The diameter of a circular cookie cake is 16 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14.

100.48 square inches
200.96 square inches
401.92 square inches
803.84 square inches

The estimated product of 153 and 246 is 37500.

In order to estimate the product of 153 and 246, both numbers need to be rounded off to the nearest 10 as follows:

Next, the rounded numbers can be multiplied as follows:

150 x 250 = 37500

In other words, an estimate of the product of 153 and 246 is 37500.

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There are 12 possible outcomes when choosing a card at random from the bag.

When dealing with probability problems, it is important to understand the concept of possible outcomes. Possible outcomes are the number of different outcomes that can occur when an experiment is performed. In this case, the experiment is choosing a card at random from a bag that contains 12 cards.

Each card in the bag is uniquely numbered, and there are four cards of each color (red, white, and black), so there are 3 groups of four cards each. When we choose a card at random from the bag, there are 12 possible cards we could choose, each with a unique number and color.

The number of possible outcomes is the total number of cards in the bag, which is:

4 red cards + 4 white cards + 4 black cards = 12 cards

Therefore, there are 12 possible outcomes when choosing a card at random from the bag.

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The complete question is given below.

A bag contains four red cards numbered 1 through 4, four white cards numbered 1through 4, and four black cards numbered 1 through 4. You choose a card at random. What is the number of possible outcomes

To find the equation of the tangent line to the curve y = 5ex cos(x) at the point (0, 5), we need to find the slope of the tangent line at that point.

First, we find the derivative of y with respect to x:

dy/dx = 5ex (-sin(x)) + 5ex cos(x)

Next, we evaluate the derivative at x = 0:

dy/dx |x=0 = 5e0 (-sin(0)) + 5e0 cos(0) = 5

So the slope of the tangent line at (0, 5) is 5.

Now we use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is the given point.

Plugging in the values we have:

y - 5 = 5(x - 0)

Simplifying, we get:

y = 5x + 5

So the equation of the tangent line to the curve y = 5ex cos(x) at the point (0, 5) is y = 5x + 5.

Step 1: Find the derivative of the function y.
Given function y = 5e^x cos(x), we will differentiate it with respect to x using the product rule.

Product rule: (uv)' = u'v + uv'
Let u = 5e^x and v = cos(x).

Step 2: Find u' and v'.
u' = d(5e^x)/dx = 5e^x
v' = d(cos(x))/dx = -sin(x)

Step 3: Apply the product rule.
y' = u'v + uv'
y' = (5e^x)(cos(x)) + (5e^x)(-sin(x))
y' = 5e^x(cos(x) - sin(x))

Step 4: Find the slope of the tangent line at the given point (0, 5).
Substitute x = 0 in the derived equation.
y'(0) = 5e^0(cos(0) - sin(0)) = 5(1)(1 - 0) = 5

Step 5: Use the point-slope form to find the equation of the tangent line.
Point-slope form: y - y1 = m(x - x1)
Given point: (0, 5) => x1 = 0 and y1 = 5
Slope (m) = 5

Step 6: Plug the values into the point-slope form.
y - 5 = 5(x - 0)
y - 5 = 5x

Step 7: Rewrite the equation in slope-intercept form (y = mx + b).
y = 5x + 5

The equation of the tangent line to the curve y = 5e^x cos(x) at the point (0, 5) is y = 5x + 5.

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A diagram and graph that shows this transformation include the following: D. On a coordinate plane, heart 1 is shifted down 3 units to form heart 2.

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.

By critically observing the geometric figures, we can reasonably infer and logically deduce that a vertical translation of heart 1 down by 3 units in order to produce heart 2 is a graph that correctly shows this transformation.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The interval of miles in which approximately 95% of tires are expected to last within is from 37,000 to 53,000 miles.

To answer your question, we'll use the given information about the bell-shaped and symmetrical distribution with a mean and standard deviation.

Mean (μ) = 45,000 miles
Standard Deviation (σ) = 4,000 miles

For a bell-shaped and symmetrical distribution, approximately 95% of the data falls within 2 standard deviations of the mean. We can use this to find the interval:

According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean. In this case, two standard deviations below the mean is 45,000 - (2*4,000) = 37,000 and two standard deviations above the mean is 45,000 + (2*4,000) = 53,000.
Lower Bound: μ - 2σ = 45,000 - 2(4,000) = 45,000 - 8,000 = 37,000 miles
Upper Bound: μ + 2σ = 45,000 + 2(4,000) = 45,000 + 8,000 = 53,000 miles

So, approximately 95% of tires would be expected to last within the interval of 37,000 to 53,000 miles. The correct answer is D. 37,000 to 53,000.

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The sample space for rolling a fair seven-sided die is S = {1, 2, 3, 4, 5, 6, 7}.

Given that,

A fair seven sided die is rolled.

We have to find the sample space of the rolling.

A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.

The subset of the sample space are events.

The die has the numbers marked from 1 to 7.

So when we roll the die,

The possible numbers are 1, 2, 3, 4, 5, 6, 7

Sample space = {1, 2, 3, 4, 5, 6, 7}

Hence the sample space is {1, 2, 3, 4, 5, 6, 7}.

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a) The probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.

b) The probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.

(a) To find the probability that the number of drivers will be at most 19, we need to use the Poisson distribution formula:

P(X ≤ 19) = e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!) + ... + e^(-20) * (20^19/19!)

Using a calculator or statistical software, we get P(X ≤ 19) ≈ 0.088.

(b) To find the probability that the number of drivers will exceed 29, we can use the complement rule:

P(X > 29) = 1 - P(X ≤ 29)

Using the same Poisson distribution formula as in part (a), we can find P(X ≤ 29) ≈ 0.963. So,

P(X > 29) = 1 - 0.963 = 0.037 (rounded to three decimal places).

Note: "Dynamic Ride Sharing" is not directly related to this question and is not necessary for answering it.
Hi! I'd be happy to help you with your question.

(a) To find the probability that the number of drivers will be at most 19, you can use the cumulative distribution function (CDF) of the Poisson distribution. The parameter for this distribution is μ = 20. The formula for the Poisson CDF is:

P(X ≤ k) = Σ (e^(-μ) * (μ^x) / x!) for x = 0 to k

In this case, k = 19. Plugging in the values and calculating the sum, we get:

P(X ≤ 19) ≈ 0.411

Therefore, the probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.

(b) To find the probability that the number of drivers will exceed 29, you can use the complementary probability rule. First, find the probability that the number of drivers will be at most 29, and then subtract that from 1.

P(X > 29) = 1 - P(X ≤ 29)

Using the Poisson CDF formula with k = 29 and μ = 20:

P(X ≤ 29) ≈ 0.996

Now, subtract this value from 1:

P(X > 29) = 1 - 0.996 ≈ 0.004

Therefore, the probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.

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Given that a student is a graduate student, the likelihood that they are a science major is roughly 0.72.

To calculate the probability of a student being a science major given they are a graduate student using the formula:

P(graduate) = (Number of graduate students) / (Total number of students) = 261 / 1073

P(science and graduate) = 188 / 1073

P(science graduate) = (P(science and graduate)) / P(graduate) = (188 / 1073) / (261 / 1073) = 188 / 261 ≈ 0.72

Therefore, the probability a student is a science major, given they are a graduate student is approximately 0.72.

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There will be $530.68 in the account at the end of 2 years, if Arianna deposits $500 in an account that pays 3% interest, compounded semiannually.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $500

Compounded semi annually n = 2

Time t = 2 years

Interest rate r = 3%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03

Plug the values into the above formula:

A = P( 1 + r/n )^( n × t )

A = $500( 1 + 0.03/2 )^( 2 × 2 )

A = $500( 1 + 0.015 )^( 4 )

A = $530.68

Therefore, the accrued amount is $530.68.

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The vector  is parallel to the plane the vector <3, -1, 2> is not orthogonal to the normal vector of the plane 6x - 2y + 4z = 1

To determine if the vector <3, -1, 2> is parallel to the plane 6x - 2y + 4z = 1, we need to check if the vector is orthogonal (perpendicular) to the normal vector of the plane.

Find the normal vector of the plane.
The normal vector of a plane is given by the coefficients of x, y, and z in the equation of the plane. In this case, the normal vector is <6, -2, 4>.

Check if the given vector is orthogonal to the normal vector.
Two vectors are orthogonal if their dot product is equal to 0. Let's compute the dot product between the given vector <3, -1, 2> and the normal vector <6, -2, 4>:

Dot product = (3 * 6) + (-1 * -2) + (2 * 4) = 18 + 2 + 8 = 28

Since the dot product is not equal to 0 (28 ≠ 0), the given vector <3, -1, 2> is not orthogonal to the normal vector of the plane.

The vector <3, -1, 2> is not orthogonal to the normal vector of the plane 6x - 2y + 4z = 1, which means it is parallel to the plane.

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The pair with different expressive power is deterministic push-down automata (DPDA) and non-deterministic push-down automata (NPDA), making the correct answer choice 'b only'.

Both DFA and NFA have the same expressive power, as they recognize the same class of languages, known as regular languages. It is possible to convert an NFA to an equivalent DFA using the powerset construction method, and both models can simulate each other effectively.

On the other hand, DPDA and NPDA have different expressive power because they recognize different classes of languages. DPDAs can recognize a subset of context-free languages called deterministic context-free languages, while NPDAs can recognize the entire class of context-free languages. There are certain context-free languages that NPDAs can recognize but DPDAs cannot, such as the classic example of a language consisting of balanced parentheses. This difference in expressive power shows that DPDAs and NPDAs are not equivalent in terms of their capabilities.

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Answer:

South Africa = 32

England = 35

Step-by-step explanation:

Half time: South Africa gets 20 points. Which scored 5/8 of the total points.
Total points = 20 divided by 5/8 = 20 x 8/5 = 32.

England get 7 points at halftime in second half. England scored 4/5 of the total. England get 1 - 4/5 = 1/5 of total points at one half.

Total Points = 7 divided by 1/5 = 7x5 =35

hope this helps

Answer:

The answer to your problem is, Between 1 3/8 kg and 2 1/16 kg of nails

Step-by-step explanation:

2 3/4 kg as an improper fraction is 11/4 kg

1/2 of 11/4 = 1/2 x 11/4

= 11/8

= 1 3/8 kg

3/4 of 11/4 = 33/16

= 2 1/16 kg

1 3/8 kg and 2 1/16 kg of nails

Thus the answer to your problem is, Between 1 3/8 kg and 2 1/16 kg of nails

The correct expansion of (3x – 2)(2[tex]x^2[/tex] + 5) is 3x • 2[tex]x^2[/tex] + 3x • 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5. Thus, option A is the right answer to the given question.

To expand an expression of multiplication of two variables to two variables is done as follows:

1. We take the first term of the first expression which in this case is 3x

2. We multiply it by the first term of the second expression. In this case, we get 3x • 2[tex]x^2[/tex].

3. Subsequently we multiply the first term with further terms and add them. In the given case, the expression we get is 3x • 2[tex]x^2[/tex] + 3x • 5

4. Then we take the second term of the first expression and repeat the above steps and add it to the existing equation.

We get x • 2[tex]x^2[/tex] + 3x • 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5 as the answer.

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Answer: y = |x|

Explanation :

It doesn't seem to be moved in translated in any way. The normal equation for this graph is y = |x|

True. It is possible for a small treatment effect to still be statistically significant if the sample size is large enough.

We have,

Statistical significance is determined by the p-value, which measures the probability of obtaining the observed results if the null hypothesis (no difference between groups) is true.

A small treatment effect may still produce a low p-value if the sample size is large enough to detect even small differences.

However, the clinical significance of the treatment effect should also be considered in addition to statistical significance.

Thus,

It is possible for a small treatment effect to still be statistically significant if the sample size is large enough.

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b)There are 0.10608 experimental outcomes that result in exactly one defect being found.

c) The probabilities of finding no defects, exactly one defect, and two defects are:

P (no defects) = 0.8836
P (1 defect) = 0.10608
P (2 defects) = 0.0036

b. To find the number of experimental outcomes that result in exactly one defect being found:

We can use the binomial distribution formula. The formula is:

[tex]P(x) = (n choose x) * p^x * (1-p)^(n-x)[/tex]
where:
- P(x) is the probability of finding exactly x defects
- n is the total number of parts we select (in this case, n = 2)
- p is the probability of finding a defect in one part (in this case, p = 0.06)
- (n choose x) is the binomial coefficient, which represents the number of ways to choose x items out of n.

So for exactly one defect, we have:

[tex]P(1) = (2 choose 1) * 0.06^1 * (1-0.06)^(2-1) = 2 * 0.06 * 0.94 = 0.10608[/tex]
Therefore, there are 0.10608 experimental outcomes that result in exactly one defect being found.

c. To compute the probabilities associated with finding no defects, exactly one defect, and two defects:

We can use the same binomial distribution formula with different values of x:

- P(no defects): x = 0

[tex]P(0) = (2 choose 0) * 0.06^0 * (1-0.06)^(2-0) = 1 * 1 * 0.8836 = 0.8836[/tex]

Therefore, the probability of finding no defects is 0.8836.

- P(1 defect): we already calculated this in part b.

P(1) = 0.10608

Therefore, the probability of finding exactly one defect is 0.10608.

- P(2 defects): x = 2

[tex]P(2) = (2 choose 2) * 0.06^2 * (1-0.06)^(2-2) = 1 * 0.0036 * 1 = 0.0036[/tex]

Therefore, the probability of finding two defects is 0.0036.

In summary, the probabilities of finding no defects, exactly one defect, and two defects are:

P (no defects) = 0.8836
P (1 defect) = 0.10608
P (2 defects) = 0.0036

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The probability that a randomly selected year of rain in Sydney, Australia has a yearly rainfall of 192.3 mm or more is approximately 0.2119, rounded to four decimal places.

To find the probability that a randomly selected year of rain in Sydney, Australia has a yearly rainfall of 192.3 mm or more, we need to standardize the value using the formula:
z = (x - μ) / σ
where x is the rainfall value we're interested in, μ is the mean rainfall, and σ is the standard deviation.
Plugging in the values, we get:
z = (192.3 - 137) / 69
z = 0.8043
Now we need to find the area under the standard normal distribution curve to the right of this z-score. Using a standard normal table or calculator, we find this to be 0.2119.

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The hotel will cost $1,320 for 15 people for eight days.

Six people staying for 12 days is a total of 6 x 12 = 72 person-days. The cost of the hotel for this period is $792, so the cost per person per day is:

792 / 72 = $11 per person per day

It should be noted thatin order ro calculate the cost for 15 people staying for eight days, we need to first calculate the total person-days for this group:

15 x 8 = 120 person-days

120 person-days x $11 per person per day = $1,320

Therefore, the hotel will cost $1,320 for 15 people for eight days.

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six people can live in a hotel for 12 days for $792. How much will the hotel cost for 15 people for eight days?

The number of popcorns that were sold at the concession stand, given the amount made, was 88 popcorns.

To find the number of popcorns that were sold, two equations are needed to show the relationship between the popcorn and nachos sold.

The equations assume x is popcorns and y is nachos:

x + y = 172

1.10 x + 2.35 y = 294.20

Using substitution:

y = 172 - x

Solve the second equation:

1. 10 x + 2. 35 ( 172 - x ) = 294. 20

1.10 x + 404. 20 - 2.35 x = 294. 20

- 1.25 x = - 110

x = 88

In conclusion, 88 popcorns were sold.

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The full question is:
At a concession stand, popcorn costs $1.10 and nachos cost $2.35. One

day, the receipts for a total of 172 popcorn and nachos were $294.20.

How many popcorns were sold?

Using the given information, we can list out all the possible pairs of candies:
AA, AB, AC, AD, BC, BD, CC, CO, DA, DC, DO, OB, OC
Therefore, the sample space for this experiment is {AA, AB, AC, AD, BC, BD, CC, CO, DA, DC, DO, OB, OC}.

I understand that you would like to know the sample space for getting two random candies at the same time from a candy machine with four types of candies: Apple (A), Blackberry (B), Cherry (C), and Double mint (D).
The sample space for this experiment is the set of all possible outcomes, which in this case is the set of all possible pairs of candies that can be obtained from the machine.
To determine the sample space, we need to list all possible combinations of two candies. Here they are:

1. AA
2. AB
3. AC
4. AD
5. BA
6. BB
7. BC
8. BD
9. CA
10. CB
11. CC
12. CD
13. DA
14. DB
15. DC
16. DD

The sample space for this experiment consists of 16 possible outcomes.

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Answer:

Step-by-step explanation:

10 20 30 40

The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.

So, if we want to find the approximate probability that a randomly selected x-value from the distribution is in a given interval, we need to determine how many standard deviations away from the mean the interval is and then use the empirical rule.

For example, let's say we want to find the approximate probability that a randomly selected x-value from the distribution is between 31 and 47.

First, we need to determine how many standard deviations away from the mean 31 and 47 are.

To do this, we can calculate the z-scores for each value using the formula:

z = (x - mean) / standard deviation

For x = 31:

z = (31 - 39) / 4 = -2

For x = 47:

z = (47 - 39) / 4 = 2

So, the interval from 31 to 47 is two standard deviations away from the mean.

Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, the approximate probability that a randomly selected x-value from the distribution is between 31 and 47 is approximately 95%.

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The best illustration of a probability distribution as it relates to next year's economy is "40 percent chance of recession, 60 percent chance of a normal economy". Option B is correct.

This choice accurately represents a probability distribution by assigning probabilities to different outcomes (recession and a normal economy) based on their likelihoods. The 40 percent chance of a recession and 60 percent chance of a normal economy provide a clear indication of the potential outcomes and their corresponding probabilities.

This distribution allows for a more realistic assessment of the future state of the economy, acknowledging the possibility of both positive and negative scenarios. By presenting these probabilities, decision-makers can better understand the potential risks and make informed choices based on the likelihood of different economic outcomes.

This probability distribution offers a balanced perspective, highlighting the uncertainty and potential variations that may occur in the next year's economy.

Option B holds true.

This question should be provided as:

Which one of these best illustrates a probability distribution at it relates to next year's economy? Multiple choice question:

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A researcher conducted a study investigating the relationship between police officer-reported on-the-job stress and the number of reports of officer misconduct.

As a researcher, the investigation into the number of reports of police officer misconduct in relation to on-the-job stress levels is an important area of study. However, it is essential to ensure that ethical considerations are followed throughout the research process to avoid any potential misconduct.

In terms of the findings,, the results showed a relationship between on-the-job stress and the number of reported incidents of misconduct. Specifically, officers who reported higher levels of stress experienced more incidents of misconduct compared to those who reported minimal stress. It is crucial to further examine the factors contributing to this relationship and develop strategies to mitigate the negative impact of on-the-job stress on police officers.

Based on your question, a researcher conducted a study investigating the relationship between police officer-reported on-the-job stress and the number of reports of officer misconduct. The stress levels were categorized as minimal, moderate, and severe. However, the specific results were not provided in your question.

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Formulating with the value of Sine and sides of a triangle we can find the distance between Pablo's head and the kite (perpendicularly above) to be 58.6 feet ( approximated to the nearest tenth).

It is given that Pablo is flying a kite with a string PK that is 129 feet long.

The string is inclined at an angle of elevation, O of 27 degrees.

Say, ∠POQ = 27°

From the diagram we can say that PK is the hypotenuse of an triangle formed namely POQ.

Say the distance between Pablo's head and the kite (perpendicularly above) be x (in feet).

We can find the value of x by application of sine as,

Sin Ф = Perpendicular / Hypotenuse

⇒ Sin 27° = x / 129

The value of Sin 27° is 0.454 ( approximated to 3 decimal places ).

⇒ 0.454 = x / 129

⇒ x = (0.454) ( 129)

⇒ x = 58.566

⇒ x = 58.6 ( approximated to the nearest tenth) in feet

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The data are matched as shown below

Data 1 - d

Data 2 - c

Data 3 - a

Data 4 - b

IQR is an abbreviation for interquartile range

The interquartile range is calculated using the formula

= top quartile - bottom quartile

Data 1

top quartile = 11

bottom quartile = 5

IQR = 11 - 5 = 6

Data 2

top quartile = 11

bottom quartile =7

IQR = 11 - 7 = 4

Data 3

top quartile = (8 + 9)/2 = 8.5

bottom quartile = (15 + 12)/2 = 13.5

IQR = 13.5 - 8.8 = 5

Data 4

top quartile = 9

bottom quartile = 12

IQR = 12 - 9 = 3

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The volume of the piñata is 3.375 cubic feet.

Now, To find the volume of the piñata, we need to calculate the volume of a cube.

Hence, We can do this by multiplying the length of one edge by itself three times.

In this case, each edge of the piñata is 1.5 feet long,

so we can write;

Volume of piñata = (1.5 feet) x (1.5 feet) x (1.5 feet)

Simplifying this expression, we get:

Volume of piñata = 3.375 cubic feet

Therefore, the volume of the piñata is 3.375 cubic feet.

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Answer:

The determinant of this matrix is

2(5) - (-7)(-2) = 10 - 14 = -4.

This matrix has an inverse, but there are some square matrices whose determinant is zero and therefore do not have an inverse. Abid's friend is correct. So a + b + c + d = 2 + (-7) + (-2) + 5 = -2.