Write the augmented matrix for the following system of equations.
-2z=-4y-9x
0=4x+6z+2
2z=2+3y

The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = \(^{52} C_{2}\)

And, the total number of ways of  getting exactly one face cards

= \(^{12} C_{1} \times ^{40} C_{1}\)  + \(^{40} C_{1} \times ^{12} C_{1}\)

= 2\(^{40} C_{1} \times ^{12} C_{1}\)

Therefore, the probability of getting exactly one face card

= \(\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }\)

\(= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }\)

\(= \frac{2(40\times 12)}{26\times 51}\)

\(=\frac{2\times 480}{1326}\)

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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Answer: -3, -2.4, -2 1/4, -1.5, -1 1/8

Step-by-step explanation:

The list that orders the numbers from least to greatest is; -3, -2.4, -2 1/4, -1.5, -1 1/8

Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. It refers to those as closed number lines. Number lines might be alternatively left empty or blank. A number ladder is a vertical number line.

We have been given number line going from negative 4 to positive 4.

Negative 2.4, negative 1.5, negative 2 and one-fourth, negative 3, negative 1 and one-eighth

For this we need to remember the number line, we have that that:

-3 <-2.4 < -2 < 1/4 <-1.5 < -1 <  -1 1/8< 0

We go from the big negative numbers, to the small negative numbers, the zero, the small positive numbers, the big positive numbers.

Therefore, the numbers from least to greast the correct options are:

-3, -2.4, -2 1/4, -1.5, -1 1/8

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Answer:

Below in bold.

Step-by-step explanation:

a) 52 = 5.2 * 10 so the result is 348.4 * 10 = 3484.

b) 6.7 is a tenth of 67 so the result is  348.4 / 10 = 34.84.

c) 348.4  - 52 = 296.4.

The complete sentences are

Draw a segment 6 centimeters long.

Then from one endpoint, draw a 30° angle.

To construct a triangle, we need to know the length of three sides, the length of two sides and the measure of the angle between them, or the length of one side and the measure of the two adjacent angles.

In the given problem we know the length of the sides hence, we can follow the given steps to draw the required triangle

Here we have

Equal length of the side of the triangle = 6 cm

Since the sides are equal the resultant triangle will be an equilateral triangle

To draw a triangle with all side lengths equal to 6 centimeters, we need to follow these steps:

Once all three sides are drawn, you can verify that the triangle is equilateral by measuring the length of each side.

Therefore,

The complete sentences are

Draw a segment 6 centimeters long.

Then from one endpoint, draw a 30° angle.

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The required maximum volume of the box is 2ft³.

Volume is a measurement of how much space an object takes up.

We can calculate the amount of something needed to fill it, like water for a bottle, tank, or aquarium.

Amount of space that stuff takes up - that's what we mean when we talk about volume.

Stuff is anything that has mass and takes up room.

When scientists are measuring volume, they usually use cubic meters.

So, calculate as:

V=x·y²

2x+y=3

y=3-2x

V = x·(3-2x)² = x·(9-12x+4x²) = 9x - 12x²+4x

V ` = 9-24x+12x² = 3(4x²-8x+3) = 3(4x²-6x-2x+3)

= 3[2x(2x-3)-(2x-3)] = 3(2x-3)(2x-1)

When the most amount is present: V ` = 0

Then,

2x-3 = 0  

2x = 3              

x = 1.5 (That's wrong, 'cause y = 0.)

or: 2x-1 = 0

2x = 1

x = 0.5,  y = 3 - 2 · 0.5 = 3 - 1 = 2

V max = 0.5 · 2² = 0.5 · 4 = 2 ft³

Therefore, the required maximum volume of the box is 2ft³.

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

yea he is wrong

Step-by-step explanation:

He is wrong because you cant not just switch the variable. If you move the variable the value will change.

To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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Change in Freezing Point ∝ Amount of Solute Added is the mathematical relation between change in freezing point and addition of solute added.

The freezing point of a fluid has been the degree at which it transforms from into a solid at atmospheric pressure.

At the freezing point, these two phases, liquid and solid, are in equilibrium, which means but both liquid or solid solvent things occur at the same time. The freezing point of a material is affected by air pressure.

The principal determinants are the kinds of molecules that make up the liquid.

If the intermolecular interactions between its molecules are strong, it has a high freezing point.

When the forces are weak, the freezing point is comparatively low.

The freezing point of a liquid or the glass transition temperature of a solids happens when liquid phases are in balance.

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As per the concept of average rate of change, the best estimate for the number of miles Michele would cycle in 2 hours is 24 miles

Here we have given the scatter plot shows the relationship between the number of hours Michele cycles on different days and numbers of miles traveled each day.

Then the average rate of change is calculated as,

=> (5 - 2) / (0.50 - 0.25)

=> 3/0.25

=> 12.

Then the best estimate for the number of miles Michele would cycle in 2 hours is calculated as,

=> 2 x 12

=> 24.

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The x-component of the vector ⃗ is -9.98 and the y-component is 8.53.

We can find the x and y components of the vector ⃗ by using trigonometry. The magnitude of the vector is given as 13.1, and the direction of the vector is 50∘ counter-clockwise from the -axis. We can use the cosine and sine functions to find the x and y components, respectively.

cos(50∘) = -0.6428, sin(50∘) = 0.7660

x-component = magnitude x cos(50∘) = 13.1 x (-0.6428) = -9.98

y-component = magnitude x sin(50∘) = 13.1 x (0.7660) = 8.53

Therefore, the x-component of the vector ⃗ is -9.98, and the y-component is 8.53.

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The x-component of the vector is approximately 8.375 and the y-component is approximately 9.955.

To find the x- and y-components of the vector, we can use trigonometry.

Given that the magnitude of the vector is 13.1 and the direction is 50° counter-clockwise from the - axis, we can determine the x- and y-components as follows:

The x-component (horizontal component) can be found using the formula:

x = magnitude * cos(angle)

x = 13.1 * cos(50°)

x ≈ 8.375

The y-component (vertical component) can be found using the formula:

y = magnitude * sin(angle)

y = 13.1 * sin(50°)

y ≈ 9.955

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The probability that a student has a brother given that they have a sister can be found to be 4 / 10 or 2 / 5.

From the table, we see that the number of students who have a brother and a sister would be 4 out of 10 students.

This means that the probability that a student has a brother given that they have a sister would be:

= Number of students who have a brother and sister / Number of students with sisters

= 4 / 10

When taken to the simplest form, this is:

= ( 4 / 2 ) / ( 10 / 2 )

= 2 / 5

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Answer:

log4 (116)=−2

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base (4)(4) of the right side (116)(116) equalsthe exponent (−2)(-2).

When the nuII hypοthesis is true, the expected vaIue οf the t statistic is 0.

The t-statistic in statistics measures hοw far an estimated vaIue οf a parameter deviates frοm its hypοthesised vaIue in reIatiοn tο its standard errοr.

T symbοI in statistics mean Test statistic fοr t-test ( t-scοre )

This is because the t statistic measures the difference between the sampIe mean and the nuII hypοthesis mean in units οf standard errοr, and when the nuII hypοthesis is true, there is nο difference between the sampIe mean and the nuII hypοthesis mean, resuIting in a t statistic οf 0.

Hοwever, it is impοrtant tο nοte that the distributiοn οf t statistics varies depending οn the sampIe size and the IeveI οf significance chοsen. Therefοre, even when the nuII hypοthesis is true, the οbserved t statistic may deviate frοm 0 due tο randοm sampIing errοr. In practice, a t statistic that is cIοse tο 0 and nοt statisticaIIy significant (i.e., dοes nοt reject the nuII hypοthesis) prοvides evidence that the nuII hypοthesis is pIausibIe.

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The query is about probability and complements. A pair of dice is rolled, and the outcome is interesting since the resultant number is odd. The aim is to identify whether the complement of this event is the event of rolling an even number or one of the other choices supplied.

An event's complement is the collection of outcomes that are not included in the event. As a result, the solution will be the set of outcomes that correspond to rolling an odd number on a pair of dice.

The alternatives are as follows: (a) a number larger than 8, (b) a number less than 5, (c) an even number, and (d) a multiple of 5.

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The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4

The second derivative of v with respect to t, we will differentiate v twice.

v = 2t² + 7t + 11

First, let's find the first derivative of v with respect to t (dv/dt):

dv/dt = d/dt (2t² + 7t + 11)

Using the power rule of differentiation, we differentiate each term separately:

dv/dt = 2(2t) + 7(1) + 0

dv/dt = 4t + 7

Now, let's find the second derivative of v with respect to t (d²v/dt²):

d²v/dt² = d/dt (4t + 7)

Again, using the power rule of differentiation, we differentiate each term separately:

d²v/dt² = 4(1) + 0

d²v/dt² = 4

Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.

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Answer:

3/25

Step-by-step explanation:

12% = 12/100 = 6/50 = 3/25

Answer: no

Step-by-step explanation:

vertical line test

Answer:

Maximum

Step-by-step explanation:

Answer:

Maximum

Step-by-step explanation:

To transform triangle ABC on the grid, a rotation, a translation, and a reflection were performed. The rotation was done by rotating the triangle around a point, the translation involved shifting the entire triangle without rotating it.

Rotation: To rotate triangle ABC, a specific point of rotation needs to be chosen. Let's say the point of rotation is point P. Each vertex of the triangle is rotated around point P by a certain angle, maintaining the same shape and size of the triangle.

Translation: For a translation, the entire triangle is shifted in a particular direction without rotating it. This can be done by moving each vertex of the triangle the same distance and direction, while maintaining the same shape and size.

Reflection: To reflect triangle ABC, a line of reflection is needed. Each vertex of the triangle is mirrored across the line of reflection, resulting in a flipped image of the triangle.

It's important to note that the specific details of the rotation, translation, and reflection (such as the angle of rotation, direction of translation, or line of reflection) were not provided in the question, so the actual graphical representation of these transformations cannot be described without further information.

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One reason for Emma's extreme hunger after working for five straight hours on her psychology paper without eating is that her blood glucose level has dropped. Option C.

Our body's supply of glucose is drained when we participate in lengthy mental or physical activity without eating, which lowers blood sugar levels. The brain receives messages from the stomach-dropping that indicate a need for food.

Emma's body sent hunger signals since the prolonged period of intense work had drained her glucose supplies. Several hormones, notably the appetite-stimulating hormone ghrelin, influence this hungry response. Emma's hunger in this situation is mostly caused by the decline in blood glucose levels.

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The complete question is:

Emma worked for five straight hours on her psychology paper and did not stop to eat. After finishing her paper she felt extremely hungry. One reason for her hunger is that her:

A. leptin levels are high

B. blood glucose level has increased

C. blood glucose level has dropped

D. ghrelin production is low

The base 10 value of the 3-digit hexadecimal number 2E5 is 741. The probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters is 27/512.

a) To convert a hexadecimal number to its decimal equivalent, you can use the following formula:

(decimal value) =\((last digit) * (16^0) + (second-to-last digit) * (16^1) + (third-to-last digit) * (16^2) + ...\)

Let's apply this formula to the hexadecimal number 2E5:

(decimal value) = \((5) * (16^0) + (14) * (16^1) + (2) * (16^2)\)

= 5 + 224 + 512

= 741

Therefore, the base 10 value of the 3-digit hexadecimal number 2E5 is 741.

b) To find the probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters, we need to determine the number of valid options and divide it by the total number of possible 3-digit hexadecimal numbers.

The number of valid options with only letters can be calculated by considering the following:

Therefore, the total number of valid options is 6 * 6 * 6 = 216.

The total number of possible 3-digit hexadecimal numbers can be calculated by considering that each digit can be any of the 16 possible characters (0-9, A-F), allowing repetition. So, we have 16 choices for each digit.

Therefore, the total number of possible 3-digit hexadecimal numbers is 16 * 16 * 16 = 4096.

The probability is then calculated as:

probability = (number of valid options) / (total number of possible options)

= 216 / 4096

To simplify the fraction, we can divide both numerator and denominator by their greatest common divisor, which in this case is 8:

probability = (216/8) / (4096/8)

= 27 / 512

Therefore, the probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters is 27/512.

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Answer: 1.133333

Step-by-step explanation:

The value of the expression \(\frac{17}{15}\) .

Simplification means simplifying processes involved in work towards consistency of efforts, costs and time. Fraction questions in mathematics frequently require lengthy calculations and complicated sums. Some pupils find it more challenging and require more time to solve. But don't worry—there is a solution for you in this article on math simplification. It will assist you in finding simple ways to simplify fractions. You'll discover what simplification is, how and where to simplify fractions, and the procedures involved in simplifying fractions in this article. Additionally, you'll learn the exact steps to take.

Here, do normal simplification using BODMAS rule.

Hence, the required value is \(\frac{17}{15}\)

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The value of 2² + {[1 x (5 - 2)] x 3 using PEDMAS is 13.

To simplify the expression 2² + {[1 x (5 - 2)] x 3}, we will use PEDMAS

First, within the innermost parentheses, we have 5 - 2, which equals 3.

So the expression becomes: 2² + {[1 x 3] x 3}.

Next, we simplify the multiplication within the curly brackets: 1 x 3 equals 3.

= 2² + {3 x 3}.

Now, we evaluate the exponent 2², which means 2 raised to the power of 2. It equals 4.

= 4 + {3 x 3}.

Finally, we multiply within the curly brackets: 3 x 3 equals 9.

= 4 + 9.

Adding 4 and 9, we get the final result: 13.

Therefore, 2² + {[1 x (5 - 2)] x 3} equals 13.

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The solution is, A. Solve the top equation for x., is the best thing to do as a first step in using substitution to solve the system of equations.

Linear equations are equations that have constant average rates of change, slope or gradient.

here, we have,

given that,

3x+y=-3

2x-3y=-13

and, we have,

A. Solve the top equation for x.

B. Solve the top equation for y.

C. Solve the bottom equation for x.

D. Solve the bottom equation for y.

we know that,

The solution is, A. Solve the top equation for x., is the best thing to do as a first step in using substitution to solve the system of equations.

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No, the Leaning Tower of Pisa is not in stable equilibrium. Stable equilibrium refers to an object being in a balanced state where even if it is displaced slightly, it will return to its original position. In the case of the tower, its leaning position indicates that it is not in stable equilibrium.

To determine how much farther the tower can lean before becoming unstable, we need to consider the concept of the center of gravity. The center of gravity is the point where the weight of an object can be considered to act. In the case of the tower, the center of gravity is not directly above its base due to the lean.

As the tower leans further, the center of gravity moves away from the base, creating a greater moment or force that tries to topple the tower. Eventually, this force will overcome the tower's ability to maintain its balance, causing it to become unstable and potentially collapse.

To calculate the maximum lean before instability, we need to determine the angle at which the tower would no longer be able to support itself. This can be done using trigonometry and the tower's dimensions. However, since the tower is a historical landmark and a significant engineering feat, measures have been taken to ensure its stability and prevent it from toppling over.

In conclusion, while the Leaning Tower of Pisa is not in stable equilibrium, it has been stabilized to prevent further leaning and potential collapse. The exact maximum lean before instability is not relevant in this context, as the tower's preservation and safety have been prioritized.

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Answer:

0.0000012  = 1.2 x 10⁶ (that is the scientific notation)

Step-by-step explanation:

The decimal  moves 6 places to the right

The 6 then becomes the exponent in a* 10^b

And (a) must be a 10 > number > 1

b = number of places the decimal moves

Answer:

1.2 * 10 ^6

Step-by-step explanation:

0.0000012

Move the decimal  6 places to the right

The 6 becomes the exponent in

a* 10^b  a must be a number 1 or greater but less than 10

b is the the number of places the decimal moves (+ to the right, - to the left)

000001.2

Then the number becomes 1.2 * 10 ^6

Answer:

4

Step-by-step explanation:

Find f(3), so substitute 3 for x

f(3) = |3-5| + 2

|-2| + 2

2 + 2

4

Answer:

32 because I Don't know please vote my answer please

Answer:

12 (10) cm 937 637 = hafe 2929888389292822