Chris rented truck for one day. There was a base fee of $16.99, and there was an additional charge of 93 cents for each mile
driven. Chris had to pay $227.17 when he returned the truck. For how many miles did he drive the truck?

Answer:

Step-by-step explanation:

-17 + 2x = x - 1

2x = 16

x = 8

The probability that the slip of paper bears a number with a single "2" in it or both of the digits are a "2" is 5/33.

The total number of slips in the bowl is 33. The slips numbered from 1 to 33 inclusive are placed in the bowl. Out of these 33 slips, 5 slips bear a number with a single "2" in it or both of the digits are a "2".There are four slips with a single "2" in it, numbered as 2, 12, 20 and 21. There is only one slip with both digits as "2" numbered as 22.Therefore, the probability that the slip of paper bears a number with a single "2" in it or both of the digits are a "2" is 5/33. This is because we have 5 slips out of 33 slips which bear a number with a single "2" in it or both of the digits are a "2".

Given that the total number of slips in the bowl is 33. The slips numbered from 1 to 33 inclusive are placed in the bowl.We have to find the probability that the slip of paper bears a number with a single "2" in it or both of the digits are a "2".Let A be the event that a slip of paper bears a number with a single "2" in it or both of the digits are a "2".We can write,Total number of slips in the bowl = 33Number of slips that bear a number with a single "2" in it = 4Number of slips that bear both digits as "2" = 1Total number of slips that bear a number with a single "2" in it or both of the digits are a "2" = 4 + 1 = 5The required probability is given by:P(A) = Number of slips that bear a number with a single "2" in it or both of the digits are a "2" / Total number of slips in the bowlP(A) = 5/33

Therefore, the probability that the slip of paper bears a number with a single "2" in it or both of the digits are a "2" is 5/33.

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Answer:

Ok

Step-by-step explanation:

Answer:

Iam not sure but i think its -14.45$

Step-by-step explanation:

45.55-20-20-20

After withdraw the amount he have - $14.45 in his account.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

The balance in Jake's checking account is $45.55.

Here, he wrote three checks for $20.00 each.

Hence, Total amount to withdraw is,

⇒ $20.00 x 3

⇒ $60.00

Hence, Left money in his account = $45.55 - $60.00

                                                     = - $14.45

Thus, After withdraw the amount he have - $14.45 in his account.

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Answer:

a = 4/5 OR 5a - 4

Step-by-step explanation:

If you set it equivalent to 0:

7a - 8 - 2a + 4 = 0

5a - 4 = 0

5a = 4

a = 4/5

If you are only simplifying:

7a - 8 - 2a + 4

5a - 4

Answer:

Let's use variables to represent the unknowns:

Let x be the number of psychology textbooks sold.

Then, the number of history textbooks sold is 2x (twice the number of psychology textbooks sold).

The problem tells us that the total number of textbooks sold is 237, so we can set up an equation:

x + 2x = 237

Simplifying and solving for x:

3x = 237

x = 79

Therefore, 79 psychology textbooks were sold and 2x = 158 history textbooks were sold.

Step-by-step explanation:

The probability that more than 38% of the people in the sample of 65 adults have high blood pressure is approximately 0.0453, or 4.53%.

To calculate the probability, we can use the normal approximation to the binomial distribution. Given that the sample size is 65, we can assume that the number of adults with high blood pressure in the sample follows a binomial distribution with parameters n = 65 (sample size) and p = 0.38 (probability of an adult having high blood pressure).

First, we need to find the mean (μ) and standard deviation (σ) of this binomial distribution:

μ = n * p = 65 * 0.38 = 24.7

σ = sqrt(n * p * (1 - p)) = sqrt(65 * 0.38 * (1 - 0.38)) = 4.71

Next, we need to find the z-score for the desired probability. To find the z-score, we subtract the mean from the desired value and divide by the standard deviation:

z = (x - μ) / σ = (x - 24.7) / 4.71

Since we are interested in finding the probability of more than 38% (0.38) of the people having high blood pressure, we want to find the probability of x > 0.38 * 65 = 24.7. Therefore, the z-score becomes:

z = (24.7 - 24.7) / 4.71 = 0

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of 0 is 0.5. However, since we are interested in the probability of more than 38%, we need to find the area under the curve beyond the z-score of 0.5, which is 1 - 0.5 = 0.5.

The probability that more than 38% of the people in the sample of 65 adults have high blood pressure is approximately 0.0453 or 4.53%. This implies that there is a relatively low chance of observing such a high proportion of individuals with high blood pressure in the given sample.

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The variable of interest in observational studies is not controlled. Option D is correct.

Observational studies are a type of study in which the researcher observes and records data without interfering with or manipulating the variables of interest. In observational studies, the researcher does not intervene or control the variables being studied, but instead, collects data by observing the natural behavior or characteristics of the study subjects.

Observational studies are useful in many fields, including medicine, psychology, sociology, and economics. They are often used to explore potential relationships between variables, to identify risk factors for diseases, to investigate the effectiveness of interventions, and to study social phenomena.

Observational studies have advantages and disadvantages. One advantage is that they can provide valuable information about real-world behavior and characteristics of individuals or groups. Therefore, it is important to carefully design and analyze observational studies to ensure that the results are accurate and reliable.

Hence, D.is not controlled is the correct option.

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Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

Factorise both sides of

ax+bx=a2−b2  

and get

(a+b)x=(a+b)(a−b).  

If  

a+b≠0,  

because division by 0 is not allowed, then divide by a + b and get

(a+b)xa+b=(a+b)(a−b)a+b.  

It reduces to

x=a−b.  

If a+b=0, then  

ax+bx=a2−b2 is  

(a+b)x=(a+b)(a−b)  

and this simplifies to

0x=0(a−b),  

that is,

0=0,  

so that the value of x is indeterminate.

Answer:

1166.4

Step-by-step explanation:

Assuming this is the whole question, you multiply the weight of a single box by the amount in a case to find the weight of a case, hence 24.3*48 =1166.4

1 box of cereal = 24.3

48 boxes of cereal = 24.3 × 48

48 boxes of cereal:-

=> 24.3 × 48

=> 1166.4

Therefore, 48 boxes of cereal weighs 1166.4

Answer:The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

Step-by-step explanation:

Answer: Y= -2/-18 or Y= 0.1111X=-2(-0.1111) +1or X=0.77778

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The answer is A because the point intercepts at (2,7), and answer A has the points (2,7) in it's answer.

Answer:

$71.00 - $20 = $51

51 divided by 6 = 8.5!

Step-by-step explanation:

Answer:

1. 8

2. 12

3. 9

I hope that helped! :)

The simplified equation using De Morgan's theorem is (x1 x3').

1. De Morgan's theorem states that the complement of a product of two or more variables is equal to the sum of the complements of those variables. In other words, if we have variables A and B, the complement of (A AND B) is equal to (A' OR B').

2. Let's simplify the given equation step by step. We'll start by applying De Morgan's theorem to the inner part of the equation, (x2 x3):

  - The complement of (x2 x3) is equal to (x2' + x3').
 
3. Now, let's substitute this result back into the original equation:

  - ( x1 ( x2 x3) ) (x1 x2 ) becomes (x1 (x2' + x3')) (x1 x2 )
 
4. Next, we can distribute the outer x1 over the inner expression (x2' + x3'):

  - Distributing x1, we get (x1 x2' + x1 x3') (x1 x2 )
 
5. Finally, we can distribute x1 x2 over (x1 x2' + x1 x3'):

  - Distributing x1 x2, we get (x1 x2 x1 x2') + (x1 x2 x1 x3')
 
  - Simplifying further, we have (x1 x2'') + (x1 x3')
 
  - Since any variable ANDed with its complement is always equal to 0, we have (x1 0) + (x1 x3')
 
  - And (x1 0) is equal to 0, so the simplified equation is just (x1 x3').
 
Therefore, the simplified equation using De Morgan's theorem is (x1 x3').

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the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

Mathis's rate of return on his investment of $1,000 in a mutual fund that sold for $1,250, including taxes, inflation, and administrative costs of $8 was 24.2%.

The rate of return represents the percentage of the net gain an investment generates.

The rate of return is determined using the quotient of the division operation between the return and the initial investment.

The return or net return is the difference between the final value and the initial value after taking into account taxes, inflation, and other administrative costs.

The initial investment = $1,000

The final sales value = $1,250

Taxes, inflation, and other costs = $8

Net sales proceeds = $1,242 ($1,250 - $8)

Returns = $242 ($1,242 - $1,000)

Rate of return = 24.2% ($242 ÷ $1,000 x 100)

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Answer:

There are four inequality notations. They are. > means greater than. ≥ means greater than or equal to. < means less than.

Step-by-step explanation:

To know about the relationship between a low alpha level (a) and the power of a statistical test. If you choose a very low alpha level, close to zero, then the correct option is:

b. the test will have very low power.

When you set a very low alpha level, it means that you are being very strict about rejecting the null hypothesis, so you will need very strong evidence to do so. As a result, the chances of committing a Type II error (failing to reject a false null hypothesis) increases, which in turn decreases the power of the test. The power of a test is the probability of correctly rejecting the null hypothesis when it is indeed false.

To explain further, power is influenced by several factors, including sample size, effect size, and alpha level. A low alpha level means that the critical region is smaller, and the probability of rejecting a true null hypothesis is reduced. This, in turn, leads to a higher probability of failing to reject a false null hypothesis, resulting in low power. In contrast, a higher alpha level will increase the power of the test, but it also increases the likelihood of committing a Type I error (rejecting a true null hypothesis). Therefore, choosing the appropriate alpha level for a test is crucial to achieving the desired balance between type I and type II error rates and maximizing the power of the test.

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To know about the relationship between a low alpha level (a) and the power of a statistical test. If you choose a very low alpha level, close to zero, then the correct option is:

b. the test will have very low power.

When you set a very low alpha level, it means that you are being very strict about rejecting the null hypothesis, so you will need very strong evidence to do so. As a result, the chances of committing a Type II error (failing to reject a false null hypothesis) increases, which in turn decreases the power of the test. The power of a test is the probability of correctly rejecting the null hypothesis when it is indeed false.

To explain further, power is influenced by several factors, including sample size, effect size, and alpha level. A low alpha level means that the critical region is smaller, and the probability of rejecting a true null hypothesis is reduced. This, in turn, leads to a higher probability of failing to reject a false null hypothesis, resulting in low power. In contrast, a higher alpha level will increase the power of the test, but it also increases the likelihood of committing a Type I error (rejecting a true null hypothesis). Therefore, choosing the appropriate alpha level for a test is crucial to achieving the desired balance between type I and type II error rates and maximizing the power of the test.

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One test that used criterion groups as a developmental strategy is the Graduate Record Examinations (GRE). The GRE is a standardized test commonly used for admission into graduate programs in various fields. During the development of the GRE, a criterion group strategy was employed.

The criterion group strategy involves selecting a group of individuals who are already deemed successful or proficient in the field being assessed. In the case of the GRE, the criterion group consisted of graduate students who were performing well academically. The test developers administered the test to this group of high-achieving individuals and analyzed their performance to establish a benchmark or criterion for success.

By examining the performance of the criterion group, the test developers were able to identify the types of questions and content areas that distinguished successful students from those who were less successful. This information was then used to design the test items and determine the scoring criteria for the GRE. The test was tailored to assess the knowledge and skills that were identified as important indicators of success in graduate-level study.

Now let's consider an example of a test that used factor analysis and/or theory as a developmental strategy. The Minnesota Multiphasic Personality Inventory (MMPI) is a psychological assessment tool that used factor analysis and theory during its development.

The MMPI is a widely used personality test that assesses various aspects of an individual's personality, psychopathology, and clinical disorders. It was developed by Starke R. Hathaway and J.C. McKinley in the late 1930s. In the development process, they employed a combination of factor analysis and theoretical considerations.

Factor analysis is a statistical technique used to identify underlying dimensions or factors that explain the relationships among a set of observed variables. In the case of the MMPI, factor analysis was utilized to identify the main dimensions or factors of personality and psychopathology that the test should measure. Through extensive data analysis and item selection, the test developers identified several key factors, such as depression, hypochondriasis, hysteria, and social introversion.

Additionally, the developers of the MMPI incorporated theoretical considerations in the selection and construction of the test items. They drew upon existing theories and knowledge in the field of personality and psychopathology to guide their item selection process. The test items were designed to capture the manifestations of specific personality traits and clinical symptoms that were theoretically relevant.

The combination of factor analysis and theoretical considerations allowed the developers of the MMPI to create a comprehensive and reliable instrument for assessing personality and psychopathology. The test has undergone several revisions and updates over the years, but its foundation in factor analysis and theory has remained integral to its development and continued use in psychological assessment.

In summary, the GRE utilized the criterion group strategy during its development, where the performance of successful graduate students served as a benchmark for test design. On the other hand, the MMPI employed factor analysis and theoretical considerations to identify key dimensions of personality and psychopathology, resulting in a comprehensive assessment tool. Both tests demonstrate the application of different developmental strategies to ensure the validity and reliability of the assessments.

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Answer:

y = 4/6x - 4

Step-by-step explanation:

y = mx + b, m = slope and b = y intercept

Rise over run

Rise = +4

Run = +6

This means the slope is 4/6.

The y intercept is at -4.

Now, plug in the numbers for y = mx + b

y = 4/6x - 4

According to the solution we have come to find that, The interquartile range (IQR):

(3) 18.33

(4) 38.5

(5) 58.5

Interquartile range (IQR) is a measure of variability or spread of a dataset. It is the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. It shows the range of the middle 50% of the data. IQR is often used as a measure of spread because it is less sensitive to outliers than the range.

First, we need to find the median of the dataset. Since there are an even number of values, we take the average of the two middle values:

Median = (30 + 36) / 2 = 33

Next, we find the median of the lower half of the dataset (values less than or equal to the median):

Q1 = 1 + 28 + 30 / 3 = 19.67

And the median of the upper half of the dataset (values greater than or equal to the median):

Q3 = 38 + 40 + 36 / 3 = 38

Finally, we calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 38 - 19.67 = 18.33

There are no outliers in this dataset.

First, we need to find the median of the dataset. Since there are an even number of values, we take the average of the two middle values:

Median = (50 + 52) / 2 = 51

Next, we find the median of the lower half of the dataset (values less than or equal to the median):

Q1 = 45 + 48 / 2 = 46.5

And the median of the upper half of the dataset (values greater than or equal to the median):

Q3 = 60 + 110 / 2 = 85

Finally, we calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 85 - 46.5 = 38.5

There are no outliers in this dataset.

First, we need to find the median of the dataset. Since there are an even number of values, we take the average of the two middle values:

Median = (60 + 60) / 2 = 60

Next, we find the median of the lower half of the dataset (values less than or equal to the median):

Q1 = 17 + 68 / 2 = 42.5

And the median of the upper half of the dataset (values greater than or equal to the median):

Q3 = 72 + 130 / 2 = 101

Finally, we calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 101 - 42.5 = 58.5

There is one outlier in this dataset, the value 130.

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At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

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The largest possible rank of a 12x9 matrix is 9.
The largest possible rank of a 9x12 matrix is also 9.

The rank of a matrix refers to the maximum number of linearly independent rows or columns in that matrix.
For a 12x9 matrix, the largest possible rank of A is equal to the number of non-pivot columns in A. Since there are more rows (12) than columns (9), the rank of a 12x9 matrix can be at most 9, because there are 9 columns and each column can be a pivot column. Therefore, the largest possible rank of a 12x9 matrix is 9.
On the other hand, for a 9x12 matrix, the largest possible rank of A is equal to the number of pivot positions in A. Since there are only 9 rows in a 9x12 matrix, and each row can be a pivot row, the rank of a 9x12 matrix can be at most 9. Therefore, the largest possible rank of a 9x12 matrix is 9.

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Answer:

15 m, 20 m, 25 m forms a right triangle.

plz mark me as brainliest.

The time it will take to cover another distance of 145 miles is; 2.5 hours

We are given;

First distance driven = 348 miles

Time taken for first distance = 6 hours

Formula for speed is;

Speed = Distance/Time taken

Thus;

Speed for fist distance = 348/6

Speed = 58 mph

Now, at the same speed she wants to cover another distance 0f 145 miles. Thus;

Time taken = distance/speed

Time taken = 145/58

Time taken = 2.5 hours

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Answer:

P(greater than 4 or factor of 5) = 1/3

Step-by-step explanation:

→ let A be the set {the numbers greater than 4}

then A : {5 , 6}

p(A) = 2/6

→ let B be the set {the factors of 5}

then B : {1 , 5}

p(B) = 2/6

P(greater than 4 or factor of 5) = p(A∪B)

Formula =================

p(A∪B) = p(A) + p(B) - p(A∩B)

………………………………………………

A∩B : {5}

then

cardA∩B = 1

Then

p(A∩B) = 1/6

Finally :

p(A∪B) = p(A) + p(B) - p(A∩B)

            = 2/6 + 2/6 - 1/6

            = 3/6

            = 1/3

The volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\) To find the volume when the area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we can use the method of cylindrical shells.

First, let's find the points of intersection between the two curves by setting them equal to each other:

\(\[x^2 = \frac{3}{x^3}\]\)

To simplify this equation, we can multiply both sides by \(\(x^3\)\):

\(\[x^5 = 3\]\)

Now, taking the fifth root of both sides:

\(\[x = \sqrt[5]{3}\]\)

So the two curves intersect at \(\(x = \sqrt[5]{3}\)\).

To calculate the volume area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we need to integrate the circumference of each cylindrical shell multiplied by its height. The height of each shell is the difference in the y-values of the two curves, and the circumference is\(\(2\pi x\)\).

Let's integrate from \(\(x = 0\)\) to \(\(x = \sqrt[5]{3}\)\):

\(\[V = \int_0^{\sqrt[5]{3}} 2\pi x \left(\frac{3}{x^3} - x^2\right) \, dx\]\)

Simplifying this expression:

\(\[V = 2\pi \int_0^{\sqrt[5]{3}} \left(\frac{3}{x} - x^3\right) \, dx\]\)

Integrating each term separately:

\(\[V = 2\pi \left[3 \ln|x| - \frac{x^4}{4}\right]_0^{\sqrt[5]{3}}\]\)

Plugging in the limits of integration:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right] - 2\pi \left[3 \ln|0| - \frac{0^4}{4}\right]\]\)

Since \(\(\ln|0|\)\)is undefined, the second term on the right side is zero:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right]\]\)

Simplifying further:

\(\[V = 2\pi \left[3 \ln 3^{\frac{1}{5}} - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

Using the properties of logarithms, we can simplify the first term:

\(\[V = 2\pi \left[3 \cdot \frac{1}{5} \ln 3 - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

\(\[V = \frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\]\)

So the volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\)

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