Simplify each algebraic expression. 5(10a−2)

The given system of linear equations has the following solution: x = -4 and x2 = 6.In the given question, we are provided with matrices that represent the final matrix form for a system of two linear equations in the variables x and x2.

Let's analyze each matrix and find the solution for the system.

Matrix:

1 0 | -4

0 1 | 6

From this matrix, we can determine the coefficients and constants of the system of equations:

x = -4

x2 = 6

Therefore, the solution to this system is x = -4 and x2 = 6.

Matrix:

1 -2 | 15

0 0 | 53

In this matrix, we can see that the second row has all zeros except for the last element. This indicates that the system is inconsistent and has no solution.

To summarize, the solution for the system of linear equations represented by the given matrices is x = -4 and x2 = 6. However, the second matrix represents an inconsistent system with no solution.

linear equations and matrices to further understand the concepts and methods used to solve such systems.

Learn more about matrix

brainly.com/question/28180105

#SPJ11

In order to answer the above question, we may thus state that the type of statistical inference in this scenario is null hypothesis testing.

A type of statistical hypothesis known as a null hypothesis claims that a particular collection of observations has no significance in statistics. The viability of theories is evaluated using sample data. Occasionally referred to as "zero," and represented by H0. The assumption made by researchers is that there may be a relationship between the factors. The null hypothesis, on the other hand, asserts that such a relationship does not exist. Although it might not seem significant, the null hypothesis is an important part of study.

The type of statistical inference in this scenario is hypothesis testing.

To know more about null hypothesis visit

https://brainly.com/question/28920252

#SPJ1

Answer:

Step-by-step explanation:

2(√x+2/2 - 1)² + 4 (√x+2/2 - 1)

2((√x+2/2)² + 1² - 2(√x+2/2)(1)) + 4√x+2/2 - 4

2(x+2/2 + 1 - 2(√x+2/2)) + 4√x+2/2 - 4

x + 2 + 2 - 4√x+2/2 + 4√x+2/2 - 4

x + 4 - 4

x

Answer:

the answer is x

Step-by-step explanation:

The expected loss per game is approximately -$0.31.

The terms we need to consider in this problem are: standard 52-card deck, face cards, and expected gain or loss.
To find the expected gain or loss per game, follow these steps:

1. Determine the probability of drawing a face card.
There are 12 face cards (Kings, Queens, and Jacks) in a standard 52-card deck. So the probability of drawing a face card is \(\frac{12}{52}\), which simplifies to \(\frac{3}{13}\).

2. Determine the probability of drawing a non-face card.
There are 40 non-face cards in the deck (52 cards - 12 face cards). So the probability of drawing a non-face card is \(\frac{40}{52}\), which simplifies to \(\frac{10}{13}\).

3. Calculate the expected gain or loss per game.
Expected gain or loss = (Probability of drawing a face card x gain from drawing a face card) + (Probability of drawing a non-face card x loss from drawing a non-face card)

4. Simplify the equation.
Expected gain or loss = \((\frac{3}{13} (2))  +  (\frac{10}{13} (-1))\)
Expected gain or loss = \(\frac{-4}{13}\)

Your expected loss per game is approximately -$0.31 (rounded to two decimal places).

To Know more about "probability" refer here:

https://brainly.com/question/30034780#

#SPJ11

Answer:

On factorizing 13824, we get

13824=2^9 ×3 ^3

So, cube root =2^3×3

Step-by-step explanation:

Answer:

(2/5)

Step-by-step explanation:

(-2/5) = -(2/5)

|-(2/5)| = (2/5)

Rate of the boat in still water: 75 km/h. Rate of the current: 9 km/h.

Let's call the rate of the boat in still water "b" and the rate of the current "c". When the boat is traveling upstream (against the current), its effective speed is b-c, and when it is traveling downstream (with the current), its effective speed is b+c.

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

372 = (b-c) * 6

408 = (b+c) * 4

We can simplify the first equation to: b-c = 62

And we can simplify the second equation to: b+c = 102

Now we have a system of two equations with two variables, which we can solve using elimination or substitution. Solving for b and c, we get:

b = 75 km/h

c = 9 km/h

Therefore, the rate of the boat in still water is 75 km/h and the rate of the current is 9 km/h.

Learn more about current from here:

https://brainly.com/question/29087214

#SPJ11

Answer:

D: SAS

Step-by-step explanation:

Answer:

Ok so I've had braces and it doesn't really hurt getting put in but it does hurt when they tighten them but you have nothing to worry about :)

Step-by-step explanation:

Answer:

They don't hurt when they put them in however you will feel mild soreness and discomfort as your mouth adjusts to them as with anything, for example, fillings, they feel gritty and uncomfortable at first but your mouth adjusts to it.

" There will be mild soreness or discomfort after the orthodontic wire is engaged into the newly placed brackets, which may last for a few days to a week."

I know its can be scary at first but its for the health of your teeth and not everyone gets that privilege, just make sure to take care of them properly.

Step-by-step explanation:

Answer:

14+9(x-1)=y

Step-by-step explanation:

If x is the number of pizza's being delivered and the first pizza costs $14 then that pizza is already accounted for by the 14 in the equation, so you subtract x by 1 before multiplying it by 9, then add the 14 to the product you then get the total cost: y

Answer:

7

Step-by-step explanation:

→ Work out area of circle

π × 10² = 100π = 314.159 (3 decimal places)

→ Divide area of circle by box area

314.159 ÷ 46 = 6.8295

→ Round answer as you can't get a decimal of a box

7

The area of a circle is given as πr².

The number of boxes of grass seeds required to cover the garden is 9 boxes.

A circle is a round-shaped figure that has no corners or edges. 

The area of a circle is given as:

Area = πr²

We have,

The radius of the circle = 10 m

Area of the garden:

= πr²

We can take,

π = 22/7 = 3.14

= 3.14 x 10 x 10

= 314 m²

The area of a box of grass seeds:

= 46 m²

The number of boxes of grass seeds to cover the garden area:

= 314 / 46

= 6.8 boxes

Thus,

The number of boxes of grass seeds required to cover the garden is 9 boxes.

Learn more about circle here:

https://brainly.com/question/24293810

#SPJ2

The likelihood that there are 1 man and 2 girls are selected is approximately 0.4357. We can use the following formula for the chance of an occurrence to determine the probability that one male and two female candidates are chosen:

P(event) equals (number of possible outcomes for the event) / (total number of possible outcomes) Out of a total of 25 pupils, the programme is choosing 1 male and 2 female participants. 

Using the combination formula, we can first determine the overall number of events that are possible: nCr equals n and (r! * (n-r)!) where r is the number of students being chosen, and n is the overall number of students (25). (3). Therefore, there are a total of the following outcomes: 25C3 = 25! / (3! * (25-3)!) = 25! / (3! * 22!) = 2300

Next, we need to determine how many different methods there are to choose 1 guy and 2 females. Utilizing the product law of chance, we can accomplish this: The number of methods is equal to the sum of the ways to select one man and two females. 

There are 11 methods to choose one guy out of 11, and there are 91 ways to choose two females out of 14. The overall number of options for choosing one man and two females is thus: 11 * 91 = 1001

Finally, we can enter these numbers into the likelihood of the occurrence formula as follows: P(1 man, 2 women) = 1001/2300 = 0.4357

Consequently, the likelihood that there are 1 man and 2 girls are selected is approximately 0.4357.

To know more about probability-

brainly.com/question/29381779

#SPJ4

Answer:

the answer is 7,184.47

Step-by-step explanation:

you can determine the weight of the concrete column in pounds = m * 2.20462 lbs/kg based on the given values of height (h), diameter (d), density (rho), and assuming a weight of 359 lbs (w) is not necessary for this calculation.

To find the weight of the concrete column in pounds, we can use the following steps:

1. Convert the diameter from millimeters to meters:

  d = 300 mm = 0.3 m

2. Calculate the cross-sectional area of the column:

  A = π * (d/2)^2

3. Calculate the volume of the column:

  V = A * h

4. Convert the density from milligrams per cubic meter to pounds per cubic meter:

  rho = 2.3 mg/m^3 = 2.3 * 10^-6 lbs/m^3

5. Calculate the mass of the column:

  m = V * rho

6. Convert the mass from kilograms to pounds:

  Weight (lbs) = m * 2.20462 lbs/kg

Using these calculations, you can determine the weight of the concrete column in pounds based on the given values of height (h), diameter (d), density (rho), and assuming a weight of 359 lbs (w) is not necessary for this calculation.

To learn more about Cross-sectional area - brainly.com/question/28579482

#SPJ11

Answer:

1/8

Step-by-step explanation:

Leonard spent 1 fourth of his money on a sandwich.

Fraction of money spent on sandwich = 1/4

He spent 2 times as much on a gift for his brother as on some comic books.

= 1/4 × 2

= 2/8

Hence, Fraction of money spent on Comic books = 2/8

He had 3 over 8 of his money left.

Let us represent his total money has: 1

The fraction of his money that he spent on the comic books is calculated as:

= 1 -( 1/4 + 2/8+ 3/8)

Lowest Common Denominator = 8

= 1 - (2 +2 + 3/8)

= 1- 7/8

= 1/8

Therefore, the fraction of his money that he spent on the comic books is 1/8

When a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

A double-napped cone is formed by rotating a straight line around another straight line that is parallel to it.

The intersection of a plane with a double-napped cone is referred to as a conic section. A degenerate conic section is formed when a plane intersects a double-napped cone at the vertex.

Thus, when a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

Learn more about conic section:

https://brainly.com/question/21098648

#SPJ11

Answer:

q=-3.4

Step-by-step explanation:

Answer:

The 23rd shape is expected to have 135 vertices

Step-by-step explanation:

The first shape has 3 vertices

Second 9 vertices

third 15 vertices

we can see that this follows an arithmetic pattern of first term 3 and common difference (15-9) = (9-3) = 6

So for the 23rd term, we will have;

a + 22d

so;

3 + 22(6)

= 3 + 132 = 135 vertices

Answer:

25

Step-by-step explanation:

25/32 = 0.78125 = 8 divided by 10.24

Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.

Answer:

Maliks

Step-by-step explanation:

By comparing this solution to the given form In Z(t) = -A(ta + 7), we can see that A = To - Ta and ta + 7 = kt.

The heat-transfer processes occurring following the death of an individual can be described using a mathematical model. The body temperature decreases over time until it reaches the ambient temperature.

This can be represented by a first-order differential equation. By solving the differential equation, the temperature of the body as a function of time can be obtained. The solution takes the form of an exponential decay with a constant factor.

(a) The word equation for the heat-transfer processes following the death of an individual can be stated as follows: "The rate of change of body temperature with respect to time is proportional to the temperature difference between the body and the environment."

(b) To convert the word equation into a mathematical model, we make the following assumptions:

- The body and the environment are in thermal equilibrium initially.

- The body loses heat solely through conduction and radiation.

- The surrounding environment remains at a constant temperature.

Let T(t) represent the temperature of the body at time t, and Ta represent the ambient temperature. The mathematical model can be expressed as:

dT/dt = -k(T - Ta)

where dT/dt represents the rate of change of body temperature, and k is a constant that determines the rate of heat loss.

(c) (i) To find the temperature of the body as a function of time, we solve the differential equation:

dT/dt = -k(T - Ta)

By separating variables and integrating, we get:

∫(1 / (T - Ta)) dT = -k ∫dt

Solving the integral and applying initial conditions, we obtain:

ln|T - Ta| = -kt + C

where C is the constant of integration.

(ii) Assuming the individual dies at time t = 0 and the body is discovered at time t = ty, we can substitute these values into the solution obtained above:

ln|To - Ta| = -k(0) + C

ln|To - Ta| = C

Therefore, the solution can be written as:

ln|T(t) - Ta| = -kt + ln|To - Ta|

T(t) - Ta = e^(-kt + ln|To - Ta|)

T(t) = Ta + (To - Ta)e^(-kt)

By comparing this solution to the given form In Z(t) = -A(ta + 7), we can see that A = To - Ta and ta + 7 = kt.

Learn more about ambient temperature here:

brainly.com/question/31229398

#SPJ11

Given the expression:

using the distributive property we get the following:

therefore, the simplified expression is 0

The translation direction of the image of triangle JKL is 10 units up.

In this problem, we are trying to determine the translation direction and number of units of the image of triangle JKL when vertex J becomes J'. The y-coordinate of vertex J originally at J(-1, -5) has changed to 5 in J'. This represents a change of 5 - (-5) = 10 units.

The change is positive, which means the translation direction is upwards. Therefore, the image of triangle JKL has been translated 10 units up.

https://brainly.com/question/23277238

#SPJ2

Answer:

First, you look at the y-intercept. It is positive 6 so you start at 6 on the y-axis. Then you look at the slope. It is negative 1/4. It is negative so the slope goes down and it goes down on the unit and 4 units right. That is how you graph y= -1/4x + 6