is 27 / 16 a rational number​

Answer:

Step-by-step explanation:

Answer:

<NMP and <QPR

Step-by-step explanation:

Look up corresponding angle examples. these angles are corresponding.

Answer:

69 years

Step-by-step explanation:

Data provided in the question

Born date of an Ancient Greek = April 1st 35 BC

Diet date of an Ancient Greek = Aril 1st 35 AD

Based on the above information

We can say that

35 + 35 = 70

We deduct 1 as there is no zero

So, it would be

= 70 - 1 year

= 69 years

Hence, An ancient greek lives 69 years and the same is to be considered

Answer:

x² - 4x - 9 = 29

x² - 4x - 9 - 29 = 0

x² - 4x - 38 = 0

Using the quadratic formula

\(x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \)

Where

a = 1 , b = -4 c = - 38

So we have

\(x = \frac{ - - 4± \sqrt{ { - 4}^{2} - 4(1)( - 38)} }{2(1)} \\ \\ x = \frac{4± \sqrt{16 +152 } }{2} \\ \\ x = \frac{4± \sqrt{168} }{ 2} \\ \\ x =2 ± \sqrt{42} \\ \\ \\ x = 2 + \sqrt{42} \: \: \: or \: \: \: x = 2 - \sqrt{42} \)

Hope this helps you

Answer:

8 , 6 , 12

Step-by-step explanation:

let's move like the crab, backwards, let's get hmmm EF first

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{10}\\ o=\stackrel{opposite}{EF} \end{cases} \\\\\\ EF=\sqrt{ 17^2 - 10^2}\implies EF=\sqrt{ 189 }\implies EF\approx 13.7 \\\\[-0.35em] ~\dotfill\)

\(\sin( F )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{17}} \implies \sin^{-1}(~~\sin( F )~~) =\sin^{-1}\left( \cfrac{10}{17} \right) \\\\\\ F =\sin^{-1}\left( \cfrac{10}{17} \right)\implies F \approx 36^o \\\\[-0.35em] ~\dotfill\\\\ \cos(D )=\cfrac{\stackrel{adjacent}{10}}{\underset{hypotenuse}{17}} \implies \cos^{-1}(~~\cos( D )~~) =\cos^{-1}\left( \cfrac{10}{17} \right) \\\\\\ D =\cos^{-1}\left( \cfrac{10}{17} \right)\implies D \approx 54^o\)

Make sure your calculator is in Degree mode.

Answer:

padlet        com     /vpena20241    

/sv1blyklvnvfbcdw

Step-by-step explanation:

The value of the integral ∫₀² 3x(1 - x²)⁷ dx is 268435456.

To evaluate the integral ∫₀² 3x(1 - x²)⁷ dx, we can use a u-substitution. Let's make the substitution u = 1 - x². Then, we can find du by taking the derivative of u with respect to x:

du/dx = -2x

Solving for dx, we have dx = -du/(2x). Now, we can rewrite the integral in terms of u:

∫₀² 3x(1 - x²)⁷ dx = ∫₀¹₆ 3x(u)⁷ (-du/(2x))

= -3/2 ∫₀¹₆ u⁷ du

Now, we can integrate the function with respect to u:

∫₀¹₆ u⁷ du = [u⁸/8]₀¹₆

= (1/8)(16⁸ - 0⁸)

= (1/8)(16⁸)

= 16⁷

= 268435456

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The stem-and-leaf plot for the given different wieghts (in kg) is displayed in the image attached below.

A stem-and-leaf plot is a graphical tool used to display data points, in such a way that, if 26, 27, and 28 are data points, 2 will be the stem in a row and along with 6, 7, 8 as the leaf.

Given the data points, 16, 15, 23, 24, 13, 21, 15, 26, 22, 24, 30, 24, 10, 17, 19, 17, 28, 31, 29, 14, the stem-and-leaf plot is displayed in the image attached below (see attachment).

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Answer:

Noah spent $3.3 for 1 gallon of gasoline.

Lydia spent $3.25 for 1 gallon of gasoline.

Step-by-step explanation:

To find how much each person spent for 1 gallon of gasoline, we divide the amount spent by the number of gallons.

Noah spent $66 for 20 gallons of gasoline.

Amount spent $66, 20 gallons. So

66/20 = $3.3

Noah spent $3.3 for 1 gallon of gasoline.

Lydia spent $81.25 for 25 gallons of gasoline.

Amount spent $81.25, 25 gallons. So

81.25/25 = $3.25

Lydia spent $3.25 for 1 gallon of gasoline.

The true statement is b) -11 < -8. This means that -11 is less than -8, and the value of -11 is smaller. When comparing negative numbers, the larger the absolute value, the smaller the number itself.

These symbols are used to indicate the relationship between two numbers and are denoted by >, <, and =, respectively.

In conclusion, understanding the concepts of greater than, less than, and equal to is an important part of mathematics and is useful in many real-world situations. By knowing the true statement, you can make accurate comparisons and solve problems more effectively.

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The curve given by the vector-valued function r(t) = 5t^2i + 8t^3j is smooth on the open interval (-∞, +∞).

A vector-valued function is considered smooth when its components, i.e., the x and y components in this case, have continuous derivatives. The given function r(t) = 5t^2i + 8t^3j has the components x(t) = 5t^2 and y(t) = 8t^3.

Both x(t) and y(t) are polynomial functions, and polynomials are infinitely differentiable, meaning they have derivatives of all orders. Therefore, the derivatives of x(t) and y(t) exist for all real values of t.

Since the derivatives of x(t) and y(t) are continuous, the original vector-valued function r(t) = 5t^2i + 8t^3j is also smooth for all real values of t. Therefore, the curve described by the function is smooth on the open interval (-∞, +∞).

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Answer:

1/80

Step-by-step explanation:

The probability of selecting each of the event in the sample space is; 1/80

We are given;

Sample Space = 80 separate events

Now, we are told that each event is equally likely to be selected.

Thus;

Probability of selecting each event = 1/80

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Answer:

Step-by-step explanation:

sale price = £376.20  

reduced by =  43%

original price = ??

sale price = original price ( reduced rate)

  £376.20 = original price ( 43% )

                                              100

original price = £874.88

The given matrix is a 2x2 matrix. The indicated element is 3A, which is located in the first row and second column of the matrix.

The given matrix has two rows and two columns, which means it is a 2x2 matrix. Each entry in the matrix is separated by a comma, and each row is separated by a semicolon. The matrix is written in the standard form [a11, a12; a21, a22], where a11 represents the element in the first row and first column, a12 represents the element in the first row and second column, a21 represents the element in the second row and first column, and a22 represents the element in the second row and second column.

The indicated element is 3A, which means that there is a variable A being multiplied by 3. This element is located in the first row and second column of the matrix, which means that it corresponds to the entry a12. Therefore, we can write the matrix as [9, 3A; 0, 5], where A is some unknown value.

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The steps in Mia's method were smaller than in Jenna's, which was an advantage.

The same result will be obtained by adding the products of multiplying the sum of two or more addends by a number as opposed to multiplying each addend separately by the number.

The direct algorithm process suggested in this paper is known as the direct calculation method (DCM), and it can deal with using confinement loss as an incremental step to simulate the effect of moving tunnel face excavation, calculating the stresses and displacements in each step, and drawing the results.

Jenna's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(30)+(5)(4) \\&=150+20 \\&=170\end{aligned}\)

Mia's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(34) \\&=170\end{aligned}\)

Both used the right approach, albeit in different ways.

One uses the distributive property, whereas the other uses direct calculation.

Consequently, Jenna and Mia came to the same conclusion.

However, Mia's approach has one advantage over Jenna's: it requires fewer steps.

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Answer:

Yes, the common difference is 4

Step-by-step explanation:

In an arithmetic sequence, you are either adding or subtracting the same number.  In this case, you are adding 4 each time.  11+4=15   15+4=19   19+4=23

Answer:

250

Step-by-step explanation:

1000 divided by 4, is 250

The unit rate would be 250 calories per mile which is the slope of the given linear function.

The unit rate of a linear function is defined as the slope of the linear function.

The slope is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The given graph represents the number of miles he ran and the number of calories burned.

Taking two points as per the given graph :(2, 500), (6, 1500)

Let

x₁ = 2, y₁ = 500

x₂ = 6, y₂ = 1500

Substitute values in the formula to get

unit rate = (1500 - 500)/(6 - 2)

unit rate = (1000)/(4)

Apply the division operation,

unit rate = 250

Therefore, the unit rate would be 250 calories per mile

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a. The solution to the initial value problem is z(t) = -e^(-t) + e^(-2t).

b. The solution to the initial value problem is x(t) = 3e^(-t) - 2e^(-4t).

c. The solution to the initial value problem is x = ±√(e^(-C) - x) if x(0) > 0, and x = ±√(-e^(-C) - x) if x(0) < 0.

(a) To solve the initial value problem £+3i+2=0 with z(0)=0 and (0) = 1, we can use the Laplace transform. Applying the Laplace transform to the differential equation, we get s²Z(s) + 3sZ(s) + 2Z(s) = 0. Substituting the initial conditions, we have s²Z(s) + 3sZ(s) + 2Z(s) = s and Z(0) = 0.

Simplifying the equation, we get Z(s) = s / (s² + 3s + 2). Now we need to decompose the right side into partial fractions. We factor the denominator as (s+1)(s+2) and write Z(s) as A / (s+1) + B / (s+2).

Finding the values of A and B, we can rewrite Z(s) as Z(s) = (A(s+2) + B(s+1)) / (s+1)(s+2). Equating the numerators, we have s = A(s+2) + B(s+1).

Solving for A and B, we get A = -1 and B = 1. Therefore, Z(s) = (-1 / (s+1)) + (1 / (s+2)).

To find the inverse Laplace transform, we use the linearity property. Taking the inverse Laplace transform of each term, we have z(t) = -e^(-t) + e^(-2t).

(b) To solve the initial value problem + 4x + 5x=0 with x(0) = 1 and ż(0) = 1, we can use the Laplace transform. Applying the Laplace transform to the differential equation, we get s²X(s) + 4sX(s) + 5X(s) = s² + s. Substituting the initial conditions, we have s²X(s) + 4sX(s) + 5X(s) = s² + s and X(0) = 1.

Simplifying the equation, we get X(s) = (s² + s) / (s² + 4s + 5). Factoring the denominator as (s+1)(s+4), we can write X(s) as A / (s+1) + B / (s+4).

Finding the values of A and B, we have A = 3 and B = -2. Therefore, X(s) = (3 / (s+1)) - (2 / (s+4)).

Taking the inverse Laplace transform, we have x(t) = 3e^(-t) - 2e^(-4t).

(c) To solve the initial value problem x2x+x=0 with x(0) = ?, we can use separation of variables. Rewriting the equation as x'(t) = -x²(t) - x(t), we can separate the variables and integrate.

∫(-1 / (x² + x)) dx = ∫dt.

Simplifying the integral, we have -ln|x² + x| = t + C, where C is the constant of integration.

Taking the exponential of both sides, we get |x² + x| = e^(-t-C).

Solving for x, we have x² + x = ±e^(-t-C).

Considering the initial condition x(0) = ?, we can determine the sign of the right side. If x(0) > 0, then x² + x = e^(-C) since e^(-t) > 0 for all t.

If x(0) < 0, then x² + x = -e^(-C) since -e^(-t) < 0 for all t.

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There are no values of m and n that make the cross product axb equal to the zero vector.

To determine the values of m and n for the vectors a = [m, -12, 9] and b = [5, n, -3] such that axb = 0, we can compute the cross product of a and b and set it equal to the zero vector [0, 0, 0]. The cross product of two vectors is given by the following formula:

axb = [a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1]

Substituting the values of a and b:

[m, -12, 9] x [5, n, -3] = [0, 0, 0]

Expanding the cross product:

[m(-3) - 9n, 9(5) - (-3)(-12), (-12)n - 5(9)] = [0, 0, 0]

Simplifying each component:

-3m + 9n = 0 (1)

45 + 36 = 0 (2)

-12n - 45 = 0 (3)

From equation (2), we can see that it is not possible to satisfy the equation, as 45 + 36 ≠ 0.

The relationship between vectors a and b can be determined by analyzing their cross product. Since the cross product is zero, it indicates that the vectors are parallel or collinear. In this case, vectors a and b are either parallel or antiparallel (pointing in opposite directions). However, without further information or constraints, we cannot determine the exact relationship between a and b.

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Answer:

\(V=4480\pi \text{ units}^3\)

Step-by-step explanation:

Rewrite the region in terms of x

\(\displaystyle x=\frac{y}{6},\,x=y,\,y=24\)

Identify inner and outer radii

The inner radius is \(\displaystyle r=\frac{y}{6}\) and the outer radius is \(R=y\) because as \(y\) goes from 0 to 24, \(x\) goes from \(\displaystyle x=\frac{y}{6}\) to \(x=y\) in that direction.

Perform Washer Method

\(\displaystyle V=\pi\int\limits^b_a {(R^2-r^2)} \, dy\\ \\V=\pi\int\limits^{24}_0 {\biggr(y^2-\biggr(\frac{y}{6}\biggr)^2\biggr)} \, dy\\\\V=\pi\int\limits^{24}_0 {\biggr(y^2-\frac{y^2}{36}\biggr)\biggr)} \, dy\\\\V=\pi\biggr(\frac{y^3}{3}-\frac{y^3}{108}\biggr)\biggr|_0^{24}\\\\V=\pi\biggr(\frac{24^3}{3}-\frac{24^3}{108}\biggr)\\ \\V=4480\pi \text{ units}^3\)

I've attached a visual to help better understand this problem!

The correct answer is "All of the above."is a factor that influences interval width.

All of the above factors can influence interval width in statistical analysis. The confidence level, sample size, and variation in the population (measured by its standard deviation) all have an impact on the width of the confidence interval.

Confidence Level: The confidence level determines the level of certainty or reliability desired in the estimation. A higher confidence level leads to wider intervals as it requires a greater margin of error.

Sample Size: Larger sample sizes generally result in narrower intervals because they provide more information about the population, reducing sampling variability.

Variation in the Population (Standard Deviation): Greater variation or dispersion in the population data leads to wider intervals as the uncertainty in estimating the true population parameter increases.

Therefore, the correct answer is "All of the above."

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Answer:

Point A

Step-by-step explanation:

The square root of 20 is 4.4 , And point A is directly on 4.4.

Hope this helps :)

Answer:

The z score of the 65-mph speed limit is -0.75

Step-by-step explanation:

The z score is given by the relation;

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

Where:

Z = Normal (Standard) or z score

x = Observed speed  score

μ = Mean, expected speed

σ = Standard deviation

Where we plug in the values for x = 65-mph, σ = 8 mph and μ = 71 mph, into the z-score equation, we get;

\(z = \frac{65-71}{8}= \frac{-6}{8} = -\frac{3}{4}\)

Hence the z score of the 65-mph speed limit =-3/4 or -0.75.

Answer: Its A Hope this helps!

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

(a/b)*(b/a)=1.

Step-by-step explanation:

Answer:

12.57

Step-by-step explanation:

We need to find of area of a circle and the formula for that is pie * radius ^2.

Pie * 2 squared = 12.57 rounded to the nearest hundredth

The expression that is equivalent to 14.5d + 8.5 - 1/2d + 1/2 + 2.5d is 17.5d + 9.5.

To simplify the given expression, we combine like terms. First, we add the terms with the variable "d." We have 14.5d + 2.5d, which gives us 17d. Then, we add the constant terms: 8.5 + 1/2 + 1/2 equals 9.5. Thus, the simplified expression is 17.5d + 9.5.To simplify the given expression, we combine like terms. First, we add the terms with the variable "d." We have 14.5d + 2.5d, which gives us 17d.

By combining like terms and performing the necessary calculations, we can simplify the expression 14.5d + 8.5 - 1/2d + 1/2 + 2.5d to 17.5d + 9.5.

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Answer:

x=2

Step-by-step explanation:

add the x onto the other side so it is positive : 7=5+x

then subtract the 5 from both sides so you can isolate the x : 2=x

rewrite the equation: x=2

☆ Hello ☆

The value of x is 2.

\( \red{ \sf \underline {\underline{Explantation: }}}\)

¿What are equations?

The equations represent an equality between two mathematical expressions that have at least one variable called unknown.

\( \sf \:Solution:\)

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - x = 5}}\\\boldsymbol{\mathsf{ - x = 5-7}}\\\boldsymbol{\mathsf{ - x = -2}}\ \\ {\mathsf{ x = 2}}\end{gathered}\)

\( \bf \:Verification:\)

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - 2 = 5}}\\\boldsymbol{\mathsf{ 5=5}}\end{gathered}\)

\(\green{ \sf \: The \: result \: is} \: \red{\longmapsto} \blue 5\)