: The given T is a linear transformation from R2 into R2, Show that T is invertible and find a formula for T1. T (x1X2)= (3x1-9x2. - 3x1 +5x2) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is (Simplify your answer.)

If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.

To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.

We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:

total = swim suits + sunglasses - both

Substituting in the given values, we get:

75 = 63 + 43 - x

Simplifying, we get:

x = 31

Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:

63 - 31 = 32

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The probability that a dessert chosen at random contains nuts given that it contains chocolate is 34.9%.

The likelihood of any event A happening when another event B related to A has already happened is known as conditional probability. This implies that the likelihood of event A relies on event B.

The conditional probability symbol is P(A|B). Conditional probability P(A|B) is crucial for any exam that is part of a competition. The concept of conditional probability P(A|B), formula, and examples with solutions are all covered in this article. The Bayes theorem predicts the likelihood that an event connected to any condition would occur. For the situation of conditional probability, this theorem is taken into account.

Let A : a certain cafe contains chocolates

B: a dessert contains Nuts

P(A) = 86% = 0.86

P(AB) = 30% = 0.3

[tex]P(B|A) =\frac{P(AB)}{P(A)}[/tex]

= 0.3/0.86

= 34.9 %

So the answer is 34.9%

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There is a .90 probability that the project will be completed before approximately day 118.

The given information can be solved by using the formula of z-score as follows:

Z = (X - μ)/σ

Where: Z = z-score

X = the time for project completion

μ = the mean time for the critical path

σ = standard deviation for the critical path

σ² = variance of the critical pathσ = √64

σ = 8

Given that the mean time for the critical path is μ = 108 days and σ = 8 days,

Therefore, the z-score of the completion of the project before 108 days is given by:

Z = (X - μ)/σ0.90

 = P(Z < z)

 = P(Z < (X - 108)/8)P(Z < (X - 108)/8)

 = 0.90

Using a z-table or calculator, we find the z-value to be 1.28.

Then,1.28 = (X - 108)/8

Multiplying both sides by 8, we get:10.24 = X - 108

Adding 108 to both sides, we get: X = 118.24

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Answer:

(15, - 4 ) , (3, - 2 ) , (- 1, 0 )

Step-by-step explanation:

given a point (x, y ) on a function f(x) , then the corresponding point on the inverse function is (y, x )

given the points on g(x) , then the corresponding points on [tex]g^{-1}[/tex] (x) are

(- 4, 15 ) → (15, - 4 )

(- 2, 3 ) → (3, - 2 )

(0, - 1 ) → (- 1, 0 )

Answer:

AB=8.1 and B=29.6

Step-by-step explanation:

1) To find the measure of AB, use the law of cosines

[tex]c^2=4^2+7^2-2(4)(7)cos(90)[/tex]

[tex]c^2 = 16+49 -56cos(90)\\c^2= 65\\c=8.1[/tex]

2) Use law of sines to find the measure of B

[tex]\frac{8.1}{sin(90)} =\frac{4}{sin(B)}[/tex]

B=29.6

The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.

This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.

Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.

It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.

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The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.

Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.

The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.

By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.

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Answer:

[tex]26 > n + 15[/tex]

[tex]11 > n[/tex]

[tex]n < 11[/tex]

Answer:

They are congruent by AA- because the only thing they have in common is the 65 degree angles but the sides are all different

Step-by-step explanation:

Answer:

The statement that describes the graph of the polynomial function f (x) = x^5 - 6x^4 + 9x^3 is that it has a local maximum at x = 0 and a local minimum at x = 2. The degree of the polynomial is 5, which means it has five zeros or x-intercepts. The leading coefficient is positive, which indicates that the graph will rise to the left and right. The function has a point of inflection at x = 1.5, where the concavity changes from up to down. Overall, the graph of this polynomial function has a typical "upside-down U" shape with local extrema and a point of inflection.

Answer: Proper fraction

Step-by-step explanation:

A proper fraction is a fraction that has its numerator value less than the denominator.

For example, ⅔, 6/7, 8/9, etc. are proper fractions.

Answer:

Since the decoration is in the shape of a triangle, we can use the formula for the area of a triangle to solve for its height. The area of a triangle is given by:

Area = (1/2) x base x height

Let's call the height of the decoration h. We know that the base after firing is 9 inches, so we can plug in the given values and solve for h:

Area = (1/2) x 9 x h

Area = 4.5h

We don't know the exact area of the decoration, but we do know that the decoration maintains its shape after firing. This means that the ratio of the areas before and after firing is the same, and so is the ratio of the heights and bases. Since the height and base are proportional, we can write:

h / 15 = 9 / 10

Simplifying the equation, we get:

h = (9/10) x 15

h = 13.5

Therefore, the height of the finished decoration is 13.5 inches.

Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran

Step-by-step explanation:

The probability of P(more than 1 hour of TV | 6th period class) is option (D) 0.765

To find P(more than 1 hour of TV | 6th period class), we need to use conditional probability formula

P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class)

The number of students who watched more than 1 hour of TV and were in the 6th period class is 13. Therefore, P(more than 1 hour of TV and 6th period class) = 13 / (13 + 10) = 13/23.

The total number of students in the 6th period class is 13 + 10 = 23. Therefore, P(6th period class) = 23 / (6 + 23) = 23/29.

Putting it all together

P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class) = (13/23) / (23/29) = 0.765 (rounded to the nearest thousandth)

Therefore, the correct option is (D) 0.765

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The given question is incomplete, the complete question is:

The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night? Yes No 3rd period class 6 6th period class 13 10 A) 0.647 B) 0.565 C) 0.435 D) 0.765

Answer:

∠ FZG = 38°

Step-by-step explanation:

∠ HZJ and ∠ FZG are vertically opposite angles and are congruent , then

∠ ZFG = ∠ HZJ = 38°

The value of the double integral is 128/27 - 32/9 + 8ln2/3. From triangular region with vertices (0, 1), (1, 2), (4, 1) d.

To evaluate the double integral, we first need to set up the limits of integration. Since the region D is a triangle, we can use the following limits:

0 ≤ x ≤ 1

1 + x ≤ y ≤ 4 - x

The integral then becomes:

∫0^1 ∫1+x^4-x 8y^2 dy dx

Evaluating the integral with respect to y first, we get:

∫0^1 ∫1+x^4-x 8y^2 dy dx = ∫0^1 [(8/3)(y^3)]1+x^4-x dx

= ∫0^1 [(8/3)(1+x^3)^3 - (8/3)(1+x^2)^3] dx

= 128/27 - 32/9 + 8ln2/3

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Answer:

11.  17

12.  -16

Step-by-step explanation:

Figure1 shows pair of corresponding angles

Figure 2 and 6 shows pair of alternate exterior angles

Figure 5 shows pair of alternate interior angle

Figure3 shows pair of consecutive exterior angles

Figure 4 shows pair of consecutive interior angles

A set of angles on the outside of each of the two lines but on the opposing sides of the transversal are known as alternate exterior angles.

When a transversal intersects two parallel lines, the angles created within are equal to the alternative pairings of those pairs.

the angles created when two parallel lines cross any other line, whether they are corresponding or matching corners with the transversal.

In the given figures

Figure1 is  showing pair of the corresponding angles

Figure 2 and 6 showing pair of the alternate exterior angles

Figure 5 is showing pair of the alternate interior angle

Figure3 is showing pair of the consecutive exterior angles

Figure 4 is showing pair of the consecutive interior angles.

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The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.

When measuring the area of a shape, we are determining the amount of surface the shape takes up.

To calculate the area enclosed by each fence, we must multiply the length and width of each.

The area enclosed by the wood fence is

6 1/2 x 2 1/4 = 14 7/8 square yards,

and the area enclosed by the metal fence is

2 3/4 x 2 1/2 = 6 7/8 square yards.

To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:

14 7/8 / 6 7/8 = 7 3/4.

This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.

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Let (x1, y1) = (9,7) and (x2, y2) = (6,3)

By distance formula,

d = (x2 - x1)² + (y2 - y1)²

d = (6 - 9)² + (3 - 7)²

d = (-3)² + (-4)²

d = 9 + 16

d = 25 units

To begin, we know that the median of the original collection of five positive integers is 4, which means that the middle number is 4. We also know that the unique mode is 3, which means that there is only one number in the collection that occurs more frequently than any other number.

Let's call the five positive integers in the original collection a, b, c, d, and e.

Since the mean of the original collection is 4.4, we can set up the equation:

(a+b+c+d+e)/5 = 4.4

Multiplying both sides by 5 gives:

a+b+c+d+e = 22

We also know that the mode is 3, which means that one of the numbers in the collection must be 3. Let's assume that a = 3, then we have:

3+b+c+d+e = 22

b+c+d+e = 19

Since the median is 4 and 3 is the unique mode, we can conclude that b, c, d, and e must be either 4 or 5. However, since there is only one unique mode, we know that there is only one number in the collection that is equal to 3. Therefore, we can conclude that the collection of five positive integers must be: 3, 4, 4, 4, 5.

If we add 8 to this collection, the new collection becomes: 3, 4, 4, 4, 5, 8. The new collection has six numbers, so the median is now the average of the two middle numbers. Since the middle two numbers are 4 and 5, the median is (4+5)/2 = 4.5.

Therefore, the new median is 4.5, expressed as a decimal to the nearest tenth.

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Answer:

16 represents the hours available to sew gloves.

2 represents the cost of producing gloves for a small pair.

Step-by-step explanation:

Answer:

Step-by-step explanation:lllllLet's start by using "R" to represent the number of apps that Rita started with, and "C" to represent the number of apps that Cora started with.

We know that Rita deleted 5 apps, so she would have (R-5) apps remaining. And we know that she still had twice the amount of Cora, which is 36.

So we can write the equation:

R-5 = 2C

And we also know that Cora had 36 apps, so we can substitute that value in for C:

R-5 = 2(36)

Simplifying the right side:

R-5 = 72

Finally, we can solve for R by adding 5 to both sides:

R = 77

So Rita started with 77 apps, and Cora started with 36 apps. We can check that Rita deleted 5 and had twice as many as Cora by plugging our values into the original equation:

77 - 5 = 72

2(36) = 72

Both sides are equal, so our solution is correct.

Just ignore this answer, its incorrect

*edited*

The theoretical probability of not picking the silver coin will be 0.38 .

Given,

200 silver coins and 123 gold coins are filled in a bag .

Now,

Total number of coins in a bag = gold + silver coins

Total number of coins in a bag  = 200 + 123

Total number of coins in a bag  = 323

Further ,

Probability of taking silver coin = 200/323

Probability of taking silver coin = 0.619.

probability of taking gold coin = 123/323

probability of taking gold coin  = 0.38

Hence the probability of not selecting silver coin is 0.38 .

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The result is the t-statistic, which is used to compare the two samples.

The t-test is used to compare the means of two independent samples. The formula for the t-test is:

[tex]t = (x1 - x2) / √[s2/n1 + s2/n2][/tex],

where x1 is the mean of the first sample, x2 is the mean of the second sample, s2 is the variance of the two samples, and n1 and n2 are the sizes of each sample.

To calculate the t-test, first you need to calculate the mean for each sample. If the sample size is small (less than 30), then you should use the sample standard deviation.

Next, calculate the variance for each sample by taking the sum of the squared differences from the mean, and dividing by n-1 (where n is the sample size).

Finally, calculate the t-test statistic by substituting the means and variances into the formula above. The result is the t-statistic, which is used to compare the two samples.

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Kendra cost $0.60 for each egg and $0.30 for each piece of toast.

Let's assume that the cost of one egg is x and the cost of one piece of toast is y.

From the given information, we can set up two equations:

2x + y = 1.5

x + y = 0.9

We can solve this system of equations by either substitution or elimination method.

Using the elimination method, we can multiply the second equation by -2 to eliminate y:

-2x - 2y = -1.8

2x + y = 1.5

Adding these two equations, we get:

-1y = -0.3

y = 0.3

Substituting y = 0.3 in either of the two equations, we get:

x = 0.6

Therefore, Kendra charges $0.60 for each egg and $0.30 for each piece of toast.

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The area of the walkway can be expressed as the sum of two terms is 9x + 7 and 10x + 4.

We are given that the area of the garden is 6(5.5x + 2.5). This means that the garden has a length of 5.5x + 2.5 units and a width of 6 units (since the problem doesn't specify which side is the length or width, we can assume either). We can use the formula for the area of a rectangle to find the area of the garden:

Area of the garden = length x width = (5.5x + 2.5) x 6 = 33x + 15

Next, we are given that the combined area of the garden and the walkway is 6.5(8x + 4). This means that the garden and the walkway together have a length of 8x + 4 units and a width of 6.5 units. We can again use the formula for the area of a rectangle to find the combined area:

Combined area = length x width = (8x + 4) x 6.5 = 52x + 26

To find the area of the walkway, we need to subtract the area of the garden from the combined area. This will give us the area of the walkway alone.

Area of the walkway = Combined area - Area of the garden

= (52x + 26) - (33x + 15)

= 19x + 11

Finally, we are asked to express the area of the walkway as the sum of two terms. This means we need to find two numbers that add up to 19 and two numbers that add up to 11. We can use trial and error to find these numbers. One possible solution is:

19x + 11 = (9x + 7) + (10x + 4)

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The probability that the first three questions have the same answer choice is 1/4, since there are four answer choices and the instructor is randomly selecting the answers according to a discrete uniform distribution. This means that each answer choice has an equal probability of being chosen. Therefore, the probability of all three questions having the same answer is 1/4.

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The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.

The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.

In the given figure, the yard is in the shape of a rectangle with dimensions (4x - 6) m and (2x + 3) m. The perimeter of a rectangle is the sum of the lengths of all four sides, which can be expressed as:

Perimeter = 2(Length + Width)

Perimeter = 2(4x - 6 + 2x + 3) m

Perimeter = 2(6x - 3) m

Perimeter = 12x - 6 m

So, a simplified algebraic expression for the perimeter of the yard is 12x - 6 m.

To find the perimeter in meters when x = 3 m, substitute x = 3 into the algebraic expression for perimeter:

Perimeter = 12(3) - 6 m

Perimeter = 30 m

Therefore, the perimeter of the yard when x = 3 m is 30 meters.

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