The cost of a gallon of gas is $3.50. What is the maximum number of of gallons you can buy for $20?

The required value of EC is 5 units.

Since DE is parallel to BC, we can use the property of similar triangles to set up a proportion:

AD/DB = AE/EC

We know that AD + DB = AB = x + 5. Since D is a point on AB, we can express AD and DB in terms of x:

AD = x, DB = x + 5 - x = 5

We also know that AE = 3 and ED = x + 1. Using these values, we can express AD in terms of ED:

AD = ED - AE = (x + 1) - 3 = x - 2

Substituting these values into the proportion, we get:

(x - 2)/5 = 3/EC

Multiplying both sides by 5EC, we get:

x - 2 = 15/EC

Multiplying both sides by EC, we get:

EC(x - 2) = 15

Expanding the left side, we get:

ECx - 2EC = 15

Solving for EC, we get:

EC = 15/(x - 2)

We are given that EC = x, so we can set these expressions equal to each other:

x = 15/(x - 2)

Multiplying both sides by (x - 2), we get:

x(x - 2) = 15

Expanding the left side, we get:

x² - 2x = 15

Bringing all terms to one side, we get:

x² - 2x - 15 = 0

We can factor this quadratic equation:

(x - 5)(x + 3) = 0

Therefore, x = 5 or x = -3. We reject x = -3 since we are given that EC > 0. Thus, the length of EC is: EC = x = 5.

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Therefore , the solution of the given problem of volume comes out to be the response is 900 cubic units.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, understanding an object's volume is necessary to calculate its measurements. It is standard practice to convert the weight of an object into mass units like grams and kilograms.

Here,

The formula V = Bh, when B is the area of the bottom and h is the height of the prism, determines the volume of a right triangle prism.

The prism has an area of because its foundation is a right triangle with 8 and 15-foot-long legs.

=> B = (1/2)bh = (1/2)(8)(15) = 60

The prism's height is specified as 15 inches.

As a result, the prism's capacity is:

=>  900 cubic units are equal to V = Bh = 60(15).

Therefore, the response is 900 cubic units.

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Answer:

900 cubic units

Step-by-step explanation:

(x-bar) refers to the sample means in statistics. It is the average of all the data values in a sample. It is calculated by dividing the sum of all the data values by the sample size.

The distribution of (x-bar) follows a normal distribution, and its expected value is equal to the population mean. The standard error of (x-bar) is calculated by dividing the population standard deviation by the square root of the sample size. It is used to estimate how much the sample mean varies from the population mean.

Sample mean (x-bar) is a statistical concept used to calculate the average of a sample, and standard error is a measure of the variability of the sample mean. The distribution of the sample mean is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

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If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle. Also if a circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long then length of the arc subtended by the angle's rays 8.4 cm. Another circle is centered at the vertex of the angle then arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

a.) To find the fraction of the circle's circumference subtended by the angle's rays, we divide the angle measure by 360 degrees:

fraction of circle's circumference = 140/360

Simplifying this fraction, we get:

fraction of circle's circumference = 7/18

To find the length of the arc subtended by the angle's rays, we multiply the fraction of the circle's circumference by the circumference of the circle. Let's call the circumference of the circle "C":

length of arc = (7/18)*C

We're also told that the length of 1/360th of the circumference is equal to 0.06 cm. So, we can write:

(1/360)*C = 0.06

Multiplying both sides by 360, we get:

C = 360*0.06 = 21.6 cm

Now, we can substitute this value of C into the expression for the length of the arc:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Therefore, the length of the arc subtended by the angle's rays is 8.4 cm.

b.) We're given that 1/360th of the circumference of the circle is 0.06 cm long. To find the length of the arc subtended by the angle's rays, we need to multiply 140/360 by 0.06:

length of arc = (140/360)*0.06

length of arc = 0.0233 cm (rounded to four decimal places)

Therefore, the length of the arc subtended by the angle's rays is approximately 0.0233 cm.

c.) We're told that the length of the arc subtended by the angle's rays is 70 cm. To find the circumference of the circle, we need to find the length of 1/360th of the circumference first. We can do this by dividing 70 by 1/360:

(1/360)*C = 70

Multiplying both sides by 360, we get:

C = 70*360 = 25,200 cm

Therefore, the circumference of the circle is 25,200 cm. We can also verify this by dividing the length of the arc by the fraction of the circumference subtended by the angle's rays:

length of arc = (7/18)*C

C = (18/7)*length of arc

C = (18/7)*70

C = 180 cm (rounded to one decimal place)

This is a different value than we got earlier, so we need to check our calculations. It turns out that the previous calculation was incorrect - we made a mistake when multiplying 7/18 by 21.6. The correct calculation gives us:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Now, we can calculate the circumference of the circle:

length of arc = (7/18)C

C = (18/7) *length of arc

C = (18/7) *70

C = 180 cm (rounded to one decimal place)

Therefore, the circumference of the circle is 180 cm.

Also, If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle.

b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long.The length of the arc subtended by the angle's rays 8.4 cm

c. Another circle is centered at the vertex of the angle.

The arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

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Answer:3.79*10^14

Step-by-step explanation:

370000000000000+9000000000000=379000000000000

=3.79 x 10^14

Answer:

(3.79×10^14)

Step-by-step explanation:

sjskakakzks

Yes, every odd integer can be written as the difference of two squares.

To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.

To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.

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The answers are 24.50, 8.50, 23.50 respectively.

Given that we are to forecast for week 3, find the error for week 4, and make a final prediction for week 7. We are to use the moving average method with k = 2.The calculation of the moving average is shown belowWeek Time Series Moving average Error 1 30 _____ _____ 2 19 _____ 5.5 3 30 24.50 -6.50 4 16 24.50 8.50 5 21 23.00 -2.00 6 25 18.50 6.50 7 Prediction -> 23.50 -2.50The forecast for week 3 is 24.50, error for week 4 is 8.50 and final prediction for week 7 is 23.50. Thus, the answers are 24.50, 8.50, 23.50 respectively.

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Answer:

The following statements about Josiah's solution are true:

He found the proportion of rock songs to the total number of songs correctly: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction.

He solved the proportion correctly: StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction.

He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).

Therefore, the statements that are true are:

He found the proportion of rock songs to the total number of songs correctly.

He solved the proportion correctly.

He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).

As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].

A function is a mathematical formula that relates every element in one set, known as the domain, to a single element in another set, known as the range. The most prevalent way to represent a function is as f(x), where f(x) stands for the output or dependent variable and "x" stands for the input or independent variable. There is a value of f(x) in the range for each value of x in the domain. Consider the function f(x) = 2x + 1 as an illustration. This function's range and scope possibilities are both limited to the real numbers.

given

We must determine the slope of the secant line that goes through the interval's endpoints in order to determine the average rate of change of a function over the interval. Since the range in this instance is [0, 1/2], we must determine the slope of the secant line that connects (0, f(0)) and (1/2, f(1/2)).

Let's first assess the function at the interval's endpoints:

f(0) = 0² + 2(0) + 1 = 1

f(1/2) = (1/2)² + 2(1/2) + 1

= 5/4

Next, we can calculate the slope of the secant line using the slope formula:

slope is equal to (f(1/2)-f(0)) / (1/2 - 0)

= ((5/4)-1) / (1/2)

= (1/4) / (1/2)

= 1/2.

As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].

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First before two trains were [tex]990[/tex] kilometers apart, it will require [tex]5.5[/tex] hours.

Train speed is calculated as total distance traveled divided by travel time. The time it takes for two trains to pass each other is equal to (a+b) / (x+y) if the lengths of the trains, say a or b, are known and they are going at speeds of y and x, respectively.

Typically, a locomotive fueled by electricity or diesel powers trains. If there are several route networks, complicated signaling methods are used. One of the quickest forms of land transportation is rail.

[tex]distance = rate * time[/tex]

distance between trains [tex]= (85 km/h) * t + (95 km/h) * t[/tex]

distance between trains [tex]= (85 + 95) km/h * t[/tex]

distance between trains [tex]= 180 km/h * t[/tex]

Now, we can set up an equation to solve for the time it takes for the trains to be [tex]990[/tex] km apart:

[tex]180 km/h * t = 990 km[/tex]

[tex]t = 990 km / 180 km/h[/tex]

[tex]t = 5.5[/tex] hours

Therefore, it will take [tex]5.5[/tex] hours before the two trains are [tex]990[/tex] km apart.

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Answer:

A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42

Step-by-step explanation:

Using central limit theorem, the probability that the class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is 0.00017332

We can use the Central Limit Theorem (CLT) to approximate the distribution of the sample mean completion time for the class. According to CLT, the distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean is given as 48 minutes, the population standard deviation is given as 15 minutes, and the sample size is 20. Therefore, the mean of the sample mean completion time is also 48 minutes, and the standard deviation of the sample mean completion time is 15/√20 ≈ 3.3541 minutes.

To find the probability that the class mean completion time is greater than 60 minutes, we can standardize the distribution of the sample mean completion time using the z-score formula:

z = (x - μ) / (σ / √n)

where x is the value we want to find the probability for (in this case, x = 60), μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we get:

z = (60 - 48) / (15 / √20) = 3.5777

Using a standard normal distribution table (or calculator), we can find the probability that a z-score is greater than 3.5777.

P = 0.00017332

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Answer:

2p - 12

Step-by-step explanation:

(24p - 10) + (-22p - 2)

24p - 10 - 22p - 2

2p - 12

So, the answer is 2p - 12

The numbers are as follows, going from lowest to highest:

-4.2, -3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4.8.

We must compare and organize these numbers from least to greatest in order to put them in numerical order. The two smallest figures, which are -4.2 and -3.5, can be used as a starting point. Afterwards, we add the remaining numbers to the list in ascending order of least to largest after comparing them to these two. We arrive at the list above after continuing this approach.

Visualizing these numbers in order can alternatively be done by using a number line. In the number line, we can mark each number and arrange them in ascending order from left to right. We can see from the number line that the least number is -4.2.

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The types of inferences that will be made about population parameters are causation, estimation, and regression on the basis of relationship.

Causation is the process of showing the cause-and-effect relationship between two variables. In this case, one variable influences the other variable. This type of inference is significant when making decisions because it helps us understand how a change in one variable leads to a change in another variable.

Estimation: In statistical analysis, estimation refers to determining the possible value of an unknown population parameter. It is impossible to calculate the population parameters directly, and hence we use sample statistics to estimate them.

Regression analysis is the statistical technique used to identify the relationship between two variables. It involves estimating the coefficients of the model that best fit the data.

This type of inference helps us predict the value of a dependent variable based on an independent variable.

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Answer:

-1/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

To prepare a buffer solution with a given pH, we need to choose a weak acid and its conjugate base, such that the pKa of the weak acid is close to the desired pH.

The pKa is related to the Ka value as follows:

pKa = -log(Ka)

So, for each of the weak acids given, we can calculate the pKa:

Phosphoric acid (H3PO4): Ka = 7.5 x 10^-3, so pKa = -log(7.5 x 10^-3) = 2.12

Acetic acid (CH3COOH): Ka = 1.8 x 10^-5, so pKa = -log(1.8 x 10^-5) = 4.74

Formic acid (HCOOH): Ka = 1.8 x 10^-4, so pKa = -log(1.8 x 10^-4) = 3.74

Now, let's consider the desired pH values and choose the best components for buffer solutions:

For a pH of 2.5, the best choice would be phosphoric acid (pKa = 2.12).

For a pH of 4.5, the best choice would be formic acid (pKa = 3.74) or a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).

For a pH of 6.5, the best choice would be a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).

Note that a buffer solution can be prepared by mixing a weak acid and its conjugate base in roughly equal amounts, so the appropriate salt can be added to the acid to form the buffer solution. For example, to prepare an acetate buffer, one could mix acetic acid with sodium acetate.

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Answer:

Yes, No, No.

Explanation:

Answer:

Place an X for the first box as [Yes], [No], [No]

Step-by-step explanation:

When we enter x=2 and y=1 into the first system of equations, we can see that both conditions are met. Thus the answer to this system is (2, 1).

When x=2 and y=1 are substituted into the second system of equations, we obtain 1=-3 and 1=-2, which are false, and so (2, 1) is not a solution for this system.

When x=2 and y=1 are substituted into the third system of equations, the results are -3=-2 and 1=-3, which are false, hence (2, 1) is not a solution for this system.

Answer: 5 ≥ y-2 is equivalent to y ≤ 7.

Step-by-step explanation: To check if 5 is greater than or equal to y-2, we need to isolate the variable y on one side of the inequality sign.

5 ≥ y - 2

First, we can add 2 to both sides to get rid of the subtraction of 2 on the right side:

5 + 2 ≥ y - 2 + 2

7 ≥ y

Therefore, we can see that y is less than or equal to 7 for this inequality to hold true.

Answer:

5/37

Step-by-step explanation:

There are 37 possible outcomes when rolling a 37-sided die, so the probability of rolling any one specific number is 1/37.

To find the probability of rolling any of the given numbers (35, 25, 33, 9, or 19), we need to add the probabilities of rolling each individual number.

Probability of rolling 35: 1/37

Probability of rolling 25: 1/37

Probability of rolling 33: 1/37

Probability of rolling 9: 1/37

Probability of rolling 19: 1/37

The probability of rolling any one of these numbers is the sum of these probabilities:

1/37 + 1/37 + 1/37 + 1/37 + 1/37 = 5/37

So the probability of rolling any of the given numbers is 5/37, which is approximately 0.1351 when rounded to four decimal places.

The solutions to the equation are x = -4 and x = 1.

The quadratic formula, which is often employed in the disciplines of mathematics, physics, engineering, and other sciences, is a potent tool for resolving quadratic problems. We must first get the values of a, b, and c from the quadratic equation in order to apply the quadratic formula. To get the answers for x, we then enter these values as substitutes in the formula and simplify.

The given equation is 4x² + 6x - 13 = 3x².

Rearranging the equation we have:

x² + 6x - 13 = 0

The quadratic formula is given as:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a = 1, b = 6, and c = -13.

x = (-6 ± √(6² - 4(1)(-13))) / 2(1)

x = (-6 ± √(100)) / 2

x = (-6 ± 10) / 2

x = -8/2 or x = 2/2

x = -4 or x = 1

Hence, the solutions to the equation are x = -4 and x = 1

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This procedure is repeated for each interval until the overall frequency of 35 is reached.

A data summary called a frequency distribution displays the frequency, or amount of occurrences, of each value or range of values in a data set. It is frequently displayed as a table or graph, with the values enumerated along one axis and the frequencies of those values listed along the other. The pattern or shape of a data collection can be described using frequency distributions, which can also be used to spot outliers or other unusual values. They can also shed light on the data's central trend and variability.

given

To complete a cumulative frequency table:

Class interval Frequency Cumulative frequency

0-10               5                                   5

10-20       8                                  13

20-30       12                                 25

30-40        7                                 32

40-50         3                                35

Total        35                               35

The number of the first class interval is 5.

For the second interval, we multiply the total frequency of 5 plus the frequency of 8 to get 13.

This procedure is repeated for each interval until the overall frequency of 35 is reached.

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The missing value in the cumulative table is 36.

The missing value in the cumulative table can be determined by examining the frequencies given in the table. Let's analyze the frequencies step by step:

1. The frequency for scores less than 145 is given as 16.
2. The frequency for scores less than 150 is given as 26.
3. The frequency for scores less than 155 is given as 36.
4. The frequency for scores less than 160 is not explicitly given in the table, but we can determine it by subtracting the frequency for scores less than 155 (36) from the frequency for scores less than 150 (26).

This gives us a value of [tex]26 - 36 = -10.[/tex]

Since a frequency cannot be negative, we can conclude that there is an error in the given table. The cumulative frequency for scores less than 160 should be 36 instead of -10.

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The 12 months of age) as percentiles of the CDC growth chart reference population.

The most likely description of Sarah's weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population is: 85th percentile at 3 months; 85th percentile at 6 months; 90th percentile at 9 months; 95th percentile at 12 months.What is percentile in statistics?In statistics, a percentile is a value below which a specific percentage of observations in a group falls. It is used to split up data into segments that represent an equal proportion of the entire group, resulting in a data set split into 100 equal portions, with each portion representing one percentage point. Sarah's weight is in the 85th percentile at 3 months, 85th percentile at 6 months, 90th percentile at 9 months, and 95th percentile at 12 months is a most likely description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population.

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Given: ,8^2x= 32^x+3

a: (2³)^2x = (2⁵)^x+3

b: Solving, we get

2^6x = 2^5x+15

Since bases are same, we have

=>6x=5x+15

=> x = 15

Answer: 6.44 square meters

Step-by-step explanation:

The area of a rectangle is given by the formula: A = L x W, where L is the length and W is the width.

Substituting the given values, we get:

A = 2.8 x 2.3 = 6.44 square meters

Therefore, the area of Ana's garden is 6.44 square meters.

The number of bicycles they need to sell to make equal money is 5. The amount they would make is $500.

In contrast to variable costs, which change depending on the volume of production or sales, fixed costs are expenses that remain constant. Rent, insurance, and salary are examples of fixed costs that are constant regardless of the volume of output or sales. Materials, labour, and shipping expenses are examples of variable costs that change according to the volume of output or sales.

Let us suppose the number of bicycle sold = x.

Then the equation for Jimmy is:

$250 + 50x

The equation for Tom is:

$400 + 20x

To make the same amount we equate the two equations as follows:

250 + 50x = 400 + 20x

30x = 150

x = 5

Substituting the value of x in equation 1 we have:

J = 250 + 50(5)

J = 250 + 250

J = 500

Hence, the number of bicycles they need to sell to make equal money is 5. The amount they would make is $500.

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With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.

The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.

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Complete question:

With respect to the average cost curves, the marginal cost curve:

A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point

B) Intersects both average total cost and average variable cost at their minimum points

C) Intersects average total cost where it is increasing and average variable cost where it is decreasing

D) Intersects only average total cost at its minimum point

A circle is a shape formed by a point moving in a plane while keeping the same distance from a fixed point. The measurement of angle EDF is 23 degrees.

To start, a circle is a shape that is created by a point moving in a plane while its distance from a fixed point remains constant. This fixed point is called the center of the circle.

Since we know that angles created by the same chord in a circle are equal, we can use this information to find the measure of angle EDF.

In this case, EF is the chord of the circle, and we are given that angle EGF measures 23°. Therefore, we can conclude that angle EDF must also measure 23° since it is created by the same chord EF.

Thus, we can say that the size of angle EDF is 23°.

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Complete question is the image attached below

Answer:

1

Step-by-step explanation:

Given values are:

x1 y1=(2,4)

x2 y2=( 4,6)

slop=(6-4)divide (4-2)=1

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