Select all statements below which are true for all invertible n×n matrices A and B

A. AB=BA
B. (In−A)(In+A)=In−A2
C. (A+B)(A−B)=A2−B2
D. A+In is invertible
E. A9B5 is invertible
F. (A+A−1)2=A2+A−2

The percent of the bags of chips weigh less than 176 grams is b 16%

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

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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Answer:

(a) The odds for and against E are (8:1) and (1:8) respectively.

(b) The odds for and against E are (7:2) and (2:7) respectively.

(c) The odds for and against E are (59:41) and (41:59) respectively.

(d) The odds for and against E are (71:29) and (29:71) respectively.

Step-by-step explanation:

The formula for the odds for an events E and against and event E are:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}\)

(a)

The probability of the event E is:

\(P(E)=\frac{8}{9}\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{8/9}{1-(8/9)}=\frac{8/9}{1/9}=\frac{8}{1}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(8/9)}{8/9}=\frac{1/9}{8/9}=\frac{1}{8}\)

Thus, the odds for and against E are (8:1) and (1:8) respectively.

(b)

The probability of the event E is:

\(P(E)=\frac{7}{9}\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{7/9}{1-(7/9)}=\frac{7/9}{2/9}=\frac{7}{2}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(7/9)}{7/9}=\frac{2/9}{7/9}=\frac{2}{7}\)

Thus, the odds for and against E are (7:2) and (2:7) respectively.

(c)

The probability of the event E is:

\(P(E)=0.59\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.59}{1-0.59}=\frac{0.59}{0.41}=\frac{59}{41}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.59}{0.59}=\frac{0.41}{0.59}=\frac{41}{59}\)

Thus, the odds for and against E are (59:41) and (41:59) respectively.

(d)

The probability of the event E is:

\(P(E)=0.71\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.71}{1-0.71}=\frac{0.71}{0.29}=\frac{71}{29}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.71}{0.71}=\frac{0.29}{0.71}=\frac{29}{71}\)

Thus, the odds for and against E are (71:29) and (29:71) respectively.

Answer:

\(y=-x+1\)

Step-by-step explanation:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:

\(-7x-7y=7\)

add 7x to both sides:

\(-7y=7x+7\)

Divide both sides by -7

\(y=-x-1\)

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

\(y=-x+b\text{ where b }\ne -1\)

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)

Now we just plug this into the general equation to get: \(y=-x+1\)

Based on the model, a player with 30 assists will have approximately 46.2 points.

a. The slope of a line in a scatter plot represents the relationship between the two variables being plotted. In this case, the slope of the model y = 1.5x + 1.2 is 1.5, which means that for every 1 unit increase in the number of assists, there is a corresponding 1.5 unit increase in the number of points.

b. To find the number of points for a player with 30 assists, we can substitute x = 30 into the model equation to get:

y = 1.5x + 1.2

= 1.5(30) + 1.2

= 45 + 1.2

= 46.2

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Answer:

D. 135 I think

The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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Import field: Tax Identification Number, Tax Number for Customers or Vendors. Tax Identification Number (customers) or Tax ID Number (vendors).

Answer:

The coefficient is.....5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

There are multiple ways of answering this question. The first one is by factoring the given polynomial.

I got the factors by thinking of factors of -10 that add up to +3 (the ac Method). I thought of +5 and -2. They add up to +3 and their product is -10.

You can also use division, but that means you'll divide the trinomial by each of the choices until you get the one that does not have any remainders.

You may also try substituting the value of x into the trinomial. For example, to test if x + 5 is a factor, then equate it to zero. You will get:

Then, substitute -5 to all x's in x^2 + 3x - 10. If the answer is zero, then x + 5 is a factor of x^2 +3x - 10.

Because the answer is zero, then x + 5 is a factor of x^2 +3x - 10.

Answer:

Step-by-step explanation:

area of triangle = ½(base)(height)

= ½(25 m)(12 m)

= 150 m²

Answer:

its 10 :)

Step-by-step explanation:

Number of points scored in a basketball game is related to the number number of shots taken during the game as below:

X=number of shots taken

Y=number of points scored

Given,

X=50

Y=75

As relation given,

Y=5.0+1.2×X

When x is 50 Y= 5+1.2×50=65

∴The residual score for his team during the game is= 75-65

                                                                                      ⇒10  

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Answer:

All real numbers

Step-by-step explanation:

If there are no holes in your graph (like a graphed point with an open circle) and your graph or equation is a line, the domain is all real numbers.

The domain is all the x's on a graph, where the graph exists, and any x that may go into the equation. Literally any x can go into a linear equation. Your graphed line goes forever in both directions, so the domain is all real numbers. (Only a vertical line would be a different answer)

Answer:

India's population will reach 2 billion during the year of 2050.

Step-by-step explanation:

India's population in t years after 2008 is modeled by the following equation:

\(P(t) = P(0)(1+r)^{t}\)

In which P(0) is the population in 2008 and r is the growth rate, as a decimal.

Population in 2008 of about 1.14 billion people. The population is growing by about 1.34% each year.

This means that \(P(0) = 1.14, r = 0.0134\). So

\(P(t) = P(0)(1+r)^{t}\)

\(P(t) = 1.14(1+0.0134)^{t}\)

\(P(t) = 1.14(1.0134)^{t}\)

If the population continues following this trend, during what year will the population reach 2 billion?

t years after 2008.

t is found when P(t) = 2. So

\(P(t) = 1.14(1.0134)^{t}\)

\(2 = 1.14(1.0134)^{t}\)

\((1.0134)^{t} = \frac{2}{1.14}\)

\(\log{(1.0134)^{t}} = \log{\frac{2}{1.14}}\)

\(t\log{1.0134} = \log{\frac{2}{1.14}}\)

\(t = \frac{\log{\frac{2}{1.14}}}{\log{1.0134}}\)

\(t = 42.23\)

2008 + 42 = 2050

India's population will reach 2 billion during the year of 2050.

Answer:

no

Step-by-step explanation:

Step-by-step explanation:

\(f(x) = {x}^{2} 2 {}^{ - x} \\ der= 2x2 {}^{ - x} + {x}^{2} 2 {}^{ - x} in2\)

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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Based on the figures given in the table, the rate of change of the function is b. 5.

This can be found as:

= (Y₂ - Y₁) / (X₂ - X₁)

Use points:

(0, 1/2) and (1, 5/2)

Solving gives:

= (5/2 - 1/2) / (1 - 0)

= 5

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Answer:

Step-by-step explanation:

To calculate the total balance on the next billing date, we need to consider the average daily balance and the unpaid balance from the previous month.

Given:

Average daily balance for November = $700

Unpaid balance at the end of November = $1,400

Annual percentage rate (APR) = 15.6%

Step 1: Calculate the interest charged for the month of November.

Interest = (Average daily balance * APR * Number of days in the month) / 365

Number of days in November = 30

Interest = (700 * 0.156 * 30) / 365 = $36.44 (rounded to the nearest cent)

Step 2: Add the interest to the unpaid balance to get the total balance on December 1.

Total balance = Unpaid balance + Interest

Total balance = $1,400 + $36.44 = $1,436.44

Therefore, the total balance on the next billing date, December 1, is $1,436.44 (rounded to the nearest cent).

The total balance on the next billing date December 1 is $1,509.20.

The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR).

Given,

Then, the percentage rate for November = \(\sf\frac{15.6}{100}\) × 700

\(\sf = \$109.20\)

Balance on 1st December = unpaid balance at the end of November + percentage rate

\(\sf = $1400 +$109.20\)

\(\sf =\$1509.20\)

Therefore, the total balance on the next billing date December 1 is $1,509.20.

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The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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9514 1404 393

Answer:

Step-by-step explanation:

For a general parabola ...

  y = ax² +bx +c

The first derivative is ...

  y' = 2ax +b

and the second derivative is ...

  y'' = 2a

The second derivative is a (non-zero) constant, so there is no point of inflection. The sign of the second derivative (the sign of 'a') tells you whether the graph opens upward (a>0) or downward (a<0).

The first derivative is 0 where ...

  y' = 0 = 2ax +b

  x = -b/(2a) . . . . . extreme point of the graph

Whether this point is a maximum (a<0) or a minimum (a>0) depends on the sign of 'a'.

The value of the function at the extreme is ...

  y = a(-b/2a)² +b(-b/2a) +c = b²/(4a) -b²/(2a) +c

  y = c -b²/(4a)

So, the extremum is ...

  (x, y) = (-b/(2a), c -b²/(4a)) . . . . . vertex of the parabola

__

1. We have a=5, b=7, c=3.

  First derivative: f'(x) = 10x +7

  Second derivative: f''(x) = 10 . . . . graph opens upward

  Zeros: the discriminant b² -4ac is 7²-4(5)(3) = -11, so no real zeros

  Vertex: (-7/10, 3 -49/20) = (-0.7, 0.55) . . . minimum

__

2. We have a=-1, b=-5, c=5/2.

  First derivative: f'(x) = -2x -5

  Second derivative: f''(x) = -2 . . . . graph opens downward

  Zeros: found from the quadratic formula: x = (-b±√(b²-4ac))/(2a)

     x = (-(-5) ±√((-5)² -4(-1)(5/2)))/(2(-1)) = (5 ±√35)/2 ≈ {-5.458, 0.458}

  Vertex: (-5/2, 5/2-25/-4) = (-5/2, 35/4) = (-2.5, 8.75) . . . maximum

Answer:

a. 1 sig. fig. _800,000,000,000,000 picoseconds (8 x 10^14 picoseconds)

b. 2 sig. figs. 830,000,000,000,000 picoseconds (8.3 x 10^14 picoseconds)  

c. 3 sig. figs. 827,000,000,000,000 picoseconds (8.27 x 10^14 picoseconds)

d. 4 sig. figs. 827,000,000,000,000 picoseconds  (8.270 x 10^14 picoseconds)

e. 5 sig. figs. 827,000,000,000,000 picoseconds  (8.2700 x 10^14 picoseconds)

Step-by-step explanation:

Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

? = 9.4 cm

Step-by-step explanation:

we do the full calculation, as the missing side length is simply the full perimeter minus all the other sides (as the perimeter is the sum of all side lengths).

? = 113.6 - 39.8 - 5.6 - 5.6 - 11.1 - 11.1 - 11.1 - 19.9 = 9.4 cm

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Answer:

109.090909....%(goes on indefinitely)

Step-by-step explanation:

If you are only consuming 1100, and your goal is 1200, as a percentage your target is 1200/1100 of what you are consuming. That simplifies to 12/11, which would mean as a percentage, your target is 109.0909090909...% of what you are consuming.

Answer:

the discount is 50% the previous price

My recommendation to Carlos and Clarita would be to prepare for 3 cats and 3 dogs. This combination offers the highest profit potential based on the given prices and costs.

In order to maximize their profit, Carlos and Clarita should choose the combination of cats and dogs that yields the highest total profit.

In order to make a reasonable recommendation, we can create a profit table based on different values of x and y:

x y Total Profit

0 0 0

1 0 6

0 1 15

1 1 21

2 1 27

1 2 30

2 2 36

3 2 42

2 3 45

3 3 51

From the table, we can see that the highest total profit is achieved when they accommodate 3 cats and 3 dogs. This combination would result in a daily profit of $51.

Therefore, my recommendation to Carlos and Clarita would be to prepare for 3 cats and 3 dogs.

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The probability of the announcement being made is 20.5%. Between 11:30 a.m. and 11:40 a.m., the probability of the announcement being made is 12.8%.

Probability is the mathematical study of chance and uncertainty. It is used to quantify the likelihood of an event happening. Probability is based on mathematical calculations and models, so it is an objective measure of the likelihood of something occurring. Probability can be used to make predictions about future events, to measure risk, and to make decisions in uncertain situations. Probability can be used to better understand the world around us and to make better decisions in all aspects of life.

The time of the announcement is an example of a continuous random variable because it is impossible to pinpoint an exact moment when the announcement will be made. The sample space for this variable is the range of times between 11:30 a.m. and noon. The density graph for these data will be bell-shaped, with the highest probability of the announcement being made in the middle of the meeting, as this will be the most likely time for the announcement to take place.

Between 11:40 a.m. and 11:50 a.m., the probability of the announcement being made is 12.8%. In the first 5 minutes of the meeting, the probability of the announcement being made is 20.5%. Between 11:30 a.m. and 11:40 a.m., the probability of the announcement being made is 12.8%.

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