because at least one of its components is not zero.

To find the area of triangle PQR, we can use the fact that the area of a triangle is half the magnitude of the cross product of two of its sides. Let's take the sides from P to Q and from P to R again, and calculate their cross product:

u x v = <(3)(1) - (-6)(3), (-6)(2) - (3)(3), (3)(3) - (3)(2)> = <21, -21, 3>

So the vector <21, -21, 3> is orthogonal to the plane through P, Q, and R. Again, we can use the cross product of u and v to find the area of triangle PQR, which is:

|u x v| = sqrt(21^2 + (-21)^2 + 3^2) = √(891)

|u x v| = 1/2 * √(891) =14.924

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Answer: Less than 1

Step-by-step explanation: 4.23 x 10^-5 simply translated to 0.0000423

which is less than 1.

Answer:

less than 1

Step-by-step explanation:

4.23 * 10^5 is less than 1

Answer:

surface tension

Answer: The answer would be A. 5

Please mark me as brainliest

Check the picture below.

Check the picture below.

Answer: the quotient of the given expression is, h5

Step-by-step explanation:

Use the exponent rule:

Given the expression:

⇒

Apply the exponent rules we have;

Simplify:

therefore, the quotient of the given expression is,

The key here is to not worry too much and just follow PEMDAS.

Here we have the expression \((5\cdot 7)^2\).  Following PEMDAS, we complete the expression inside the parentheses first, or \(5\cdot 7 = 35\). This gives us \((35)^2\) or just \(35^2.\)

Hope this helps.

1.9 and 0.7 because you have to add 0.6 and 1.3 to get one of the numbers and you have to subtract 0.6 from 1.3 to get the other number

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

The time he start shopping is 2 : 00 PM

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

Time spent = 25 minutes

Time he left the store = 2 : 25PM

Using the above as a guide, we have the following:

Time he started = Time he left the store - Time spent

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

Time he started = 2 : 25PM - 25 minutes

Evaluate

Time he started = 2 : 00 PM

Hence, the time he start shopping is 2 : 00 PM

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Answer:

D. 10 (6y-9-2x)

Step-by-step explanation:

10×6y 10× -9 10×-2x

60y -90 -20x

Answer:

3/4(n)+1

3/4(8)+1=

6+1=7

3/4(12)+1=

9+1=10

3/4(14)+1=

10.5+1=11.5

3/4(20)+1=

15+1=16

I hope this helps:

Answer:

50 I think

Step-by-step explanation:

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6