Consider the matrices
A= 4 7 , B= -2 3 . C= 3 4 -1, and D= 6
-3 8 0 5 2
-5 -2

What are the dimensions of the product matrix of two of these matrices?
Drag the matrix dimensions to each box to match the product.

BD 2 x 1
CA 3 x 3
DC 2 x 3

Answer: As much wood as a woodchuck could chuck, If a woodchuck could chuck wood.

Step-by-step explanation: As much wood as a woodchuck could chuck, If a woodchuck could chuck wood.

Answer:

wood, that's how much a wood chuck can chuck

The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

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Answer:

3(s+8) = 36

= 3(4+8) = 36

=3(12) = 36

= 3×12 = 36

Answer:

s = 4

Step-by-step explanation:

To solve for "s", we need to simplify the distributive property on the LHS.

\(\rightarrow 3(s + 8) = 36\)

\(\rightarrow 3s + 24 = 36\)

Now, let's solve for "s".

\(\rightarrow 3s + 24 = 36\)

\(\rightarrow3s + 24 - 24 = 36 - 24\)

\(\rightarrow3s = 12\)

\(\rightarrow \boxed{s = \dfrac{12}{3} = 4}\)

Step-by-step explanation:

The complete frequency distribution table for the data has been attached to this response.

The frequency column contains values that are the number of times the given range of hours appear in the data. For example, numbers in the range 0 - 2 hours, appear 9 times in the data. Also, the numbers in the range 3 - 5 appear  6 times. The same logic applies to other ranges.

The relative frequency column contains the ratio of the number of times the given range of hours appear in the data, to the total number of outcomes. The total number of outcomes is the sum of all the frequencies on the frequency column. This gives 38 as shown.

So, for example, to get the relative for the numbers in the range 0-2, divide their frequency (9) by the total outcome or frequency (38). i.e

9 / 38 = 0.24

Also, to get the relative for the numbers in the range 3-5, divide their frequency (6) by the total outcome or frequency (38). i.e

6 / 38 = 0.16

Do the same for the other ranges.

Given data:

The given value of x is x=4.

Substitute x=4 in first option.

2(4)+7=22

15=22

As, the above equaion is not satisfy so, the given option is wrong.

Substitute x=4 in second option.

6(4)÷8=3

24÷8=3

3=3

As above equation is sat

Answer:

16

Step-by-step explanation:

Set up a proportion

\(\frac{3}{45} = \frac{x}{240}\)

Then, cross multiply.

\(720 = 45x\\16 = x\\x = 16\)

The slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

​f(x) = 1 / 2+3x and point P = (2 , 1/8)

f(x+h) = 1/(2 + 3a + 3h)

f(a) = 1/(2 + 3a)

m(tan) = [1/(2 + 3a + 3h) - 1/(2 + 3a)]/h

After simplifying:

m(tan) = -3/[(2+3a)(2+3a+3h)]

h = 0

m(tan) = -3/(2+3a)²

The equation of the line:

y - 1/8 = [-3/(2+3a)²](x - 2)

Thus, the slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).

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Answer:

Step-by-step explanation:

From the information given:

The joint density of \(y_1\)  and  \(y_2\) is given by:

\(f_{(y_1,y_2)} \left \{ {{y_1+y_2, \ \ 0\ \le \ y_1 \ \le 1 , \ \ 0 \ \ \le y_2 \ \ \le 1} \atop {0, \ \ \ elsewhere \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \right.\)

a)To find the marginal density of \(y_1\).

\(f_{y_1} (y_1) = \int \limits ^{\infty}_{-\infty} f_{y_1,y_2} (y_1 >y_2) \ dy_2\)

\(=\int \limits ^{1}_{0}(y_1+y_2)\ dy_2\)

\(=\int \limits ^{1}_{0} \ \ y_1dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)

\(= y_1 \ \int \limits ^{1}_{0} dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)

\(= y_1[y_2]^1_0 + \bigg [ \dfrac{y_2^2}{2}\bigg]^1_0\)

\(= y_1 [1] + [\dfrac{1}{2}]\)

\(= y_1 + \dfrac{1}{2}\)

i.e.

\(f_{(y_1}(y_1)}= \left \{ {{y_1+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)

The marginal density of \(y_2\) is:

\(f_{y_1} (y_2) = \int \limits ^{\infty}_{-\infty} fy_1y_1(y_1-y_2) dy_1\)

\(= \int \limits ^1_0 \ y_1 dy_1 + y_2 \int \limits ^1_0 dy_1\)

\(=\bigg[ \dfrac{y_1^2}{2} \bigg]^1_0 + y_2 [y_1]^1_0\)

\(= [ \dfrac{1}{2}] + y_2 [1]\)

\(= y_2 + \dfrac{1}{2}\)

i.e.

\(f_{(y_1}(y_2)}= \left \{ {{y_2+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)

b)

\(P\bigg[y_1 \ge \dfrac{1}{2}\bigg |y_2 \ge \dfrac{1}{2} \bigg] = \dfrac{P\bigg [y_1 \ge \dfrac{1}{2} . y_2 \ge\dfrac{1}{2} \bigg]}{P\bigg[ y_2 \ge \dfrac{1}{2}\bigg]}\)

\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} f_{y_1,y_1(y_1-y_2) dy_1dy_2}}{\int \limits ^1_{\frac{1}{2}} fy_1 (y_2) \ dy_2}\)

\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} (y_1+y_2) \ dy_1 dy_2}{\int \limits ^1_{\frac{1}{2}} (y_2 + \dfrac{1}{2}) \ dy_2}\)

\(= \dfrac{\dfrac{3}{8}}{\dfrac{5}{8}}\)

\(= \dfrac{3}{8}}\times {\dfrac{8}{5}}\)

\(= \dfrac{3}{5}}\)

= 0.6

(c) The required probability is:

\(P(y_2 \ge 0.75 \ y_1 = 0.50) = \dfrac{P(y_2 \ge 0.75 . y_1 =0.50)}{P(y_1 = 0.50)}\)

\(= \dfrac{\int \limits ^1_{0.75} (y_2 +0.50) \ dy_2}{(0.50 + \dfrac{1}{2})}\)

\(= \dfrac{0.34375}{1}\)

= 0.34375

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.

Given the equation in the question;

3 / 5x-2 = 2 / 3x-1

To solve for x, cross multiply the equation

3 / 5x-2 = 2 / 3x-1

3( 3x - 1 ) = 2( 5x - 2 )

Apply distributive property

3( 3x - 1 ) = 2( 5x - 2 )

3×3x + 3×-1 = 2×5x + 2×-2

9x - 3 = 10x - 4

Subtract 10x from both sides

9x - 10x - 3 = 10x - 10x - 4

9x - 10x - 3 = - 4

Add 3 to both sides

9x - 10x - 3 + 3 = - 4 + 3

9x - 10x  = - 4 + 3

-x = -1

Divide both sides by -1

-x/-1 = -1/-1

x = 1

Therefore, the value of x is 1.

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Answer:

6.12

Step-by-step explanation:

Answer:

Q. Equal

Step-by-step explanation:

"The same" means equal. Its kind of like equations.

1 is equal to 1 they are the same number

answer: Equal

Step-by-step explanation: being the same in quantity, size, degree, or value.

Answer:

b. Non-proportional

Step-by-step explanation:

A table of values that represents a proportional relationship will have the same ratio of every pair in the given table. That is, y/x will result in the same value all through for every given pair.

The table of values given does not show a proportional relationship, because the ratio of y to x of each given pair of values are different and unequal:

y/x = 3/1 ≠ 5/2 ≠ 7/3 ≠ 9/4

Therefore, it is non-proportional.

Answer: 286/19, 15.052632 and 1

                                                     15

                                                        19

Calculate; 858/57

You can see the division procedure, below.    

   \(\bf{\red{ \ \ \ \ \ 1 \ 5 }} \\ \bf{57 \ |\overline{8 \ 5 \ 8}}\\ \bf{ \ \ \underline{ - \ 5 \ 7}}\\ \bf{ \ \ \ \ \ 2 \ 8 \ 8}\\ \bf{ \ \ \underline{- \ 2 \ 8 \ 5}}\\ \bf{\ \ \ \ \ \ \ \ \ \ \ 3}\)

The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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The mixed numbers that have 12 as the LCD are 2 11/12 and 6 4/5. All other fractions do not have 12 as the denominator and are not equivalent.

Mixed numbers consist of a whole number and a fractional part. To add or subtract mixed numbers, the fractions must have the same denominator (the bottom number of the fraction).

The LCD (lowest common denominator) is the smallest number that all of the denominators can be divided into evenly. In this case, the LCD is 12.

2 11/12 and 6 4/5 both have 12 as the denominator. The denominator of 11/12 can be divided by 11 and 12, so it is the same as 12/12. The denominator of 4/5 can be divided by 4 and 12, so it is the same as 48/12 (4 x 12 = 48). Therefore, both fractions have the same denominator.

The other fractions do not have 12 as their denominator. 3 1/7 can be divided by 3, 7, and 12, so it is the same as 21/12 (3 x 7 = 21). 5 3/4 can be divided by 4, 5, and 12, so it is the same as 60/12 (4 x 5 = 60). 8 38/47 can be divided by 8, 47, and 12, so it is the same as 376/12 (8 x 47 = 376). Since none of these fractions are equal to 12/12, they are not equivalent to the other two fractions.

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Question :

Which mixed numbers have 12 as the LCD (lowest common denominator)?

2 11/12

3 1/7

5 3/4

6 4/5

8 38/47

Answer:

Step-by-step explanation:

yooyyo

(A) W is test MSE, X is variance, Y is squared bias, Z is training MSE is the best description of each line in linear regression model

From the given plot, we can see that:

The blue line (W) is decreasing with increasing number of predictors, which indicates that it represents variance.

The green line (X) is increasing with increasing number of predictors, which indicates that it represents training MSE.

The red line (Y) is decreasing with increasing number of predictors, which indicates that it represents test MSE.

The purple line (Z) is roughly constant and does not show any clear trend with increasing number of predictors, which indicates that it represents squared bias.

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Answer:

Step-by-step explanation:

All the unknown angles are

∠x = 95°

∠y = 105°

∠w = 30°

∠v = 70°

∠z = 80°

We have two geometrical figures.

We have to determine the unknown angles.

The sum of all the angles of a triangle is 180°.

According to the question -

Refer to image attached it is labelled with unknown angles.

Now -

In the figure a -

∠x + 85° = 180°     {Supplementary Angle}

∠x = 95°

and

∠y + 75° = 180°      {Supplementary Angle}

∠y = 105°

In figure b -

∠w = 30°         {Vertically Opposite angles}

∠v + 110° = 180°      {Supplementary angle}

∠v = 70°

Now, in the triangle -

∠w + ∠v + ∠z = 180°     { Sum of angles of Δ = 180° }

∠z = 180° - 100°  

∠z = 80°

Hence, all the unknown angles are

∠x = 95°

∠y = 105°

∠w = 30°

∠v = 70°

∠z = 80°

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Answer:

f(-4)   =20

Step-by-step explanation:

f(-4) =  \((4)^{2}\) +4 ( Insert -4 in)

f(-4) = 16+4

f(-4)   =20

Answer:

dose in MCG = 10.2 mcg

Total volume to be sent home = 1.836 ml (1836μl)

Step-by-step explanation:

weight of patient = 680g

dosage in mcg of medication = 15mcg/kg

This means that

for every 1kg weight, 15mcg is given,

since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.

1000g = 15mcg

1g = 15/1000 mcg = 0.015 mcg

∴ 680g = 0.015 × 680 = 10.2 mcg

Dosage in MCG = 10.2 mcg

Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:

50mcg = 1 ml

1 mcg = 1/50 ml = 0.02 ml

∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml

since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.

therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)

The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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Answer:

Step-by-step explanation:

Answer:

WT=63

Step-by-step explanation:

\( \frac{56}{5 \times x + 3} = \frac{40}{4 \times x - 3} \\ x = 12\)

So

\(5 \times x + 3 = 5 \times 12 + 3 = 63\)

Answer:

30 = 2·2·3

48 = 2·2·2·2·3

GCF = 6 (2·3)

LCM = 240 (2·3·5·8)

Step-by-step explanation:

Given:

The graph of a sine function.

To find:

The sine function.

Solution:

The general form of a sine function is

\(y=Asin(Bx+C)+D\)            ...(i)

Where, |A| is amplitude, \(\dfrac{2\pi}{B}\) is period, \(-\dfrac{C}{B}\) is phase shift and D is mid-line.

From the given graph it is clear that the minimum value of the function is -4 and the maximum value is 0.

\(|A|=\dfrac{Maximum-Minimum}{2}\)

\(|A|=\dfrac{0-(-4)}{2}\)

\(|A|=\dfrac{4}{2}\)

\(|A|=2\)

The graph is reflected across the mid-line, so A=-2.

And,

\(D=\dfrac{Maximum+Minimum}{2}\)

\(D=\dfrac{0+(-4)}{2}\)

\(D=\dfrac{-4}{2}\)

\(D=-2\)

Period of the function is 4π because it completer its one cycle in the interval of 4π.

\(4\pi=\dfrac{2\pi}{B}\)

\(B=\dfrac{2\pi}{4\pi}\)

\(B=\dfrac{1}{2}\)

Phase shift is \(\dfrac{\pi}{4}\).

\(-\dfrac{C}{B}=\dfrac{\pi}{4}\)

\(-\dfrac{C}{\frac{1}{2}}=\dfrac{\pi}{4}\)

\(C=-\dfrac{1}{2}\times \dfrac{\pi}{4}\)

\(C=-\dfrac{\pi}{8}\)

Putting \(A=-2,B=\dfrac{1}{2},C=-\dfrac{\pi}{8},D=-2\) in (i), we get

\(y=-2\sin\left(\dfrac{1}{2}x-\dfrac{\pi}{8}\right)-2\)

Therefore, the required equation is \(y=-2\sin\left(\dfrac{1}{2}x-\dfrac{\pi}{8}\right)-2\).