En el siguiente diagrama, Midtown se encuentra exactamente a mitad de camino entre Uptown y Downtown. ¿Cuál es la distancia entre Downtown y Midtown?

2.6 km
90 grados
2.1 km
1.5 km

Answer:

see explanation

Step-by-step explanation:

(a)

Given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition when x = 3, y = 18 , then

18 = 3k ( divide both sides by 3 )

6 = k

y = 6x ← equation of proportion

(b)

(i)

when x = 12 , then

y = 6 × 12 = 72

(ii)

when y = 42

42 = 6x ( divide both sides by 6 )

7 = x

The variance of the sample is 6561. The variance measures the spread or dispersion of the data points around the mean. In this case, it represents the average squared deviation from the mean of the 36 observations.

The variance of a sample can be calculated using the formula:

Variance = Standard Deviation^2

Given that the standard deviation of a sample of 36 observations is 81, we can square this value to find the variance.

Variance = 81^2 = 6561

Therefore, the variance of the sample is 6561. The variance measures the spread or dispersion of the data points around the mean. In this case, it represents the average squared deviation from the mean of the 36 observations.

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The Theissen weight for a catchment shaped as an equilateral triangle with rain gauges on each corner is the smallest value among the weights assigned to each gauge, representing the area of influence for rainfall measurement.

The Theissen weight, also known as the Voronoi weight, is a method used in hydrology to estimate rainfall over a catchment area based on the proximity of rain gauges. In this scenario, we have an equilateral triangle-shaped catchment with rain gauges located at each corner. The Theissen weight for each gauge is determined by drawing lines bisecting the sides of the triangle from the corresponding gauge to the midpoint of the opposite side. The area within each bisected triangle represents the influence of that gauge on the catchment. The smallest Theissen weight is then the minimum value among the weights assigned to each gauge, indicating the smallest area of influence for rainfall measurement within the catchment.

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The cost of one rose bush is $10 and the cost of one pot of ivy is $10.

Let's assume the cost of one rose bush is represented by "R" and the cost of one pot of ivy is represented by "I".

According to the given information:

Jaidee spent $140 on 2 rose bushes and 12 pots of ivy:

2R + 12I = 140 ...(1)

Beth spent $120 on 6 rose bushes and 6 pots of ivy:

6R + 6I = 120 ...(2)

We now have a system of two equations with two variables. To solve this system, we can use either substitution or elimination method. Let's use the elimination method.

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of "R" in both equations equal:

6R + 36I = 420 ...(3)

12R + 12I = 240 ...(4)

Now, subtract equation (4) from equation (3):

(6R + 36I) - (12R + 12I) = 420 - 240

-6R + 24I = 180 ...(5)

Now we have a new equation (5) that relates "R" and "I".

Let's solve equations (5) and (2) together:

-6R + 24I = 180 ...(5)

6R + 6I = 120 ...(2)

Add equation (5) and equation (2):

(6R - 6R) + (24I + 6I) = 180 + 120

30I = 300

Divide both sides of the equation by 30:

I = 10

Now substitute the value of "I" into equation (2) to find the value of "R":

6R + 6(10) = 120

6R + 60 = 120

6R = 120 - 60

6R = 60

Divide both sides of the equation by 6:

R = 10

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Answer:the answer is A

Step-by-step explanation:

The step is

Real number - rational(irrational)_ - integer - whole - then natural

The true statement regarding number sets are b. all irrational numbers are real numbers.

Irrational numbers are those numbers which have a non-repeating, non-terminating pattern after decimal place.

According to the given statements we have to determine which is true.

a. all integers are not whole numbers as 0 contains in the set of whole numbers but not in the set of integers.

b. all irrational numbers are real numbers this is a true statement because all the real numbers consist of rational and irrational numbers.

We don't need to check other options because we have been asked which of the following is true not which of the following is/are true.

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a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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Answer:

If the sequence is arithmetic:

\(\boxed{\sf a_n=168n-328}\)

\(\sf a_9=1184\)

If the sequence is geometric:

\(\boxed{ \sf a_n=2(4)^{n-1}}\)

\(\sf a_9=131072\)

Step-by-step explanation:

An explicit formula allows you to find the nth term of a sequence.

As the question has not specified if the given terms are from an arithmetic or geometric sequence, I will provide answers for both.

-------------------------------------------------------------------

Explicit formula: Arithmetic sequence

\(\sf a_n=a+(n-1)d\)

where:

Given:

Substitute the values into the formula to create two equations:

\(\begin{aligned}\sf a_2 & =\sf 8\\\sf a+(2-1)d&=\sf 8\\\sf a+d&=\sf 8\end{aligned}\)

\(\begin{aligned}\sf a_5 & =\sf 512\\\sf a+(5-1)d&=\sf 512\\\sf a+4d&=\sf 512\end{aligned}\)

Subtract the first equation from the second to eliminate a, and solve for d:

\(\begin{aligned}\implies \sf (a+4d)-(a+d) & = \sf 512-8\\\sf 3d & = \sf 504\\\sf d & = \sf 168\end{aligned}\)

Substitute the found value of d into one of the equations and solve for a:

\(\begin{aligned}\sf a+d & = \sf 8\\\implies \sf a+168 & = \sf 8\\\sf a & = \sf -160\end{aligned}\)

Substitute the found values of a and d into the formula to create an explicit formula:

\(\implies \sf a_n=-160+(n-1)168\)

\(\implies \sf a_n=-160+168n-168\)

\(\implies \sf a_n=168n-328\)

To find a₉, substitute n = 9 into the found explicit formula:

\(\implies \sf a_9=168(9)-328\)

\(\implies \sf a_9=1512-328\)

\(\implies \sf a_9=1184\)

-------------------------------------------------------------------

Explicit formula: Geometric sequence

\(\sf a_n=ar^{n-1}\)

where:

Given:

Substitute the values into the formula to create two equations:

\(\begin{aligned}\sf a_2 & =\sf 8\\\sf ar^{2-1}&=\sf 8\\\sf ar&=\sf 8\end{aligned}\)

\(\begin{aligned}\sf a_5 & =\sf 512\\\sf ar^{5-1}&=\sf 512\\\sf ar^4&=\sf 512\end{aligned}\)

Divide the second equation by the first to eliminate a, and solve for r:

\(\begin{aligned}\implies \sf \dfrac{ar^4}{ar} & = \sf \dfrac{512}{8}\\\sf r^{4-1} & = \sf 64\\ \sf r^3 & = \sf 64\\ \sf r & = \sf \sqrt[\sf 3]{\sf 64} \\ \sf r & = \sf 4\end{aligned}\)

Substitute the found value of r into one of the equations and solve for a:

\(\begin{aligned}\sf ar & = \sf 8\\\implies \sf 4a & = \sf 8\\\sf a & = \sf 2\end{aligned}\)

Substitute the found values of a and r into the formula to create an explicit formula:

\(\implies \sf a_n=2(4)^{n-1}\)

To find a₉, substitute n = 9 into the found explicit formula:

\(\implies \sf a_9=2(4)^{9-1}\)

\(\implies \sf a_9=2(4)^8\)

\(\implies \sf a_9=131072\)

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The statement 'if you are balancing an object on its center of mass, there must be equal amounts of mass on both sides of the center of mass" is false.

A place at which the entire mass of a body or all the masses of a system of particles appears to be concentrated is defined as the center of mass of a body or system of particles.

We have statement:

If you are balancing an object on its center of mass, there must be equal amounts of mass on both sides of the center of mass.

As we know, center of a mass is an object balance point it doesn't need to have equal amounts of mass on both sides of the center of mass.

Thus, the statement 'if you are balancing an object on its center of mass, there must be equal amounts of mass on both sides of the center of mass" is false.

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The triangles to use in finding the distance x are KLM and MNP. The distance x between the shoreline and buoy is 80 m.

Triangles are said to be similar when on comparing their corresponding properties, some common properties exist. The common properties are the sides and measure of angles.

Thus on comparing triangles KLM and MNP, we have;

MP/ KL = PN/ KM

20/ x = 25/ 100

make x the subject of formula

x = (20 *100)/ 25

  = 2000/ 25

  = 80

x = 80

The distance x between the shoreline and the buoy is 80 m.

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Answer:

7 cm ; 10 cm ; 14 cm

Step-by-step explanation:

x = y + 3

z = 2y

x + y + z = 31

y + 3 + y + 2y = 31

4y = 31 -3

4y = 28

4/4 y = 28/4

y = 7

z = 7(2) = 14

x = 7 + 3 = 10

Answer:

A) 75%

B) 74%

Step-by-step explanation:

A) 18/24=0.75

B) 37/50= 0.74

Answer:

9

Step-by-step explanation:

Answer:

Based on the graph, we can see that the graphs of f(x) and g(x) intersect at some value of x, which is the solution for f(x) = g(x). From the given options, the only approximate solution that seems to match with the graph is X = 1.

We can see that the point where the two graphs intersect is somewhere between x = 0 and x = 1, and X = 1 is the closest approximate solution to the intersection point. Therefore, X = 1 is the approximate solution for f(x) = g(x) based on the given graph.

Step-by-step explanation:

please follow me for more if you need any help

Answer:

\( \sqrt{ {1}^{2} + {2}^{2} + {( - 2)}^{2} } = \sqrt{1 + 4 + 4} = \sqrt{9} = 3\)

(1, 2, -2) is 3 units away from the origin.

(0, 0, 5) is 5 units away from the origin.

So (0, 0, 5) is farther away from the origin.

Answer:

Step-by-step explanation:

Since it's a right angled triangle we can use trigonometric ratios to find the value of x

To find the value of x we can use either sine or cosine

\( \sin(30) = \frac{5}{x} \\ x \sin(30) = 5 \\ x = \frac{5}{ \sin(30) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

\( \cos(60) = \frac{5}{x} \\ x \cos(60) = 5 \\ x = \frac{5}{ \cos(60) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

Hope this helps you

Answer:

the number could be

495

496

497

499

Step-by-step explanation:

when rounding, it can be rounded up if it is 5 or above. if it is 4 or below then it is rounded down.

hope that helped.

The linear equation that passes through these two points is:

y = -4x

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know the two points (-2, 8) and (5, -20), so the slope is:

a = (-20 - 8)/(5 + 2) = -28/7 = -4

So the line is:

y = -4*x + b

To find the value of b, we can replace the values of the point (-2, 8), so we will get:

8 = -4*(-2) + b

Now we can solve this for b.

8 = -4*(-2) + b

8 = 4*2 + b

8 = 8 + b

8 - 8 = b

0 = b

Then the linear equation is:

y = -4*x

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Answer:

S.I = (P × R × T)/100

where;

P - principal

R - rate

T - time

Answer:

I think its A

Step-by-step explanation:

Please mark brainliest

The total number of gold and blue squares are 18 and 13 respectively.

Here, we are given that Megan is making a quilt from squares of material.

The quilt has 9 rows and each row has 6 squares.

There are 4 corner squares in the quilt which will be white. Around 1 corner square there will be 3 squares that share a side with the white square.

Thus, there will be a total of 12 gold square around the 4 corner squares.

Further, there are two center squares in the middle row that are white.

Around these 2 center white squares there will be 6 squares that share a side with them. Hence, these 6 square will also be gold.

Therefore, the total number of gold squares will be-

6 + 12

= 18

Now, the white squares = 4 + 6 = 10

and gold squares = 18

and the total number of squares = 9 × 6 = 54

Thus, the number of remaining squares = 54 - 18 - 10

= 26

Out of these remaining 26 squares half will be blue and half pink.

Thus, the number of blue squares will be-

26/2

= 13

Hence, we find that the total number of gold and blue squares are 18 and 13 respectively.

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(a) The logarithmic equation that represents the given exponential equation \(e^x=9\) is \(x = \ln(9)\). (b) The exponential equation that represents the given logarithmic equation \(\ln 6=y\) is \(6 = e^y.\)

(a) To rewrite the equation as a logarithmic equation, we use the fact that logarithmic functions are the inverse of exponential functions.

In this case, we take the natural logarithm (\(\ln\)) of both sides of the equation to isolate the variable x. The natural logarithm undoes the effect of the exponential function, resulting in x being equal to \(\ln(9)\).

(b) To rewrite the equation as an exponential equation, we use the fact that the natural logarithm (\(\ln\)) and the exponential function \(e^x\) are inverse operations. In this case, we raise the base e to the power of both sides of the equation to eliminate the natural logarithm and obtain the exponential form. This results in 6 being equal to e raised to the power of y.

Therefore, the logarithmic equation that represents the given exponential equation \(e^x=9\) is \(x = \ln(9)\). (b) The exponential equation that represents the given logarithmic equation \(\ln 6=y\) is \(6 = e^y.\)

Question: Rewrite each equation as requested. (a) Rewrite as a logarithmic equation. \(e^x=9\) (b) Rewrite as an exponential equation.\(\ln 6=y\)

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Answer:

Another name for inverse is reciprocal

Answer:

The answer is reciprocal

Answer:

approx. 68%

Step-by-step explanation:

this is a normal distribution.

in a normal distribution, approximately 68% of the data is within one standard deviation of the mean (we also have 95% of data is within two standard deviations of the mean, and 99.7% of data is within three standard deviations of the mean).

one standard deviation in our question is 113.

315 is one standard deviation below the mean because 428 - 113 = 315.

541 is one standard deviation above the mean because 428 + 113 = 541.

so we expect approx. 68% of the data to be between 315 and 541.

The enlargement transformation user to produce the new pentagon is called a dilation.

Dilation or Scaling involves increasing or decreasing the size of an object while maintaining its shape and proportions. In this case, the original pentagon is scaled up or down uniformly to create the new pentagon.

It involves making use of a certain scale factor to make increment or decrease an object. In this case a scale factor greater than 1 was used as the new pentagon was said to be enlarged.

Therefore, the enlargement transformation is a dilation.

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The statement that best describes irrational number is any real number that cannot be expressed as a ratio a/b

Any number that cannot be stated as a fraction for any integers is considered to be irrational. The decimal expansions of irrational numbers are neither periodic nor do they come to an end. Every number that is transcendental is illogical.

All real numbers that are not rational numbers are referred to be irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.

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Step-by-step explanation:

∵ DE∥FG

∴∠EDF=∠GFH

∵∠DFE=180º-∠DEF-∠EDF

and ∠FHG=180º-∠FGH-∠GFH

∴∠DFE=∠FHG

Answer:

Step-by-step explanation:yes

Therefore, p = 0.33. Thus, the value of p is 0.33.

Given,

K(w) = 0.2 for w€ [0. p],

K(w) = 0.1 for w€ (p. p + 1],and

K(w) = -0.15 otherwise.

It is known that E(K) = 0

We need to find the value of p. Calculation of E(K)

E(K) = ∫₀^p (0.2)w dw + ∫ₚ^(p+1) (0.1)w dw + ∫_(p+1)^∞ (-0.15)w dw

E(K) = 0.1p² + 0.1p + (-0.15)(∞² - (p+1)²) - 0.2(0.5p²)

Since

E(K) = 0,0 = 0.1p² + 0.1p - 0.15(∞² - (p+1)²) - 0.1p²0.1p² - 0.1p² + 0.15(∞² - (p+1)²) = 0.1p

Simplifying the above equation

0.15(∞² - (p+1)²) = 0.1p2.25∞² - 2.25p² - 1.5p - 2.25 = 0

Multiplying by -4 to simplify the equation

9p² + 6p - 9∞² + 9 = 0

On solving, we get,

{-1 - (4*(-9)(-9² + 9))/2*9, -1 + (4*(-9)(-9² + 9))/2*9}{-16, 0.33}

Therefore, p = 0.33. Thus, the value of p is 0.33.

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