The ratio of runners to walkers in the fund raiser was 6 to 1. If there were 10 walkers, how many runners were there?

Answer:

x = 6

Step-by-step explanation:

• the diagonals of a parallelogram bisect each other , then

5x + 11 = 4x + 17 ( subtract 4x from both sides )

x + 11 = 17 ( subtract 11 from both sides )

x = 6

Since it's divided equally diagonally, 4x+17 and 5x+11 are equal.

Let's set them equal to each other and solve.]

\(4x+17=5x+11\)

Subtract 4x from both sides to combine like terms.

\(17=x+11\)

Now subtract 11 from both sides to isolate the variable and solve for x.

\(6=x\)

Flip the equation to put in standard form and now you have x :)

\(x=6\)

hope this helped!

n should be a whole number, we round up to the nearest integer, giving n = 540. Therefore, if Russel wants 0.99 certainty, n should be at least 540.

To determine how large n should be in order to have a certain level of certainty about the true probability p, we can use the concept of confidence intervals.

For a binomial distribution, the estimate of the probability p is X/n, where X is the number of successes (in this case, the number of times tails is obtained) and n is the number of trials (the number of times the coin is flipped).

To find the confidence interval, we need to consider the standard error of the estimate. For a binomial distribution, the standard error is given by:

SE = sqrt(p(1-p)/n)

Since p is unknown, we can use a conservative estimate by assuming p = 0.5, which gives us the maximum standard error. So, SE = sqrt(0.5(1-0.5)/n) = sqrt(0.25/n) = 0.5/sqrt(n).

To ensure that the true p is within 0.1 of the estimate X/n with at least 0.95 certainty, we can set up the following inequality:

|p - X/n| ≤ 0.1

This inequality represents the desired margin of error. Rearranging the inequality, we have:

-0.1 ≤ p - X/n ≤ 0.1

Since p is unknown, we can replace it with X/n to get:

-0.1 ≤ X/n - X/n ≤ 0.1

Simplifying, we have:

-0.1 ≤ 0 ≤ 0.1

Since 0 is within the range [-0.1, 0.1], we can say that the estimate X/n with a margin of error of 0.1 includes the true probability p with at least 0.95 certainty.

To find the value of n, we can set the margin of error equal to the standard error and solve for n:

0.1 = 0.5/sqrt(n)

Squaring both sides and rearranging, we get:

n = (0.5/0.1)^2 = 25

Therefore, n should be at least 25 to know with at least 0.95 certainty that the true p is within 0.1 of the estimate X/n.

If Russel wants 0.99 certainty, we need to find the value of n such that the margin of error is within 0.1:

0.1 = 2.33/sqrt(n)

Squaring both sides and rearranging, we get:

n = (2.33/0.1)^2 = 539.99

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Answer: y + 2 = -7/6 ( x - 4 )

Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

21 = 2.50 + 5x

21 - 2.50 = 5x

18.50 = 5x

x = 18.50 / 5

x = 3.7 bags of avocados

To get 3 bags of avocados or 9 avocados

= $5 × 3

= $15

Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

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Answer: multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14)

Step-by-step explanation:

becaue... multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14)

A statement of inequality that correctly compares two numbers is: D. 6,365.1 < 6,365.999.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

In this scenario, a statement of inequality that correctly compares two numbers is 6,365.1 < 6,365.999.

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Answer:

y=7miles

Step-by-step explanation:

The total perimeter is 21 miles and we know two sides of the triangle are 7 miles, or 14 miles together.

We need to know the one other side of the triangle, so we can subtract the 14 miles we know from the total 21 miles.

21-14=7miles

Answer:

y=7 mi

Step-by-step explanation:

If you know that each side of this triangle is 7 and they are each side is the same length, you can make an educated guess  that the answer is 7. If you need An easier method 7x3=21. a triangle has 3 sides so your answer would be 7

Answer:

slope of y = -5.5 is 0.

Slope of 4x - 4y = 22 is 1

Step-by-step explanation:

y = -5.5 is a horizontal line going through -5.5.  The slope does not go up or down so we say that the slope is zero.

4x - 4y = 22   Subtract 4x from both sides

4x - 4x - 4y = -4x + 22

-4y = -4x + 22  Divide all the way through by -4

\(\frac{-4y}{-4}\) = \(\frac{-4x}{-4}\) + \(\frac{22}{-4}\)

y = x - \(\frac{22}{4}\)

The sloe is the number before the x.  If we do not see a number, we assume it is 1.

Answer

B

Step-by-step explanation:

Answer: The answer is A. Yes, because every x-value corresponds to exactly one y-value. i hope its right

1) Notice that, in this case, the center is at (0,0) the focus at (0,4) and the Vertex is at (0,7)

2) Since the focus is at the y-axis, and the center is at the origin we can start from the following formula:

Answer:

Step-by-step explanation:

Let the time of the complete race be x.

Then we have the following equation:

Answer: 6 1/4 minutes

Step-by-step explanation:

97.72% of children in the baseball league are taller than 44 inches.

We may apply the characteristics of the normal distribution to calculate the proportion of kids in the league who are taller than 44 inches.

Using the following formula, we can determine the z-score for a child that is 44 inches tall:

z = (x - μ) / σ

where x is the child's height, is the population's mean height, and is the population's standard deviation.

Therefore,

z = (44 - 48) / 2 = -2

This indicates that a youngster that is 44 inches tall is 2 standard deviations shorter than the population's mean height.

The percentage of the population that is above a z-score of -2 can then be determined using a standard normal distribution table. The percentage of the population that is above a z-score of -2, according to the conventional normal distribution table, is almost 97.72%.

Hence, 97.72% of children in the league are taller than 44 inches.

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The right triangle, like the other triangles, has three sides, three vertices, and three angles. The difference between the other triangles and the right triangle is that the right triangle has a 90  angle.

To find missing angles and sides and round to the nearest tenth, you can use different methods depending on the given information and the type of triangle or shape involved.

Some common methods include:
Trigonometric ratios (sine, cosine, tangent) for right triangles.
Angle sum property or exterior angle property for triangles.
Pythagorean theorem for right triangles.
Law of cosines and law of sines for non-right triangles.
To help find the missing angles and sides of a triangle, you need certain information about the triangle, such as known angle and side measurements, or information about the properties of the triangle.

Without this information, no concrete calculations can be made.

Provide the necessary information or describe the problem in more detail and we will help you find the missing corners and sides of the triangle and round it to tenths.

Remember to always check if any additional information is given, such as side lengths or angles ' 7 and to apply the appropriate formula or property to find the missing value.

Round your answer to the nearest tenth as specified.

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The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.

1. Identify the exact differential equation.

2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).

3. Multiply the integrating factor with the equation to make it exact.

4. Integrate both sides of the equation to obtain the general solution.

5. Check the solution by differentiating it to confirm that it satisfies the original equation.

6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.

The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.

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x=2

10-2(2x+1)=4(x-2)

10-4x-2=4x-8

10-2=8x-8

8=8x-8

16=8x

2=x

Answer:

X = 2

Step-by-step explanation:

\( \sf \: First, solve \: the \: brackets. \)

\( \sf \: 10 - 2(2x + 1) = 4(x - 2) \\ \sf10 - 4x - 2 = 4x - 8 \: \: \: \: \: \: \: \)

\( \sf \: Combine \: like \: terms .\)

\( \sf8 - 4x = 4x - 8\)

\( \sf \: Subtract \: 4x \: from \: both \: sides \: to \: remove \: 4x.\)

\( \sf \: 8 - 4x - 4x = 4x - 8 - 4x \\ \sf8 - 8x = - 8\)

\( \sf \: Subtract \: 8 \: from \: both \: sides \: to \: remove \: 8.\)

\( \sf8 - 8 - 8x = - 8 - 8 \\ \sf - 8x = - 16\)

\( \sf \: Divide \: both \: sides \: by \: -8.\)

\( \sf \: x = 2\)

Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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Answer:

10 units squared

Step-by-step explanation:

Main steps

Step 1. Identify which leg to use as a base

Step 2. Calculate the base length

Step 3. Calculate the height

Step 4. Calculate the area

Step 1. Identify which leg to use as a base

We are given that the shape is a triangle.  The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}bh\) where b is the "base" of a triangle, and h is the "height".

One common misconception is that the base must be at the bottom (although it is easy to think of it that way).  Rotating the shape, any of the three sides could be at the bottom, and thus any of the three sides could be the base.

The "height" of the triangle depends on which leg is being used as a base.  The height for a given base is always the shortest distance from the vertex opposite the base to the line that contains the base.  This shortest distance always ends up being the line segment that is perpendicular to the base.

In this case, since side BC is along the gridlines, it will be easiest to use side BC as the base, because the perpendicular line for the height will be along gridlines.  The height is the distance from A to the side BC (which is a line segment between (-3,2) and (1,2)).

Step 2. Calculate the base length

The base length is the distance between the two endpoints of the line segment.  The distance formula is \(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Using Point B as Point 1, and Point C as Point 2:

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

\(D=\sqrt{(0)^2+(5)^2}\)

\(D=\sqrt{0+25}\)

\(D=\sqrt{25}\)

\(D=5\) units

So the base length is 5 units

b=5 units

Since these point are on a graph, it can be verified by counting the squares between the two points, however if work needs to be shown, the Distance formula is the "work".

Step 3. Calculate the height

The "height" for the base from step 2 is a line segment between (-3,2) and (1,2).  This distance can again be found using the distance formula:

Using Point A as Point 1, and the point (1,2) on BC as Point 2:

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

\(D=\sqrt{(-4)^2+(0)^2}\)

\(D=\sqrt{16+0}\)

\(D=\sqrt{16}\)

\(D=4\) units

So the height for the base from Step 2 is 4 units.

h=4 units

Again, these point are on a graph, so this answer can be verified by counting the squares between the two points.

Step 4. Calculate the area

Using the formula for the area of a triangle discussed in Step 1, the area can be calculated:

\(A_{triangle}=\frac{1}{2}(5~\text{units})(4~\text{units})\)

\(A_{triangle}=10 \text{ units}^2\)

If the two cubes each of edge 12cm are joined, then the surface area of new cuboid is 1440 sq. cm.

The surface area of a three-dimensional object is the total area of the object's exposed surfaces. It can be thought of as the sum of the areas of all the faces of the object. For example, the surface area of a cube is the sum of the areas of its six faces. It is typically measured in square units, such as square centimeters or square inches.

The formula for calculating the surface area of a cuboid is 2(lw + lh + wh)

Where l is the length, w is the width, and h is the height of the cuboid.

According to the question, when two cubes each of edge 12cm are joined, it forms a cuboid with length = 24cm , width = 12cm and height = 12cm.

So the surface area for the cuboid is given by,

S.A = 2(lw+lh+wh)

   = 2(12*24+12*12+12*24)

    =1440 sq. cm

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Cos β = √3/3 corresponds to the cosine of a 60-degree angle.

To find the value of cos β given that cos β = √3/3, we can use the concept of special right triangles and trigonometric ratios.

Let's consider a right triangle where one of the angles is β. Since cos β is positive (√3/3), we can determine that β is an acute angle within the first quadrant.

In a right triangle, the adjacent side is the side adjacent to the angle, and the hypotenuse is the longest side, opposite the right angle.

Using the Pythagorean theorem, we can find the length of the remaining side. Let's assume the adjacent side has length √3, and the hypotenuse has length 3.

Using the formula for cos β:

cos β = adjacent side / hypotenuse

cos β = √3 / 3

Now, we can compare this to the trigonometric values for special angles. In a 30-60-90 degree triangle, the cosine of 30 degrees is also √3/2, but since β is an acute angle in the first quadrant, we know that cos β = √3/3 corresponds to the 60-degree angle in a 30-60-90 triangle.

Therefore, we can conclude that β is a 60-degree angle, and cos β = √3/3 corresponds to the cosine of a 60-degree angle.

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The value of x in the given equation will be 2/5

From the data,

We have to determine the value of x.

The given equation is: 18x-16=-12x-4

For determining the value of x, we will first shift the like terms on one side of the equation.

So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.

So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,

We will get it as:

18x+12x = -4+16

30x=12

Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.

So, the value of x will be = 12/30 = 2/5

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The correct question may be:

What is the value of x

18x-16=-12x-4

Enter your answer in the box.

So, based on the theoretical likelihood, we anticipate that 35 times out of 140 repeats, both spins will be odd numbers.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.

Here,

The theoretical probability of both spins being odd numbers is 9 over 36, which means that for every 36 times the experiment is repeated, we expect 9 of those times to result in both spins being odd numbers.

If the experiment is repeated 140 times, we can use the theoretical probability to estimate the number of times both spins will be odd numbers as follows:

140 * (9/36) = 35

So, based on the theoretical probability, we predict that both spins will be odd numbers 35 times out of 140 repetitions.

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And The Answer is:

..........a)12

The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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Answer:

-1

Step-by-step explanation:

\(6x + y = 10 \\ y = 10 - 6x \\ y = 10 - 6x,x∈ℝ\)

Answer:

y = 10 - 6x

Step-by-step explanation:

6x + y = 10

=> y = 10 - 6x

Answer:

x=180-125

=55

z=55

y=180-(55+55)

y=70

Answer:

26

Step-by-step explanation:

Subtract the mean (84) from each of the four scores, obtaining

2, -3, 3, - 2

These are the "deviations."

Next, square each of these four deviations, obtaining

(2)^2 = 4, and:

(-3)^2 = 9, and:

(3)^2 = 9, and:

(-2)^2 = 4

Then the sum of the squared deviations of the scores from the mean is 26.

Answer:

the picture above is the graph :)