Use the graph of y = tan x to find all values of x, 0 ≤ x ≤ 2π, for which the following is true.

tan x is undefined

The Correct Answer is A:-5 :)

Answer:

The statements that are correct are:

c) [tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]

d) [tex]a^2b^7[/tex] is invertible.

e) [tex]a+b[/tex] is invertible.

Step-by-step explanation:

We are given that:

a and b are invertible n×n matrices.

We have to tell which of the following statements are true.

a)

[tex](ab)^{-1}=a^{-1}b^{-1}[/tex]

This statement is false.

Since:

[tex](ab)^{-1}=b^{-1}a^{-1}[/tex] and it may not be equal to the term [tex]a^{-1}b^{-1}[/tex]

b)

[tex]aba{-1}=b[/tex]

This expression could also be written as:

[tex]ab=ba[/tex]

Since on Post multiplying by a on both the sides.

But here we don't know whether the matrices are commutative or not.

Hence, the statement is false.

c)

[tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]

This statement is true.

since,

[tex](in+a)(in+a^{-1})=in(in+a^{-1})+a(in+a^{-1})\\\\=in^2+in.a^{-1}+a.in+aa^{-1}\\\\=in+a^{-1}+a+in\\\\=in+a^{-1}+a[/tex]

where in denote the identity matrix.

and we know that:

[tex]in^2=in[/tex]

d)

[tex]a^2b^7[/tex] is invertible.

This statement is true.

Since we know that prodct of invertible matrices is also invertible.

As [tex]a[/tex] is invertible so is [tex]a^2[/tex].

Also [tex]b[/tex] is invertible so is [tex]b^7[/tex].

Hence Product of  [tex]a^2[/tex] and  [tex]b^7[/tex] is also invertible.

i.e. [tex]a^2b^7[/tex] is invertible.

e)

[tex]a+b[/tex] is invertible.

This statement is true as sum of two invertible matrices is invertible.

f)

[tex](a+b).(a-b)=a^2-b^2[/tex]

This statement is false.

Since,

[tex](a+b).(a-b)=a(a-b)+b(a-b)\\\\=a.a-a.b+b.a-b.b\\\\=a^2-ab+ba-b^2[/tex]

Now as we are not given that:

[tex]ab=ba[/tex]

Hence, we could not say that:

[tex](a+b).(a-b)=a^2-b^2[/tex]

The correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:

(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]

(d). [tex]{a^2}{b^7}[/tex] is invertible.

(e). [tex]a+b[/tex] is invertible.

Further Explanation:

Given:

The matrix [tex]a[/tex] and [tex]b[/tex] are invertible [tex]\left({n\times n}\right)[/tex] matrices.

Calculation:

(a)

The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.

[tex]\begin{aligned}{\left({ab}\right)^{-1}}&={a^{-1}}{b^{-1}}\\\left({ab}\right){\left({ab}\right)^{-1}}&=\left({ab}\right){a^{-1}}{b^{-1}}\\I&\ne ab{a^{-1}}{b^{-1}}\\\end{aligned}[/tex]

The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.

(b)

The statement is [tex]ab{a^{-1}}=b[/tex].

Now multiply by a both the side.

[tex]\begin{aligned}ab{a^{-1}}a&=ba\\ab&\ne ba\\\end{aligned}[/tex]

The statement is [tex]ab{a^{-1}}=b[/tex] is false.

(c)

The statement is [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex].

Solve the above equation to check whether it is invertible.

[tex]\begin{aligned}\left({in+a}\right)\left({in+{a^{-1}}}\right)&=in\left({in+{a^{-1}}}\right)+a\left({in+{a^{-1}}}\right)\\&=i{n^2}+in\cdot{a^{-1}}+a\cdot in+a{a^{-1}}\\&=in+{a^{-1}}+a+in\\&=in+{a^{-1}}+a\\\end{aligned}[/tex]

The statement is true.

(d)

The statement is [tex]{a^2}{b^7}[/tex].

The product of invertible matrices is always invertible.

As [tex]a[/tex] is invertible so [tex]{a^2}[/tex] is also invertible.

As [tex]b[/tex] is invertible so [tex]{b^7}[/tex] is also invertible.

Hence, the product of [tex]{a^2}[/tex] and [tex]{b^7}[/tex] is also invertible.

The statement is true.

(e)

The statement [tex]a+b[/tex] is true as [tex]a+b[/tex] is always invertible.

(f)

The statement is [tex]\left({a+b}\right)\cdot\left({a-b}\right)={a^2}-{b^2}[/tex].

Solve the equation to check the inevitability.

[tex]\left({a+b}\right)\times\left({a-b}\right)={a^2}-ab+ba-{b^2}[/tex]

The statement is not true as [tex]ab=ba[/tex].

Hence, the correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:

(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]

(d). [tex]{a^2}{b^7}[/tex] is invertible.

(e). [tex]a+b[/tex] is invertible.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: Invertible, matrices, matrix, statement, function, true, determinants, elements, inverse.

Answer:

Area of the triangle will be 162.3 cm²

Step-by-step explanation:

From the figure attached,

In the triangle ABC angle ACB = 23°, side BC = 27.6 cm and hypotenuse AC = 30 cm

Now we have to calculate the area of the given right angle triangle.

Since area of a right angle triangle is represented by

Area = [tex]\frac{1}{2}\times b\times h[/tex]

Where b = adjacent side

h = opposite side

To calculate the opposite side of the triangle we will apply Pythagoras theorem in the ΔABC.

AC² = AB² + BC²

AB² = AC² - BC²

AB² = (30)² - (27.6)²

      = 900 - 761.76

      = 138.24

AB = √138.24

     = 11.76

Area of the triangle = [tex]\frac{1}{2}(AB)(BC)[/tex]

                                 =  [tex]\frac{1}{2}(11.76)(27.6)[/tex]

                                 = 162.28 cm² ≈ 162.3 cm²

for a, make a dot on the line plot at each of the given lengths

b) there are more fishes greater than 1 1/2

Answer:

The correct option is A.

Step-by-step explanation:

Given information: Length of Arc TR is 116° and the measure of ∠WSX is 45°.

According to the angle of Intersecting Secants Theorem,

[tex]\text{Angle of Intersecting Secants}=\frac{1}{2}(\text{Major arc - Minor arc})[/tex]

Using this property we get

[tex]45^{\circ}=\frac{1}{2}(Arc(TR)-Arc(WX))[/tex]

[tex]45^{\circ}=\frac{1}{2}(116^{\circ}-Arc(WX))[/tex]

Multiply 2 on both the sides.

[tex]90^{\circ}=116^{\circ}-Arc(WX)[/tex]

[tex]Arc(WX)=116^{\circ}-90^{\circ}[/tex]

[tex]Arc(WX)=26^{\circ}[/tex]

The measure of arc WX is 26°. Therefore the correct option is A.

Answer with explanation:

Smallest Polygon = Triangle , which has 3 sides

Sum of angles of triangle = 180°→→, Using the angle sum property of triangle.

We can find the Sum of angles of triangle, using the formula

   = (n-2)×180°

  = (3-2)×180°

 = 1 × 180°

 = 180°

A Quadrilateral has four sides.

Sum of angles of Quadrilateral = 360°

Or , using the formula

=(4-2)×180°

=2 × 180°

=360°

For, n sided Polygon

Sum of it's Interior angles = (n-2) × 180°

To prove this, we should divide that polygon into triangles, and multiply number of triangles by angle of 180°.

For, example, Quadrilateral can be divided into two triangles , sum of interior angles of Quadrilateral =2 × 180°=360°

Answer:-9 degrees

Step-by-step explanation:The average drop in temperature per minute is 9 degrees.

An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.

Basing from the graph, we can actually see that the interval is:

10 Fahrenheit degrees

The expected net winnings are  -$36. That is you lose $36 according to chance.

We have given

A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars.

We have to determine expected net winnings

The expected value is what the player can expect to win or lose if they were to play many times with the same game.

let's say that you have a 3/13 chance of winning $3 and a 2/13 chance of winning $10 and an 8/13 chance of winning $0. 

Therefore if the dice is rolled 13 times then the expected to win 3X$3 + 2X$10 = $29 

But you pay $5 per roll so 13 rolls would cost me 13X$5 = $65 

Therefore the expected net winnings are $29-$65 = -$36 

Therefore the expected net winnings are  -$36.

So you lose $36 according to chance.

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3 girls to 5 boys

3+5 =8

120/8 = 15

3 *15 = 45 girls

0.5x-9 = 4x+5

add 9 to both sides

0.5x = 4x+14

subtract 4x from each side

-3.5x =14

x = 14/*3.5

x = -4

Answer: He traveled 54.28 miles per hour as an average.

Step-by-step explanation:

Since we have given that

Number of miles traveled in first hour = 52 miles

Number of miles traveled in second hour = 64  miles

Number of miles traveled in third hour = 49 miles

Average per hour is given by

[tex]=\dfrac{3}{\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}}\\\\\\=\dfrac{3}{\dfrac{1}{52}+\dfrac{1}{64}+\dfrac{1}{49}}\\\\\\=\dfrac{3}{\dfrac{784+637+832}{40768}}\\\\\\=\dfrac{3}{\dfrac{2253}{40768}}\\\\\\=\dfrac{40768\times 3}{2253}\\\\\\=\dfrac{122304}{2253}\\\\\=54.28\ miles/hr[/tex]

Hence, he traveled 54.28 miles per hour as an average.

Answer:

The new mean height will be greater than 65.4 inches.

Step-by-step explanation:

The mean height of a group of students is 65.4 inches. A student joins the group who is 73 inches tall.

Mean is 65.4 inches

A student joins the group who is 73 inches tall.

73 is greater than the means 64.4 inches

So mean will increase definitely

Mean will vary depends on the total number of students

The new mean height will be greater than 65.4 inches.

a) The probability is approximately 0.9973.

b) The store takes in at most [tex]$\$ 15,600.00$[/tex].

a) To estimate the probability that the store's revenues were at least [tex]$\$9,500$[/tex], we need to find the z-score corresponding to this revenue value and then find the probability associated with that z-score in the standard normal distribution.

First, we calculate the z-score:

[tex]\[ z = \frac{X - \mu}{\sigma} = \frac{9500 - 3200}{2000} = \frac{6300}{2000} = 3.15 \][/tex]

Using a standard normal distribution table or a calculator, we find that the probability corresponding to [tex]$z = 3.15$[/tex] is approximately 0.9987.

So, the estimated probability that the store's revenues were at least [tex]$\$9,500$[/tex] is approximately 0.9987.

b) To find out how much the store takes in on the worst [tex]$10\%$[/tex] of such days, we need to find the revenue value corresponding to the [tex]$90\%$[/tex] percentile of the distribution.

Using the standard normal distribution table or a calculator, we find that the [tex]$90\%$[/tex] percentile corresponds to a z-score of approximately 1.28.

Now, we can find the revenue value:

[tex]\[ X = \mu + z \times \sigma = 3200 + 1.28 \times 2000 = 3200 + 2560 = 5760 \][/tex]

So, on the worst [tex]$10\%$[/tex] of such days, the store takes in at most [tex]$\$5,760.00$[/tex].

The correct question is:

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of [tex]$\$ 32$[/tex] and a standard deviation of [tex]$\$ 20$[/tex]. Suppose the store had 294 customers this Sunday.

a) Estimate the probability that the store's revenues were at least [tex]$\$ 9,500$[/tex].

b) If, on a typical Sunday, the store serves 294 customers, how much does the store take in on the worst [tex]$10 \%$[/tex] of such days?

a) The probability is [tex]$\square$[/tex].

b) The store takes in at most [tex]$\$ \square$[/tex].

To graph an absolute value function with a given vertex and 'a' value, first plot the vertex. Then use the 'a' value to find and plot other points. Connect the points to create the graph.

To graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½, you first plot the vertex on the graph. This point will be the lowest (if 'a' is positive) or highest (if 'a' is negative) point on the graph. The vertex of the absolute value function is the point of reflection. Next, create a table to find extra points on the graph. Because 'a' is ½, count over 1 and up (or down depending on if 'a' is positive or negative) half the distance. Similarly, count over 2 and up (or down) the distance to find more points. Once you've plotted these points, you'll see the absolute value function starting to take shape. Connect the dots to create the two arms of the absolute value function that point upwards or downwards depending on the value of 'a'. This will result in a 'V' shaped graph if 'a' is positive or an upside-down 'V' shape if 'a' is negative.

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