Amari’s car uses 1 1/2 gallon of gas every 3/4 of a mile. How many gallons are used in 4 miles?

Answer:

A

Step-by-step explanation:

using the rule of radicals

\(\sqrt{ab}\) = \(\sqrt{a}\) × \(\sqrt{b}\)

note that 0.231 × 100 = 23.1

given

\(\sqrt{23.1}\)

= \(\sqrt{100(0.231)}\)

= \(\sqrt{100}\) × \(\sqrt{0.231}\)

= 10 × k

= 10k

The value of √23.1 using the value √0.231 = k is 10k.

Thus, option (A) is correct.

Let's first find the value of "k" when √0.231 = k:

√0.231 = k

Now, the value of √23.1 using the value of "k":

√23.1 = √(10 × 2.31)

As √2.31 = k, substitute it in:

√23.1 = √(10 × 2.31)

         = √10 × √2.31

         = 3.162 × √2.31

Also, √2.31 = 1.52

So, the required value

√23.1 = 3.162 × 1.52

          = 4.807

let's check the given options to find the closest value to 4.807:

A. 10k = 10 × √0.231 = 4.807.

B. 0.1k = 0.1 × √0.231  = 0.04806

C. 100k = 100 × √0.231 = 48.06  

D. 20k = 20 × √0.231 = 9.6124

Therefore, The value of √23.1 is 10k.

Thus, option (A) is correct.

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This can be done by finding the CPI or another price index for the same period. Once you have the GDP deflator, you can use the formula above to calculate the real GDP.

If you only know the nominal GDP, you cannot determine the real GDP. In order to determine the real GDP, you need to take into account inflation. This is done by adjusting the nominal GDP for inflation using a price index, such as the Consumer Price Index (CPI).The formula for calculating real GDP is:Real GDP = Nominal GDP / GDP DeflatorThe GDP deflator is a measure of inflation that takes into account changes in the prices of all goods and services produced in an economy. It is calculated by dividing nominal GDP by real GDP and multiplying by 100. This gives us a ratio of the current price level to the base year price level.

The base year price level is assigned a value of 100.Using this formula, we can see that if we know the nominal GDP and the GDP deflator, we can calculate the real GDP. For example, if the nominal GDP is $10 trillion and the GDP deflator is 120, the real GDP would be:Real GDP = $10 trillion / 1.2 = $8.33 trillionTherefore, in order to determine the real GDP if you only know the nominal GDP, you need to obtain the GDP deflator.

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The given table represents a discrete probability distribution.

To determine whether the table represents a discrete probability distribution, we need to check if it satisfies two conditions: the sum of probabilities equals 1 and all probabilities are non-negative.

In the given table, the sum of probabilities is 0.3 + 0.3 + 0.1 + 0.3 = 1, which satisfies the first condition.

Additionally, all probabilities in the table are non-negative, as each value of p(x) is greater than or equal to 0. This satisfies the second condition.

Therefore, since the table satisfies both conditions, it represents a discrete probability distribution. It provides the probabilities for each value of x, indicating the likelihood of each outcome occurring in a discrete random variable scenario.

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The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

The probability that a class of 50 has an average midterm mark that is less than 75 is value=0

Average is the mathematics mean, and is calculated by means of adding a group of numbers and then dividing with the aid of the count of these numbers. for instance, the average of 2, three, three, five, 7, and 10 is 30 divided with the aid of 6, that is five.

The common is described as the implied value that is identical to the ratio of the sum of the number of a given set of values to the whole wide variety of values gift within the set.

There are three primary sorts of common: imply, median, and mode. each of those techniques works slightly differently and frequency effects in barely specific regular values. The suggestion is the maximum normally used average. To get the suggested fee, you add up all of the values and divide this total by using the number of values.

The probability that a class of 50 has an average midterm mark that is less than 75

n = 50

P(<75)=P(Z<75)

P(Z<75−786√50)

P(Z<−3.5355)

We will look for the value in the StandardNormal able. We will get the value=0

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This can be derived using Chebyshev's inequality, as Chebyshev's inequality and the law of large numbers are different in nature.

Let M_n be the maximum of n independent U(0, 1) random variables.

To derive the exact expression for P(|M_n − 1| > ε), we need to follow the below steps:

First, we determine P(M_n ≤ 1-ε). The probability that all of the n variables are less than 1-ε is (1-ε)^n

So, P(M_n ≤ 1-ε) = (1-ε)^n

Similarly, we determine P(M_n ≥ 1+ε), which is equal to the probability that all the n variables are greater than 1+\epsilon

Hence, P(M_n ≥ 1+ε) = (1-ε)^n

Now we can write P(|M_n-1|>ε)=1-P(M_n≤1-ε)-P(M_n≥1+ε)

P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n.

Thus we have derived the exact expression for P(|M_n − 1| > ε) as P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n

Now, to show that $lim_{n\to\∞}$ P(|M_n - 1| > ε) = 0 , we can use Chebyshev's inequality which states that P(|X-\mu|>ε)≤{Var(X)/ε^2}

Chebyshev's inequality and the law of large numbers are different in nature as Chebyshev's inequality gives the upper bound for the probability of deviation of a random variable from its expected value. On the other hand, the law of large numbers provides information about how the sample mean approaches the population mean as the sample size increases.

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Answer:8

Step-by-step explanation:

The coordinates of R between points Q and R are (5/4, -2)

From the question, we have the following parameters that can be used in our computation:

Q(9, -5) and S(-10, 3)

We have the partition to be

m : n = 3 : 5

The coordinate is then calculated as

R = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

R = 1/8 * (3 * -10 + 5 * 8, 3 * 3 + 5 * -5)

Evaluate

R = (5/4, -2)

Hence, the coordinate is (5/4, -2)

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They need to deliver 15 packages to earn the same amount.

Let x be the number of packages they need to deliver to earn the same amount.

Then, Tim's total pay would be:

250 + 36x

Similarly, Rita's total pay would be:

370 + 28x

We can set these two expressions equal to each other to find the value of x:

250 + 36x = 370 + 28x

Subtracting 28x from both sides, we get:

250 + 8x = 370

Subtracting 250 from both sides, we get:

8x = 120

Dividing both sides by 8, we get:

x = 15

Therefore, they need to deliver 15 packages to earn the same amount.

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Given the LCM of x and 180 is 360, we can use the prime factorization method:

180 = \(2^{2}\) × \(3^{2}\) × 5

360 = \(2^{3}\) × \(3^{2}\) × 5

Then, we must ensure that the necessary powers are used to make the LCM equal 360. To do this,  \(2^{3}\), \(3^{2}\), and 5 must all be prime factors of x.

\(2^{3}\) × \(3^{2}\) × 5 ⇒ 8 × 9 × 5 ⇒ 360

Because 360 is the only value that meets this criteria, 360 is the smallest possible value of x.

Answer:

5

Step-by-step explanation:

trust me my dad has a maths degree and is a professor in physics

Answer:

Since angle 1 = angle 3 (vert opp angles),

angle 1 = angle 3 = 180°-129° (adj angles on a str line)

                            = 51°

angle 4 = angle 2 = 129° (vert opp angles)

Hence,

angle 1 = 51°

angle 3 = 51°

angle 4 = 129°

By incorporating this information into the similarity measure, we can produce more accurate and informative results in clustering and classification tasks.

To modify the definition of clustering similarity to take into account the position of shared neighbors in the two nearest neighbor lists, we can introduce a weighting factor that considers the rank of the shared neighbor in each list. This can be achieved by multiplying the regular SNN similarity value by a weight factor that is calculated as the reciprocal of the sum of the ranks of the shared neighbors in the two lists. For example, if two points have a shared neighbor that is ranked 2nd in one list and 3rd in the other list, the weight factor would be 1/(2+3) = 0.2. This weight factor would then be multiplied by the regular SNN similarity value to produce a modified SNN similarity score that gives higher similarity to points that share the same nearest neighbors ranked higher in the nearest neighbor lists. This modification is justified because it takes into account the fact that having shared neighbors that are ranked higher in the nearest neighbor lists is a stronger indicator of similarity than having shared neighbors that are ranked lower.

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To find the general solution for the given ordinary differential equation (ODE):

xdy - [y + xy^(2)(1 + ln(x))]dx = 0

We can rearrange the terms and separate the variables:

xdy = [y + xy^(2)(1 + ln(x))]dx

Dividing both sides by x and rearranging the terms:

dy/y + y(ln(x) + 1)dx = dx

Now, let's integrate both sides:

∫(dy/y) + ∫[y(ln(x) + 1)]dx = ∫dx

Integrating the left-hand side with respect to y and the right-hand side with respect to x:

ln|y| + y(ln(x) + 1) = x + C

where C is the constant of integration.

We can simplify the equation further:

ln|y| + yln(x) + y = x + C

Combining the logarithmic terms:

ln|y| + yln(x) = x + C - y

To eliminate the logarithm, we can take the exponential of both sides:

e^(ln|y| + yln(x)) = e^(x + C - y)

Using the properties of exponents:

|y| * x^y = e^(x + C - y)

We can rewrite the absolute value expression as a piecewise function:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

So, the general solution to the given ODE is the combination of these two equations:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

These equations represent the family of solutions to the given ordinary differential equation (ODE).

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A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5\()^2\)

n=(15.996\()^2\)

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Answer:

The answer is given below

Step-by-step explanation:

The equation of a quadratic function is given by:

ax² + bx + c where a, b and c are the coefficients of the quadratic equation. The value of a determines whether the graph opens up or down (if a is positive opens up and if a is negative opes down), the value of c determines the y intercept (if c is positive, we have a positive intercept and if c is negative the intercept is negative).

The chosen equation is -x² -4x + 5. Since it has y-intercept of 5 and opens down (coefficient of x² is -1)

Let us assume a vertical stretch of 4, the new equation becomes:

4(-x² -4x + 5)

-4x² - 16x + 20

-4x² - 16x + 20 = 0

a = -4, b = -16 and c = 20

Using the quadratic formula:

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}\\ x=\frac{-(-16) \pm \sqrt{(-16)^2-4(-4)(20)} }{2(-4)}=\frac{16 \pm 24}{-8} \\x= -5 \ or \ x=1\)

Coefficient values weight varies by 25%, which is explained by the link with height.

Coefficient values have always been around -1 and 1, with -1 reflecting perfect negative linear correlation and 1 indicating perfect positive linear correlation.

The correlation coefficient in a correlation study reflects the strength of the linear relationship between two variables.

r represents the correlation coefficient.

Given this, the adult height-weight correlation is -0.50.

r = -0.50

The weight variance is, r² = (-0.50)² = 0.25

As a result, the weight variation is 25%, which is explained by the height relationship.

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Answer:

c. 2n-6

Step-by-step explanation:

6 less than 2xSteve so 2n-6

The number of different possible passwords possible is 6760000

The number of ways the passwords are possible is 10^4 * 26^2

10^4 * 26^2= 10000 * 676

10^4 * 26^2 = 6760000

Hence the number of different possible passwords possible is 6760000

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Answer:

its D

Step-by-step explanation:

11, 12, 13

Step-by-step explanation:

gb ndndhdyydhsbdgr

On March 15, 44 BCE, during the "ides of March," some 40 Roman senators assassinated Julius Caesar.

On the "ides of March," roughly 40 Roman senators killed Julius Caesar (March 15) in 44 B.C.E.

After Caesar's death, a protracted series of civil wars broke out, leading to the Roman Republic's demise and the establishment of the Roman Empire.

Julius Caesar was stabbed to death in Rome, Italy, on March 15, 44 BCE.

The Third Expansionary Period In its third period of growth, which lasted from 145 to 44 B.C.E., Rome grew to dominate the whole Mediterranean region.

Rome seized control of Egypt, Syria, and Asia Minor in the east. Julius Caesar, a general, took control of much of Gaul in the west (modern-day France).

Therefore, on March 15, 44 BCE, during the "ides of March," some 40 Roman senators assassinated Julius Caesar.

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The limit of the given expression exists and is equal to 1 + [1 + √(5)]/2.

To solve this problem, we can't simply substitute 1 into the expression because that would result in an undefined expression (division by zero). Instead, we have to use the concept of limits.

First, we can simplify the expression by factoring the numerator using the quadratic formula: (x² - x - 1) = (x - [1 + √(5)]/2)(x - [1 - √(5)]/2). Then, we can cancel out the (x-1) factor in both the numerator and denominator.

After simplification, we get the expression (x + [1 + √(5)]/2), which is a continuous function. Since the function is continuous at x = 1, we can substitute x = 1 into the expression to find the limit.

Therefore, the limit as x approaches 1 of (x² - x - 1)/(x - 1) exists and is equal to 1 + [1 + √(5)]/2.

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The level of measurement that is most appropriate for position of persons in a line is given as follows:

D.) Ordinal.

There are four levels of measurement for the data, given as follows:

The measures of central tendency for each level are given as follows:

For the position of the people in the line, we use the median, which is the midpoint of the line, hence the level of measurement is ordinal.

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The Wilcoxon signed-rank test is employed to see if there is a substantial difference between two related samples. Here the new cognitive therapy group and placebo group are related samples as they both belong to the same sample of cognitive therapy's study. The Wilcoxon signed-rank test is performed on the rank-based data as the data is not normally distributed. Following is the calculation for Wilcoxon’s signed rank test:The null hypothesis for the Wilcoxon signed-rank test is that there is no difference between the new cognitive therapy and placebo treatments. While the alternative hypothesis is that there is a difference between the two treatments.

The Wilcoxon signed-rank test is performed as follows:
Rank all the data, with the lowest value being ranked 1 and the highest value being ranked 12.
Calculate the difference between the new cognitive therapy and placebo group scores.
Take the absolute values of the differences.
Rank the differences in ascending order and ignore the signs.
Calculate the sum of the ranks of the new cognitive therapy group.
Calculate the test statistic T.
For this dataset, the calculations of the Wilcoxon signed-rank test are as follows:
Data Ranked (New therapy) Difference Absolute Difference Ranked Differences + Rank Therapy Differences - Rank Placebo 5 1 4 3 4 4 6 2 4 4 2 2 4 4 8 7 1 1 1 12 10 2 2 3 5 1 6 13 12 1 8 7 7 4 4 1 5 5 5 1 14 13 1 2 1 15 7 8 7 7 5 9 10 3 5 8 56 12 44 12 12 11 7 Total 49
Calculating T:

\($$T =\) \(\frac{Total\ of\ positive\ ranks - \frac{n(n+1)}{4}}{\sqrt{\frac{n(n+1)(2n+1)}{24}}}$$\)

Here, n is the number of pairs, which is 12.
T = 3.52
Using the Wilcoxon signed-rank test table, the critical value at the 0.05 level for n = 12 is 18.
Since T (3.52) is less than the critical value (18), the null hypothesis cannot be rejected.
There is no evidence to suggest that there is a difference between the new cognitive therapy and placebo treatments.

The coterminal angle of 5π/3

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

Examples of coterminal angles are 30°, -330, 390°. We can get the coterminal angles of a given angle by adding or subtracting 360 from the given angle.

5π/3

π is a symbol in radian that is equivalent to 180° in degrees.

therefore;

5 × 180/3

= 5× 60

= 300°

The coterminal angle of 300°

= 300+360

= 660°

converting it back to radian

= 660/180 = 66/18π

= 33/9 = 11/3π

Therefore the coterminal angle of 5π/3 is 11π/3

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Answer: 2.5

Step-by-step explanation: subtract 2x from both sides and get 4x-2=8 so then add 2 on both sides to get 4x=10 and last step is to divide both sides by 4 which wild get you x=2.5

Answer:

for every three pens there is five pencils

Answer:

The ratio of pencils to pens is 5 to 3

For every 3 pens, there are 5 pencils.

The ratio of pencils to pens is 5 : 3

.Step-by-step explanation:

Answer:

|1|

Step-by-step explanation:

Because absolute value measures the positive distance from the numeral to 1, the answer could be negative or positive one, which is what the graph shows. So, |1| is the answer.

The sum of angles in a shape is the addition of all angles in the shape. The value of b is 90.

From the attached pentagon, we have:

\(Sum = 540^o\) -- sum of angles.

This means that:

\(Sum = b + \frac 32b + 2b - 90 + 90 + b + 45\)

Collect like terms

\(Sum = b + \frac 32b + 2b + b- 90 + 90 + 45\)

Evaluate like terms

\(Sum = \frac{11}2b +45\)

Substitute 540 for sum

\(\frac{11}2b +45 = 540\)

Collect like terms

\(\frac{11}2b =-45 + 540\)

\(\frac{11}2b =495\)

Isolate b

\(b =495 \times \frac 2{11}\)

\(b =\frac {990}{11}\)

\(b =90^o\)

Hence, the value of b is 90.

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