Angle 1 and angle 2 are vertical angles if m angle 1 = 7x+20 and m angle 2 = 9x-14 find m angle 2​

The 90% confidence interval for the proportion of 8th graders involved in after school activities is c) (0.780, 0.900).

To find the confidence interval, we need to use the formula:

CI = p ± zα/2 * √(p(1-p)/n)

where:

p is the sample proportion (84% or 0.84 in decimal form)

zα/2 is the z-score for the desired confidence level (90% or 1.645 for a two-tailed test)

n is the sample size (100)

Substituting the values, we get:

CI = 0.84 ± 1.645 * √(0.84(1-0.84)/100)

CI = 0.84 ± 0.078

CI = (0.762, 0.918)

Rounding to three decimal places, we get the final answer of (0.780, 0.900) as the confidence interval for the proportion of 8th graders involved in after school activities. Therefore, the correct answer is (c).

For more questions like Z-score click the link below:

https://brainly.com/question/15016913

#SPJ11

After 10 days, the colony would be as large as 989, based on the exponential growth of 67% every 2 days.

An exponential growth refers to a constant rate or percentage of growth in the number or value of some variables.

Exponential growth can be modeled using the exponential growth function and used to determine the future quantity or amount of the variables.

Initial number of the bacteria microorganisms = 55

Growth rate = 67% every 2 days

Daily growth rate = 33.5% (67% ÷ 2)

The number of days involved, t = 10 days

The ending number of the bacteria microorganisms = Future Amount = 55(1 + 33.5%)^t

= 55(1.335)^10

= 989

Learn more about exponential growth functions at https://brainly.com/question/13223520.

#SPJ1

Answer:

55 0.67 ^5

Step-by-step explanation:

The future amount = ? micro organisms

Answer:

To find the distance between two points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the two points are (3, 4) and (6, 8), so we have:

d = sqrt((6 - 3)^2 + (8 - 4)^2)

d = sqrt(3^2 + 4^2)

d = sqrt(9 + 16)

d = sqrt(25)

d = 5

Therefore, the distance between the points (3, 4) and (6, 8) is 5 units.

It's worth noting that the values 5√22 and √7 do not match the above

Answer:

Math is a broad field that encompasses several branches, each with its own units of measurement. Some examples of units in math include:

In geometry:- Units of length, such as meters, centimeters, and inches

Units of area, such as square meters, square centimeters, and square feet

Units of volume, such as cubic meters, cubic centimeters, and cubic feet- Units of weight or mass, such as kilograms, grams, and pounds - Units of time, such as seconds, minutes, and hours

Units of temperature, such as Celsius and

Fahrenheit

Units of angle measurement, such as degrees and radians

Units of speed or velocity, such as meters per second or miles per hour

Units of frequency, such as Hertz or cycles per second

Units of energy or work, such as joules, calories, and foot-pounds

Units of power, such as watts and horsepower

These are just a few examples of the many units used in math. The type of unit used depends on the specific problem or application.

HOPE IT HELPS

PLEASE MARK ❣️‼️ ME AS BRAINLIEST .

On the interval (-1, 1), the Fourier series for f(x) is f(x) = 1/2 + ∑[2/πn cos(nπx)] - [2/πn sin(nπx)].

To find the Fourier series for the given function f(x) on the interval (-1, 1), we need to determine its Fourier coefficients. The Fourier coefficient for the nth term can be calculated using the following formula:

an = (2/L) ∫f(x) cos(nπx/L) dx, where L is the period of the function, which in this case is 2.

bn = (2/L) ∫f(x) sin(nπx/L) dx, where L is the period of the function, which in this case is 2.

We can evaluate these integrals separately for the intervals (-1, 0) and (0, 1) and then add the results to obtain the final Fourier coefficients.

For the interval (-1, 0), we have:

an = (2/2) ∫[1 + x] cos(nπx/2) dx from x = -1 to x = 0

an = [(1 + x) sin(nπx/2)/πn] from x = -1 to x = 0

an = [0 - (-1) sin(nπ/2)/πn] - [(1 + 0) sin(0)/πn]

an = 2/πn

bn = (2/2) ∫[1 + x] sin(nπx/2) dx from x = -1 to x = 0

bn = [-(1 + x) cos(nπx/2)/(πn)] from x = -1 to x = 0

bn = [-1 cos(nπ/2)/(πn) - (1 + 0) cos(0)/(πn)]

bn = -2/πn

For the interval (0, 1), we have:

an = (2/2) ∫[1 - x] cos(nπx/2) dx from x = 0 to x = 1

an = [(1 - x) sin(nπx/2)/πn] from x = 0 to x = 1

an = [(1 - 0) sin(nπ/2)/πn] - [(1 - 1) sin(nπ)/πn]

an = 2/πn

bn = (2/2) ∫[1 - x] sin(nπx/2) dx from x = 0 to x = 1

bn = [- (1 - x) cos(nπx/2)/(πn)] from x = 0 to x = 1

bn = [-(1 - 1) cos(nπ)/πn] - [(1 - 0) cos(nπ/2)/(πn)]

bn = 0

Therefore, the Fourier series for f(x) on the interval (-1, 1) is:

f(x) = 1/2 + ∑[2/πn cos(nπx)] - [2/πn sin(nπx)], where the sum is taken from n = 1 to infinity.

Learn more about Fourier series on:

https://brainly.com/question/13419597

#SPJ11

Answer: 5y^2 +3y+12

Step-by-step explanation:

6y^2+3y+1

y^2-11

equals

5y^2+3y+12

The length of the remaining piece of wooden beam after the cut out in terms of polynomial y is 5y² + 3y + 12

Length of the wooden beam = 6y² + 3y + 1

Length cut out from the wooden beam= y² - 11

Length of the remaining piece of beam = Length of the wooden beam - Length cut out from the wooden beam

= (6y² + 3y + 1) - (y² - 11)

= 6y² + 3y + 1 - y² + 11

= 5y² + 3y + 12

Hence, 5y² + 3y + 12 is the remaining length of the wooden beam.

Read more on polynomial:

brainly.com/question/4142886

To find the orthogonal trajectories of the given family of curves, we first need to understand what the term "orthogonal" means. In simple terms, two lines or curves are said to be orthogonal if they intersect at a right angle. Now, coming back to the problem, the given family of curves can be written as x^2 - 2y^2 = c, where c is a constant.

To find the orthogonal trajectories, we need to differentiate this equation with respect to y, treating x as a constant. This gives us:
-4xy = dy/dx

Now, we need to find the equation of the curves that intersect the given family of curves at a right angle, i.e., the slopes of the curves must be negative reciprocals of each other. Therefore, we can write:
dy/dx = 4xy/k

where k is a constant. To solve this differential equation, we can separate the variables and integrate:

∫dy/4xy = ∫dx/k

ln|y| - ln|x^2| = ln|c| + ln|k|

ln|y/x^2| = ln|ck|

y/x^2 = ±ck

Therefore, the orthogonal trajectories of the given family of curves are given by y = ±kx^2/c, where k is a constant. These curves intersect the original family of curves at right angles.

1. Identify the family of curves: The given equation is x^2 + 2y^2 = c, where c is a constant. This represents a family of ellipses with different sizes depending on the value of c.

2. Calculate the derivative: To find the orthogonal trajectories, we first need to find the derivative of the given equation with respect to x. Differentiate both sides with respect to x:

d/dx(x^2) + d/dx(2y^2) = d/dx(c)
2x + 4yy' = 0

3. Find the orthogonal slope: The slope of the orthogonal trajectory is the negative reciprocal of the original slope. Since the original slope is y', the orthogonal slope is -1/y':

Orthogonal slope = -1/y'

4. Replace the original slope with the orthogonal slope:

2x + 4y(-1/y') = 0

5. Solve for y':

y' = -2x/(4y)

6. Solve the differential equation: Now we have a first-order differential equation to find the equation of the orthogonal trajectories:

dy/dx = -2x/(4y)

Separate variables and integrate both sides:

∫(1/y) dy = ∫(-2x/4) dx

ln|y| = -x^2/4 + k

7. Solve for y:

y = e^(-x^2/4 + k) = C * e^(-x^2/4), where C is a new constant.

The orthogonal trajectories of the given family of curves are represented by the equation y = C * e^(-x^2/4).

Learn more about orthogonal at : brainly.com/question/2292926

#SPJ11

a) Yes, it is reasonable to use t-distribution to perform a test about average gas price. (b) There is evidence that average gas price on August 8, 2012 was higher than national average at 5% significance level. (c) 95% confidence interval lies between $3.813 and $4.137.

a) Yes, it is reasonable to use the t-distribution to perform a test about the average gas price since the sample size n = 10 is small and the population standard deviation is unknown.

b) To test for the evidence, we can perform a one-sample t-test.

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (3.975 - 3.63) / (0.2266 / sqrt(10))

t = 2.728

Using a t-table the critical t-value is 1.833 which is less than calculated t-value (2.728) ), therefore, we reject the null hypothesis and conclude that there is evidence that the average gas price was significantly higher than the national average at the 5% significance level.

c) The standard error can be calculated as:

standard error = sample standard deviation / sqrt(sample size)

standard error = 0.2266 / sqrt(10)

standard error = 0.0717

Using a t-table, the t-value is 2.262. Therefore, the 95% confidence interval is:

(sample mean) ± (t-value * standard error)

3.975 ± (2.262 * 0.0717)

3.975 ± 0.162

(3.813, 4.137)

So we can be 95% confident that the true mean gas price in Illinois on August 8, 2012 lies between $3.813 and $4.137.

Know more about confidence interval here:

https://brainly.com/question/20309162

#SPJ11

a) Based on the output, the maximum likelihood estimate of 1 is A) 0.353.

b) The correct interpretation of the maximum likelihood estimate of 1 in the context of this question is C) It represents the predicted change in fuel consumption as attic insulation rating changes by 1 unit.

c) Based on the output, the maximum likelihood estimate of 0 is D) 0.976.

d) To find the estimated residual for the observation at x3 = 0.9, first, calculate the predicted fuel consumption using the equation: y = 0 + 1x.
y = 0.976 + (0.353 * 0.9) = 1.2957.

The actual fuel consumption at x3 = 0.9 is 1.34. Therefore, the residual is:
1.34 - 1.2957 = 0.0443.

The closest answer to this value is A) 0.046.

https://brainly.com/question/31496399

#SPJ11

The series after solving the following term f(x) = [tex]e^{-2x}[/tex] is given as:

[tex]e^{-2x}[/tex] = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞.

The fundamental concepts in mathematics are series and sequence. A series is the total of all components, but a sequence is an ordered group of items in which repeats of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.

By using the formulae to solve issues, one may gain a deeper understanding of the principles. The main distinction between them and sets is that in a sequence, certain terms might appear again in different locations. A series can be finite or infinite in length and has length equal to the number of terms.

Given f(x) = [tex]e^{-2x}[/tex], center x = 0

f(x) = [tex]e^{-2x}[/tex] = [tex]1 - 2x + \frac{(2x)^2}{2!} +\frac{(2x)^3}{3!} +\frac{(2x)^4}{4!} +\frac{(2x)^5}{5!} +.....|x|[/tex]

[tex]e^{-2x}[/tex] = 1 - 2x + 4([tex]\frac{x^2}{2}[/tex]) - 8([tex]\frac{x^3}{6}[/tex]) + 16([tex]\frac{x^4}{24}[/tex]) - 35([tex]\frac{x^5}{100}[/tex])+.....|x| < ∞

[tex]e^{-2x}[/tex] = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞

Learn more about Series:

https://brainly.com/question/24643676

#SPJ4

Answer:

First, we need to convert the mixed number −3 1/3 to a fraction. −3 1/3 = −(3 + 1/3) = −(10/3).

Now, we can divide the fraction by the decimal. −(10/3) ÷ (-2.4) = −(10/3) ÷ (-24/10) = −(10/3) x (10/-24) = 10/-7.2 = -1.388888889.

Therefore, the value of the expression is −1.388888889.

Step-by-step explanation:

1. Convert the mixed number to a fraction.

```

-3 1/3 = -(3 + 1/3) = -(10/3)

```

2. Multiply the numerator and denominator of the fraction by -1.

```

-(10/3) = (-1)(10/3) = -10/3

```

3. Divide the numerator and denominator of the fraction by -24.

```

-10/3 = (-10/3) ÷ (-24/10) = 10/-7.2 = -1.388888889

```

Therefore, the value of the expression is −1.388888889.

Here is a visual representation of the steps:

```

-3 1/3 ÷ (-2.4)

= -(10/3) ÷ (-24/10)

= -(10/3) x (10/-24)

= 10/-7.2

= -1.388888889

```

No, The relation is not a function.

Domain = {9, 4, 1, 0}

Range = {-5, - 3, - 1, 0, 1, 3, 5}

We have to given that;

The relation is,

{(9,−5),(4,−3),(1,−1),(0,0),(1,1),(4,3),(9,5)}

We know that;

A relation between a set of inputs having one output each is called a function.

Here, Relation have;

(9, - 5) and (9, 5)

Thus, It does not satisfy the definition of function.

And, The value of domain of relation is,

Domain = {9, 4, 1, 0}

And, The value of range of relation is,

Range = {-5, - 3, - 1, 0, 1, 3, 5}

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

The solution of the given inequality is x less than 3/23.

The given inequality is 8>23x+5.

Subtract 5 on both the sides of an inequality, we get

8-5>23x+5-5

3>23x

Divide 23 on both the sides of an inequality, we get

3/23>x

x<3/23

Therefore, the solution of the given inequality is x less than 3/23.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ1

Answer:

Step-by-step explanation:

Key March Highlights: Travel spending totaled $93 billion in February—5% above 2019 levels and 9% above 2022 levels. Leisure travel demand does not appear to be abating with America’s excitement to travel at record highs and more than half (55%  Data Question 2 The following table shows the number of visitors to a park from January to April: Month January

To find a root-finding method with a third order of convergence, consider using the "Halley's method." Halley's method is an iterative numerical technique used for finding roots of a function. It has a third-order convergence, meaning the number of correct digits approximately triples with each iteration, resulting in a faster convergence rate compared to methods with lower orders of convergence.

Here's a step-by-step explanation of Halley's method:

1. Choose an initial guess x_0 for the root of the function f(x).

2. Calculate the first and second derivatives of the function f(x), denoted as f'(x) and f''(x), respectively.

3. Update the guess using the formula:
  x_(n+1) = x_n - (2 * f(x_n) * f'(x_n)) / (2 * (f'(x_n))^2 - f(x_n) * f''(x_n))

4. Check for convergence by comparing the difference between consecutive guesses (x_(n+1) - x_n) to a predefined tolerance level.

5. If the convergence criterion is not met, repeat steps 3 and 4 until convergence is achieved or a maximum number of iterations is reached.

convergencehttps://brainly.com/question/30089745

#SPJ11

To reflect a figure over the y-axis, we simply change the sign of its x-coordinates while keeping the y-coordinates the same. So, the coordinates of the vertices after a reflection over the y-axis would be:

A'(-2, 1), B'(-1, 3), C'(1, 2), D'(2, 0)

When we reflect a figure over the y-axis, we are essentially flipping the figure horizontally along a vertical line passing through the origin.

This means that every point on the original figure is reflected across this vertical line, resulting in a new figure that is a mirror image of the original.

Thus, the coordinates of the vertices after a reflection over the y-axis are A'(-2, 1), B'(-1, 3), C'(1, 2), and D'(2, 0).

For more details regarding coordinates, visit:

https://brainly.com/question/16634867

#SPJ1

We can find its derivative and evaluate it at x=36 to find the slope of the tangent line, and then use the point-slope formula to find the equation of the line.

To find the derivative of y = Vx, we use the power rule, which states that if y = xn, then y' = nx^(n-1). In this case, y = Vx⁽¹/²⁾, so y' = V(1/2)x(-1/2) = V/(2sqrt(x)). Evaluating this at x=36, we get y' = V/12. Therefore, the slope of the tangent line is m = V/12. Using the point-slope formula, we get the equation of the tangent line as y - 6 = (V/12)(x - 36).

In summary, to find the equation of the tangent line to the curve at the point (36,6), we first found the derivative of the function y = [tex]Vx^{1/2}[/tex], which is y' = V/(2sqrt(x)). Evaluating this at x=36, we get y' = V/12, which is the slope of the tangent line. Using the point-slope formula, we then found the equation of the tangent line as y - 6 = (V/12)(x - 36).

To explain this answer in more detail, we can first note that the function

y = [tex]Vx^{1/2}[/tex]  represents a square root function with a vertical stretch factor of V. This means that the graph of the function is a curve that starts at the origin and increases slowly at first, then more rapidly as x gets larger. The point (36,6) is on this curve, and we are asked to find the equation of the tangent line to the curve at this point.

To find the slope of the tangent line, we use the formula Mtan = lim f(x) - f(a)/ x-a\a, where f(x) is the function and a is the point where we want to find the tangent line. In this case, a = 36 and f(x) = Vx^(1/2), so we have [tex]Mtan=lim Vx^{1/2} - V(36)^{1/2}/ x-36/a[/tex]. We can simplify this expression by multiplying the numerator and denominator by the conjugate of the numerator, which is [tex]Vx^{1/2} +V(36)x^{1/2}[/tex] As x approaches 36, we can use L' Hopital's rule to evaluate the limit, which gives us Mtan = V/12.

Now that we have the slope of the tangent line, we can use the point-slope formula to find the equation of the line. The point-slope formula states that if the slope of a line is m and a point on the line is (x1,y1), then the equation of the line is y - y1 = m(x - x1). In this case, the point is (36,6) and the slope is V/12, so the equation of the tangent line is y - 6

Learn more about tangent:

brainly.com/question/10053881

#SPJ11

(1) The probability of getting a soft chicken is 16.67%.

(2) The probability of getting a crunch beef is 16.67%.

(3) The probability of getting a fish  (crunchy or soft) is 33.33%.

The probability of getting a soft chicken is calculated as follows;

total outcome = 6

number of soft chicken = 1

Probability = 1/6 = 16.67%

The probability of getting a crunch beef is calculated as follows;

total outcome = 6

number of crunch beef = 1

Probability = 1/6 = 16.67%

The probability of getting a fish  (crunchy or soft) is calculated as follows;

total outcome = 6

number of soft fish = 1

number of crunch fish  = 1

P(soft or crunch) = 1/6 + 1/6 = 2/6 = 1/3 = 33.33%

Learn more about probability here: https://brainly.com/question/25870256

#SPJ1

The given statement "Quantitative Easing was used extensively in the aftermath of the(the late 1990s/2000s) dot com crisis is false because Quantitative Easing was not used extensively in the aftermath of the dot com crisis in the late 1990s/2000s.

Quantitative easing (QE) was not used extensively in the aftermath of the dot-com crisis in the late 1990s and early 2000s. In fact, QE as a monetary policy tool gained prominence after the global financial crisis of 2008. The dot-com crisis primarily affected the technology sector, causing a stock market downturn, but it did not lead to a widespread financial crisis that would have necessitated the use of QE.

Therefore, the given statement is false.

To know more about quantitative easing refer:

https://brainly.com/question/31706435

#SPJ11

Answer: 87

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given right angle XOV and 30° angle XOW, you want to know the measure of angle WOV. You also want to find the measure of angle YOZ, which is opposite angle VOW, where XOY is a right angle, and WOZ is a straight angle.

The angle addition theorem tells you that ...

  ∠XOW +∠WOV = ∠XOV

Angle XOV is given as a right angle, and angle XOW is shown as 30°, so we have ...

  30° +∠WOV = 90°

  ∠WOV = 60° . . . . . . . . . subtract 30° from both sides

Angle WOV is 60° using the angle addition theorem.

Rays OY and OV are opposite rays, as are rays OZ and OW. This means angles YOZ and VOW are vertical angles, hence congruent.

  ∠YOZ = ∠WOV = 60°

Angle YOZ is 60° using the congruence of vertical angles.

As in part 2, angle WOZ is a straight angle, so measures 180°. The angle addition theorem tells you this is the sum of its parts:

  ∠ZOY +∠YOX +∠XOW = ∠ZOW

  ∠ZOY +90° +30° = 180°

  ∠ZOY = 60° . . . . . . . . . . . . . subtract 120° from both sides

Angle YOZ is 60° using the measure of a straight angle.

<95141404393>

If S is the substance of M4(R) consisting of all lower triangular matrices, then dim S = 10.
To find the dimension of S, we need to count the number of linearly independent matrices in S. A lower triangular matrix in M4(R) has the form:

[ a 0 0 0 ]
[ b c 0 0 ]
[ d e f 0 ]
[ g h i j ]
where a, b, c, d, e, f, g, h, i, and j are real numbers.

Since S consists of all lower triangular matrices, we can choose the entries of the matrices in S freely, subject to the constraint that the upper diagonal entries must be 0. Therefore, we have 10 free parameters (a, b, c, d, e, f, g, h, i, and j) that we can choose independently, and the remaining entries are determined by the fact that the matrix is lower triangular. Therefore, the dimension of S is 10.

(b) If S is the subspace of M5(R) consisting of all matrices with trace 0, then dim S = 20.

To find the dimension of S, we need to count the number of linearly independent matrices in S. A matrix in M5(R) with trace 0 has the form:

[ a b c d e ]
[ f g h i j ]
[ k l m n o ]
[ p q r s t ]
[ u v w x y ]

where a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, and y are real numbers and a + g + m + s + y = 0. Since there is one constraint on the entries of the matrix, we have 24 free parameters that we can choose independently. However, there is also a linear dependence between the entries of the matrix, since the trace is 0. Specifically, we have the constraint a + g + m + s + y = 0. Therefore, we have 23 free parameters, and the remaining entries are determined by the trace constraint. Therefore, the dimension of S is 23 - 1 = 22.

(a) If S is the substance of M4(R) consisting of all lower triangular matrices, then dim S = 10.

Explanation:

In the set of all 4x4 lower triangular matrices, the elements on and below the main diagonal can have non-zero values, while the elements above the main diagonal must be zero. There are a total of 4+3+2+1=10 elements in the lower triangular part. Since these 10 elements can be any real numbers, the dimension of S (the substance of M4(R) consisting of all lower triangular matrices) is 10.

(b) If S is the subspace of M5(R) consisting of all matrices with trace 0, then dim S = 24.

Explanation:

In a 5x5 matrix, there are a total of 5x5=25 elements. The trace of a matrix is the sum of its diagonal elements. If a 5x5 matrix has a trace of 0, then the sum of its diagonal elements must be 0. This means that we have freedom to choose any real values for 24 elements (the other 20 off-diagonal elements and 4 of the diagonal elements), and the last diagonal element is determined by the other 4 diagonal elements to ensure the trace is 0. Therefore, the dimension of S (the subspace of M5(R) consisting of all matrices with trace 0) is 24.

Learn more about matrix at : brainly.com/question/28180105

#SPJ11

We fail to reject the null hypothesis since the calculated t-statistic (0) is not greater than the critical values (-2.093 and 2.093). There is not enough evidence to suggest that the mean score in 2018 differs significantly from the mean score in 2017.

Based on the information given, the mean score on the math SAT in 2017 was not provided. However, assuming that the question is asking about the mean score in 2018, we can use the given values to answer the question.

(a) In order to determine if the assumptions for a hypothesis test are satisfied, we need to check if the sample is random and if the data is normally distributed. As long as the sample was selected randomly and independently of each other and the population is normally distributed, the assumptions for a hypothesis test are satisfied.

(b) We can perform a hypothesis test to investigate if the mean score in 2018 differs from the mean score in 2017 using the following steps:

Null Hypothesis (H0): The mean score in 2018 is equal to the mean score in 2017.
Alternative Hypothesis (Ha): The mean score in 2018 is not equal to the mean score in 2017.

We can use a two-tailed t-test to test the hypothesis since the population standard deviation is not known. Assuming a level of significance of 0.05, and using a t-distribution table with a degree of freedom of n-1=19, the critical values are -2.093 and 2.093.

The sample mean score in 2018 is given as 580. The mean score in 2017 is not provided in the question. Assuming that the mean score in 2017 is also 580, we can calculate the t-statistic as follows:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
t = (580 - 580) / (15 / sqrt(20))
t = 0

Since the calculated t-statistic (0) is not greater than the critical values (-2.093 and 2.093), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the mean score in 2018 differs significantly from the mean score in 2017.

More on hypothesis: https://brainly.com/question/31475463

#SPJ11

The actual distance between two cities is 70 miles when 1 inch is equal to 20 miles

Given that Daniel is planning to drive from City X to City Y.

The distance between two cities is [tex]3\frac{1}{2}[/tex] inches

Given that 1 inch = 20 miles

We have to find the actual distance between two cities in miles

[tex]3\frac{1}{2}[/tex]  = 3.5

Now multiply 3.5 with 20 to find distance in miles

3.5×20

70 miles

Hence, the actual distance between two cities is 70 miles when 1 inch is equal to 20 miles

To learn more on Distance click:

https://brainly.com/question/15172156

#SPJ1

Answer:

2nd and 4th

Step-by-step explanation:

In the second quadrant, the x-coordinate is negative and the y-coordinate is positive. If we let the x-coordinate be -a, then the y-coordinate will be a. Therefore, the point will have the form (-a, a), and the y-coordinate will be the opposite of the x-coordinate.

In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative. If we let the x-coordinate be a, then the y-coordinate will be -a. Therefore, the point will have the form (a, -a), and again, the y-coordinate will be the opposite of the x-coordinate.

The minimum and maximum heights that the ladder can safely lie against the wall is 6.7 and 6.99 meters.

The minimum and maximum height that the ladder can safely lie against the wall is

sin theta = perpendicular/hypotenuse

Now keeping the each value of theta with hypotenuse to find the perpendicular height.

sin 70 = perpendicular/7.1

Keep the value

Perpendicular = 0.94 × 7.1

Multiply the digits

Perpendicular = 6.7 meters

sin 80 = perpendicular/7.1

Perpendicular = 0.99 × 7.1

Perform multiplication

Perpendicular = 6.99 meters

Thus, minimum and maximum heights are 6.7 and 6.99 meters.

Learn more about perpendicular -

https://brainly.com/question/64787

#SPJ1

a. i. The circumference of circle A is 128.81 m

ii. The circumference of circle B is 144.53 m

b. The relatonship between the radius and circumference is the same for all circles

The circumference of a circle is the perimeter of the circle.

a.

i. Circumference of circle A

Since circle A has a radius of 21 meters, the circumference is given by C = 2πr where r = radius

So, substituting the values of the variables into the equation, we have that

C = 2πr

= 2π × 21 m

= 41π m

= 41 × 3.142

= 128.81 m

ii Circumference of circle B

Since circle A has a radius of 28 meters, the circumference is given by C = 2πr where r = radius

So, substituting the values of the variables into the equation, we have that

C = 2πr

= 2π × 28 m

= 46π m

= 46 × 3.142

= 144.53 m

b.

The relatonship between the radius and circumference is the same for all circles since the circumference of a circle is always proportional to its radius.

Learn more about circumference of circle here:

https://brainly.com/question/18571680

#SPJ1

The value of expression is, - 39.5

Given that;

All the Values are,

m = - 12

n = 23

p = 4.5

Now, We can formulate;

⇒ m - p - n

Substitute all the values, we get;

⇒ - 12 - 4.5 - 23

⇒ - 39.5

Thus, The value of expression is, - 39.5

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

x = 5

Step-by-step explanation:

o find the equation of the line that is perpendicular to line G, we need to find the slope of line G first. The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Using the points (-8, 3) and (7, 3) on line G, we get:

slope of line G = (3 - 3) / (7 - (-8)) = 0

Since the line we want to find is perpendicular to line G, its slope will be the negative reciprocal of the slope of line G. That is:

slope of perpendicular line = -1 / slope of line G = undefined

An undefined slope means that the line is vertical. Therefore, the equation of the line that is perpendicular to line G and passes through the point (5, -3) is simply:

x = 5