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Greeley [361]
2 years ago
11

If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.

Mathematics
1 answer:
alexgriva [62]2 years ago
5 0

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]

The inverse of the matrix is

\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]

So, the Inverse Transformation is given by

T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})

So, no option is correct. And the answer is

T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})

Learn more about linear transformations here-

brainly.com/question/13005179

#SPJ10

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A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 340 babies were​ born, a
Bas_tet [7]

Answer:

The 99% confidence interval estimate of the percentage of girls born is (0.8, 0.9).

b)Yes, the proportion of girls is significantly different from 0.5.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

Z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

In the study 340 babies were​ born, and 289 of them were girls. This means that n = 340, \pi = \frac{289}{340} = 0.85

Use the sample data to construct a 99​% confidence interval estimate of the percentage of girls born.

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{340}} = 0.85 - 2.575\sqrt{\frac{0.85*0.15}{400}} = 0.80

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{340}} = 0.85 + 2.575\sqrt{\frac{0.85*0.15}{400}} = 0.90

The 99% confidence interval estimate of the percentage of girls born is (0.8, 0.9).

Does the method appear to be ​effective?

b)Yes, the proportion of girls is significantly different from 0.5.

4 0
3 years ago
In parallelogram DEFG, DH equals X +3, HF equals 3Y, GH equals 2X -5 and HE equals 5Y plus to find the values of X and Y
daser333 [38]

The values of X and Y are 30 and 11 respectively

<h3>How to determine the values of X and Y?</h3>

The figure that represents the complete question is added as an attachment

The given parameters are:

DH = X +3

HF  = 3Y

GH = 2X -5

HE = 5Y

From the attached parallelogram, we have:

DH = HF

GH = HE

Substitute the known values in the above equation

X + 3 = 3Y

2X - 5 = 5Y

Make X the subject in X + 3 = 3Y

X = 3Y - 3

Substitute X = 3Y - 3 in 2X - 5 = 5Y

2(3Y - 3) - 5 = 5Y

Expand

6Y - 6 - 5 = 5Y

Evaluate the like terms

Y = 11

Substitute Y = 11 in X = 3Y - 3

X = 3*11 - 3

Evaluate

X = 30

Hence, the values of X and Y are 30 and 11 respectively

Read more about parallelograms at:

brainly.com/question/3050890

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8 0
1 year ago
Four time a number is no more than one hundred and eight
Reil [10]

Answer:

</ is what I use for equal to or less than

4x </ 108 for the inequality

x </ 27

Step-by-step explanation:

Is that what you needed?

4 0
2 years ago
Read 2 more answers
g A test was conducted to determine if there is a difference between Canadian and American average heart rates. A group of 36 Ca
melisa1 [442]

Answer:

The test statistic  | t |  =4.45

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the first sample size n₁ = 36

Given that the second sample size n₂ = 34

Mean of the first sample x₁⁻ = 68.5

Mean of the second sample x₂⁻ = 70

<u><em>Step(ii):-</em></u>

Test statistic

       t = \frac{x^{-} _{1}-x^{-} _{2}  }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} }  } )}

     t = \frac{68.5-70}{\sqrt{2(\frac{1}{36}+\frac{1}{34} ) } }

    t = \frac{-1.5}{0.337} = -4.45

The test statistic  | t | = |-4.45| =4.45

6 0
3 years ago
Un joven retira el 25% de sus ahorros y gasta el 33.3% en adornos para su
ki77a [65]

Answer:

$3003.2

Step-by-step explanation:

Step 1

Paso 1

Averiguamos cuánto era el 25% de sus ahorros.

Se nos dice en la pregunta que gastó el 33.3% en decoraciones para su nueva casa y si los adornos cuestan $ 250.00.

Esto significa

33.3 % × x = 250

33.3 x/ 100 = 250

Cruz multiplicar

33.3x = 250 × 100

x = 25.000 / 33.3

x = 750.75075075

Por lo tanto, la cantidad o el costo de los adornos = 33.3% del 25% de sus ahorros = $ 750.8

Paso 2

De la pregunta:

Un joven retira el 25% de sus ahorros y

Por lo tanto:

Sea y = monto total de sus ahorros

25/100 × y = $ 750.8

25y = 100 × 750.8.

y = 100 × 750.8 / 25

y = $ 3003.2

Por lo tanto, tenía $ 3003.2 en su cuenta.

6 0
3 years ago
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