What is the distance between the points (8, -3) and (1,5) ?

Answer:

11.1d + 3.2h - 15

Step-by-step explanation:

Answer:

−3.1d+3.6h−17

Step-by-step explanation:

Combine like terms:

=6h+−7.1d+−17+4d+−2.4h

=(−7.1d+4d)+(6h+−2.4h)+(−17)

=−3.1d+3.6h+−17

hope this helps :D

The students should use a t-test to analyze the significance of the data they collected is a true statement.

In this scenario, the population standard deviation is unknown and the sample size is small (n=25). Therefore, a t-test should be used instead of a z-test. The t-test is a statistical hypothesis test that is used to determine if there is a significant difference between the means of two groups when the sample size is small and/or the population standard deviation is unknown.

Using a t-test will allow the students to analyze the significance of their data in a more appropriate and accurate way, taking into account the small sample size and the fact that they do not know the population standard deviation.

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The set of observations on a variable measured at successive points in time or over successive periods of (c) time series .

A Time Series is a set of observations on a variable that is measured at successive points in time or over successive periods.

Which means that the values of the variable that are recorded at regular intervals or successive points, such as daily, weekly, monthly, or annually, and are analyzed to identify the patterns, trends, and relationships over time.

The Time series analysis can be used in various fields, including economics, finance, engineering, and the natural sciences, to make predictions, identify cause-and-effect relationships, and inform decision-making.

The given question is incomplete , the complete question is

A set of observations on a variable measured at successive points in time or over successive periods of

(a) geometric series

(b) time invariant set

(c) time series

(d) logarithmic series

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The required value of z-statistic for the sample size of 20 and standard deviation of 5.4 beads is equals to 2.065.

Using the formula for the z-statistic

z = ( X - μ ) / (σ /√n )

X is the sample mean  = 52.5

μ is the population mean = 50

σ is the population standard deviation = 5.4

and n is the sample size = 20

Plugging in the values given in the problem, we have

z = ( 52.5 - 50 ) / (5.4 /√20 )

Simplifying the expression under the square root we get,

z = 2.5 / 1.209

  = 2.067

Rounding to three decimal places, we get a z-statistic of approximately 2.065.

Therefore, the z-statistic for the given sample mean and standard deviation is equal to 2.065.

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By calculating , The values of x are 8,4,7,1.5 respectively.

What is Quadrilateral ?

Quadrilateral can be defined in which it contains four sides and the sum of the four angles in a quadrilateral is always 360 degrees.

Given in figures ,

we have to find the value of x in which that males the quadrilateral a parallelogram.

So, in the given figure As the diagonal of quadrilateral bisects each other

so ,

4x+2 = 5x - 6

5x-4x = 6+2

x = 8

In the second figure,

similarly ,

2x+3 = x+7

2x-x = 7-3

x = 4

In the third figure ,

3x+5 = 5x- 9

5x-3x = 9+5

2x = 14

x = 14/2

x = 7

In the fourth figure ,

6x = 3x+2

3x = 2

x = 1.5

Hence, The values of x are 8,4,7,1.5 respectively.

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The hypotheses for the manufacturer's belief that the average number of items produced per week has increased after opening two new factories are: Null Hypothesis (H0): The average number of items produced per week is the same as before and has not increased after opening two new factories, and Alternative Hypothesis (H1): The average number of items produced per week has increased after opening two new factories.

Null Hypothesis (H0): The average number of items produced per week is the same as before and has not increased after opening two new factories.

Alternative Hypothesis (H1): The average number of items GV7B NHYUJMIK,L per week has increased after opening two new factories.

In hypothesis testing, the null hypothesis (H0) is the assumption that there is no significant difference or effect, while the alternative hypothesis (H1) is the opposite, suggesting that there is a significant difference or effect.

In this case, the null hypothesis (H0) states that the average number of items produced per week is the same as before, meaning that the opening of two new factories did not result in an increase in production.

On the other hand, the alternative hypothesis (H1) suggests that the average number of items produced per week has increased after opening two new factories, indicating a significant effect of the new factories on production.

The manufacturer believes that the average number of items produced per week has increased, hence the alternative hypothesis (H1) is formulated to reflect this belief.

Therefore, the hypotheses for the manufacturer's belief that the average number of items produced per week has increased after opening two new factories are: Null Hypothesis (H0): The average number of items produced per week is the same as before and has not increased after opening two new factories, and Alternative Hypothesis (H1): The average number of items produced per week has increased after opening two new factories.

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Answer: i belive its 140 i really coudn't tell.

Step-by-step explanation:          

I used the protactor and  I aligned it agaist the problem. Hope this helps. :)  

By that i meant i got my protactor and I aligned it on the tiny dot you can see, the arrow  pointed onto the number.  I really don't think there is much to explain. If their is any confusion i will re-write it.

Answer:

the answer for this question is 110

The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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If the two firms do not cooperate, the payoff that North Springs and South Springs receive in the dominant-strategy equilibrium and the Nash equilibrium would depend on the specific game or scenario being played. Without more information about the specific game being played and the strategies of the two firms, it is impossible to provide a definitive answer.

However, in general, the dominant-strategy equilibrium refers to the situation where each player chooses their best strategy, regardless of what the other player does. The Nash equilibrium refers to the situation where each player chooses their best strategy given what the other player is doing. In some cases, the dominant-strategy equilibrium and the Nash equilibrium may be the same, but in other cases, they may differ.

So, in order to determine the payoff that North Springs and South Springs receive in these equilibria, more information about the game being played and the strategies of the two firms would be needed.
Based on the information given, we can analyze the payoff for both North Springs and South Springs firms in the dominant-strategy equilibrium and the Nash equilibrium.

Dominant-Strategy Equilibrium:
1. Identify each firm's dominant strategy (the best response regardless of the other firm's action).
2. Combine the dominant strategies for both firms to find the outcome.

Nash Equilibrium:
1. Identify each firm's best response given the other firm's action.
2. Find the outcome where both firms are simultaneously choosing their best responses.

Without specific numerical payoffs, I cannot provide the exact payoff amounts. However, once you have the payoff matrix, you can follow the steps mentioned above to find the payoffs for North Springs and South Springs in the dominant-strategy equilibrium and the Nash equilibrium.

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After answering the given query, we can state that The Pythagorean formula can also be used to determine the cone's cut-off end's diameter: d = (r2 - y2)/2 = (7.2 - 0.6)/2 = 14.27 inches (approximately)

An item with a level base and a smooth, tapering tip or vertex is referred to as a cone in three dimensions. A cone is formed by joining a succession of line segments, half-lines, or lines that link every point on the base in a plane without vertices. A cone is a three-dimensional construction with a smooth shift from a flat, usually circular base to the vertex or peak, which acts as the base's center's axis. An apparent three-dimensional geometric form with a vertically smoothed curved surface is called a cone.

x/h equals (r + y)/r

(r - (h - x - 3)) = (r - (h - x - 3)) = x/h/r

x = r - y = r - (h - x - 3)

x = (2r - h + 3)/2

V = (1/3)πr^2h

2,034.72 = (1/3)πr^2h

2,034.72 = (1/3)πr^2(h - x - 3)

2,034.72 = (1/3)πr^2(h - ((2r - h + 3)/2) - 3)

After simplifying and finding "r," we arrive at:

7.2 centimeters is r.

The height of the removed portion can now be determined using the calculation for "x":

Inches are equal to x = (2r - h + 3)/2 = (2(7.2) - 24 + 3)/2 = 0.6

The Pythagorean formula can also be used to determine the cone's cut-off end's diameter:

d = (r2 - y2)/2 = (7.2 - 0.6)/2 = 14.27 inches (approximately)

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The value of simplified form of the expression is,

⇒ √2 (13 - √3)

We have to given that;

The expression is,

⇒ 3√2-√6+10√2

Now, We can simplify as;

⇒ 3√2 - √6 + 10√2

⇒ 3√2 - √2 × √3 + 10√2

⇒ 13√2 - √2 × √3

⇒ √2 (13 - √3)

Thus, The value of simplified form of the expression is,

⇒ √2 (13 - √3)

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Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

The given equation of the line is

5x - 2y = -6

Ax + By = C1

Bx - Ay = C2

are perpendicular.

Then the perpendicular to the line 5x - 2y = -6 is 2x + 5y = C2

We have to find the value of C2

The line is passing through the point (5, -4)

Substitute the values in the equation and find the value of C2

2(5) + 5(-4) = C2

C2 = 10 -20

= -10

The equation will be 2x + 5y = -10

Rearrange the terms and make it slope intercept form

2x + 5y = -10

5y = -10 -2x

5y = -2x - 10

y = (-2/5)x - 2

Hence,  equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

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Answer:

the area should be in in2

So, the parametric equations for the line through the origin parallel to the vector 2j + 3k are: x = 0; y = 2t; z = 3t.

To find parametric equations for the line through the origin parallel to the vector 2j + 3k, we can use the general form:

x = x₁ + at

y = y₁ + bt

z = z₁ + ct

In this case, since the line passes through the origin, the initial point (x₁, y₁, z₁) is (0, 0, 0).

Given that the line is parallel to the vector 2j + 3k, we can set the coefficients a, b, and c to the corresponding components of the vector.

Therefore, the parametric equations for the line are:

x = 0 + 0t = 0

y = 0 + 2t = 2t

z = 0 + 3t = 3t

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Answer:

After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.

The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:

A = A0 * (1/2)^(t/T)

where:

A0 is the initial amount (80 mg)

t is the time elapsed (17,190 years)

T is the half-life (5,730 years)

A = 80 * (1/2)^(17,190/5,730)

A = 80 * (1/2)^3

A = 80 * (1/8)

A = 10 mg * 1/2

A = 5 mg

a. the population in 1790 was 3.93 million. b. the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790. c. the population of the United States in 1820 was approximately 31.12 million.

(a) To find the population in 1790, we plug in t = 0 into the given formula:

N = 3.93 x 1.03^0 = 3.93

Therefore, the population in 1790 was 3.93 million.

(b) To express the population in 1820 using functional notation, we plug in t = 30 into the given formula:

N = 3.93 x 1.03^30

Therefore, the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790.

(c) To calculate the value of the population in 1820, we plug in t = 30 into the formula and round to two decimal places:

N = 3.93 x 1.03^30 ≈ 31.12

Therefore, the population of the United States in 1820 was approximately 31.12 million.

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Answer:

y = 5, y = -5

Step-by-step explanation:

In this question, you would have to solve the equation for "y".

Solve:

-3y² = -75

Divide both sides by -3.

y² = 25

Square root both sides to cancel out the exponent.

√y² = √25

y = ±√25

Simplify the square root for both positive and negative terms.

y = 5

y = -5

Your final answer would be y = 5 and y = -5

Step-by-step explanation:

By getting our values from the graph,

When x = 1, the blue line has y-value -5.

When x = 9, the dotted line has y-value -6.

Hence,

f(1) + 5 * g(9) = (-5) + 5(-6) = -35.

Answer:

From the above graph,

→When x=1, y=f(1)=-5

→When x=9, y=g(x)=-6

• 5×f(1)+5×g(9)

=5{f(1)+g(9)}

=5{(-5)+(-6)}

=5(-11)

=-55

In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.

In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.

We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.

How to solve?

For 8 men in a line: 8! = 40320  

In order to separate 2 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways= 40320 * 126 * 120 = 609638400

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Answer:

A. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

A continuous data is any data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable. Any quantity such as height, volume, weight, density, length, pressure, temperature, speed, distance, time are generally a continuous data.

Hence, the exact heights of different elephants represents a continuous data because the data can take on any value in an interval.

On the other hand, a discrete data is any data set in which the number of possible values are either finite or countable. Thus, a discrete data can only take on specific values. For example, the value of a fair die, number of sweets in a jar, number of eggs in a crate etc.

the ratio 1 is to 2 is equivalent to 3: 6

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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Answer:

y = 1/2x - 2

Step-by-step explanation:

In order for a line to be perpendicular to another, the lines must have opposite reciprocal slopes.

Example of an opposite reciprocal slope: -2 ⇒ 1/2

Insert the information into the point-slope formula:

\(y-y_1=m(x-x_1)\\\\y-2=\frac{1}{2}(x-8)\\\\y-2=\frac{1}{2}x-4\\\\y=\frac{1}{2}x-2\)

Answer:

6 pi

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

The diameter is 2 so the radius is 1/2 d = 1

V = pi (1)^2 * 6

V = 6 pi

Answer:

Step-by-step explanation:

Given the frequency vibrations for a certain guitar string modeled by the equation

F = 200√T where:

T is amount of tantrums in pounds

If the frequency of the vibrations is 600 vibrations per second, the amount of pounds in tantrums will be gotten by substituting F = 600 into the equation and calculating T as shown:

600 = 200√T

Divide both sides by 200

600/200 = 200√T /200

3 = √T

Square both sides

3² = (√T)²

9 = T

T = 9

Hence 9 pounds of tantrum was used to plug the string