Which expression represents the expanded version of the expression below?

4x(3x+7)

The expression that models the area of the new room once the wall is knocked down is 4x^2 + 13x - 4.

To find the area of the new room, we need to multiply the length by the width. The length of the first room is given as (2x + 7), and the length of the second room is given as (2x - 1). Since the wall is being knocked down, we can combine the lengths to get the new length of the room, which is (2x + 7) + (2x - 1) = 4x + 6.

Now, we multiply the new length (4x + 6) by the width, which remains the same in both rooms. Let's assume the width is 'w.' So, the area of the new room is (4x + 6) * w.

Since we are not given the width value, we cannot simplify the expression further. Therefore, the area of the new room can be represented as (4x + 6) * w, which is equivalent to 4xw + 6w.

The expression that models the area of the new room once the wall is knocked down is 4x^2 + 13x - 4.

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The Logarithmic function is a mathematical operation that is used to determine the logarithm of a number.

The logarithm of a number x is the exponent to which a fixed number, the base, must be raised to produce x. The most common bases used are 10 and e. The formula for determining the logarithm of a number x base d is: log base d of x = (log base d of x)/(log base d of b).

For example, if we want to calculate the log base 10 of a number x, we would use the formula: log base 10 of x = (log base 10 of x)/(log base 10 of b). We can calculate the log base 10 of a number x by taking the logarithm of x and dividing it by the logarithm of the base, 10. The result will be the log base 10 of x.

For example, if we want to calculate the log base 10 of 25, we would calculate the logarithm of 25 and divide it by the logarithm of 10. The calculation would be: log base 10 of 25 = (log base 10 of 25)/(log base 10 of 10) = (1.3979)/(1) = 1.3979. This means that the log base 10 of 25 is 1.3979.

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Answer: The form of payment that Courtney can lose and not get back would be cash.

Step-by-step explanation:

The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.

Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated  verification process.

Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!

-From Certified 5th Grade Honors Student

ANSWER:

0

EXPLANATION:

3/7=0.4

if the number to the right of decimal point is 0.5 and higher,then add 1 to the left of the decimal point.

if the number to the right is less than 0.5,leave the number to the left and remove the digit to the right decimal point.

Hey there!

The answer to your question is y = -3/4x - 3

If an equation in slope-intercept form is parallel to another equation, they will both have the same slope. So, we know part of the equation:

y = -3/4x + b

Now, we have to solve for b. We know that it has to pass through the given point, (4, -6), so we can plug the points into the equation, and solve for b:

-6 = (-3/4)(4) + b

-6 = -3 + b

-3 = b

We know that "-3" is b, so that means the equation in slope-intercept form is y = -3/4x - 3

Hope it helps, and have an amazing day! You've got this!

The equation of the line is 4y + 3x +12 = 0.

If a line has a given slope m and cuts a given intercept c on the y axis, then then equation of the line can be written as y = mx + c .

Given,

The line is parallel to the line y = -3/4x + 1​.

Also, the line y = -3/4x + 1​ has slope equal to -3/4.

Therefore, value of m = -3/4.

The required line is y = -3/4x + c

But, the line also passes through (4,-6).

Therefore,                 -6 = -3/4(4) +c

or                                c = -6 + 3

                                   c = -3

Substituting c and m in y = mx + c:

                                       y = -3/4x + (-3)

Hence, the required line is 4y + 3x +12 = 0.

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Answer:

1/10 = rare

Step-by-step explanation:

Answer:  165,24

Step-by-step explanation: do 17 x 1.35 then get the answer for it and times it by 7.2 hope this helps

Answer:

  B.  False

Step-by-step explanation:

You want to know if it is true that when each of seven persons in a group shakes hands with each of the other six persons, a total of forty-two handshakes occurs.

The count of 42 handshakes includes every one of 7 shaking hands with each of the remaining 6, without regard to whether they met before.

The count will include A shaking hands with B, and B shaking hands with A. That handshake will be counted twice, so the number 42 overstates the actual number of handshakes by a factor of 2.

It is false that there will be 42 handshakes. (There will be only 21.)

The distributions of the numbers X and Y of resulting heads and tails [(pλ)^k / k! e^(-pλ)] [(1-p)^λ / (1-p+ p/k+1)]  and [(pλ)^m / m! e^(-pλ)] [(1-p)^λ / (1-p+ p/m+1)]. Here,  X and Y are independent.

Let X be the number of heads and Y be the number of tails. Then we have:

X + Y = N

We want to find the distributions of X and Y. Let's start with X:

P(X = k) = P(X = k | N = n)P(N = n)

where P(X = k | N = n) is the probability of getting k heads given that the number of flips is n. This is simply a binomial distribution with parameters n and p:

P(X = k | N = n) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient.

The probability of N being equal to n is given by the Poisson distribution:

P(N = n) = e^(-λ) λ^n / n!

Therefore, we have:

P(X = k) = ∑ P(X = k | N = n)P(N = n)

   = ∑ (n choose k) p^k (1-p)^(n-k) e^(-λ) λ^n / n!

   = e^(-λ) / k! ∑ (n choose k) p^k (1-p)^(n-k) λ^n

   = e^(-λ) / k! (pλ + (1-p)λ)^k ∑ ((pλ + (1-p)λ)/λ)^n / (k+1)^n

   = e^(-λ) / k! (pλ + (1-p)λ)^k e^(pλ+(1-p)λ) / (k+1)

   = [(pλ)^k / k! e^(-pλ)] [(1-p)^λ / (1-p+ p/k+1)]

The first factor in the last expression is the Poisson distribution with parameter pλ, which means that X has a Poisson distribution with parameter pλ.

Similarly,  Y has a Poisson distribution with parameter (1-p)λ is  [(pλ)^m / m! e^(-pλ)] [(1-p)^λ / (1-p+ p/m+1)]

Now we need to show that X and Y are independent. To do this, we need to show that for any values k and m:

P(X = k and Y = m) = P(X = k) P(Y = m)

Using the expressions we found earlier for P(X = k) and P(Y = m), we have:

P(X = k and Y = m) = e^(-λ) / k! [(pλ)^k e^(-pλ)] [(1-p)^m λ^m e^(-(1-p)λ)]

P(X = k) P(Y = m) = e^(-λ) / k! [(pλ)^k e^(-pλ)] [(1-p)^λ / (1-p+ p/m+1)] e^(-λ) / m! [(1-pλ)^m e^(pλ)]

Notice that the two expressions are the product of two factors, one depending on k only, and the other depending on m only. Therefore, the joint distribution of X and Y factorizes into the product of their marginal distributions, which means that X and Y are independent.

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Answer:

Monkey says NO

Step-by-step explanation:

Monkey says A^2 + B^2 = C^2. Monkey do math, gets C = 8.5. So close, monkey sad. Not right triangle.

The proportional relation on the graph can be written as:

y = (4/5)*x

We have a graph that relates the height of a tree, y, in feet, with the time, x, in years.

We know that this is a proportional relationship, so it has the form:

y = k*x

Where k is the constant of proportionality.

Notice that the line passes through (10, 8), replacing these values we will get:

8 = k*10

Solving for k we get:

8/10 = k

4/5 = k

Then the proportional relation is:

y = (4/5)*x

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Answer:

7 :)

Step-by-step explanation:

Sharonda is plotting quadrilateral PQRS on the graph below She will plot the fourth and final vertex, S, at (9, 5), the length of side PS will be 11 units.

A quadrilateral is a four-sided polygon. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. There are several types of quadrilaterals, including: Square, rectangle, parallelogram, rhombus, trapezoid, and kite.

Length of side PS can be calculated using the distance formula,

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Where,

P(-2, 5) = (\(x_1,y_1\)) (the coordinate of P is gotten from the graph).

Given that,

S(9, 5) = (\(x_2,y_2\))

PS = \(\sqrt{(9-(-2))^2+(5-5)^2}\)

PS = \(\sqrt{11^2+0^2}\)

PS = \(\sqrt{121}\)

PS = 11units.

Thus, the answer is 11 units.

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Step-by-step explanation:

Length of the room is 5 ft and the width is 8 ft.

Perimeter is equal to the sum of all sides of the room.

The shape of room is rectangle.

The perimeter of rectangular room is given by :

\(P=2(L+B)\\\\P=2(5+8)\\\\P=26\ ft\)

Area of a rectangular shaped room is given by :

\(A=L\times B\\\\A=5\times 8\\\\A=40\ ft^2\)

So, the perimeter and area of the rug are 26 feet and 40 sq feet.

Answer:

d

Step-by-step explanation:

u just have to plug in the numbers

f(-3)= -3^2

f(-3)= 9

g(4)=2(4)-3

g(4)=5

9+5=14

I hope I'm right and hope I helped:)

Tom bought 4 magazines and 12 protein bars

Given,

Tom wants to buy some protein bars and magazines for a trip.

The cost of one protein bar = $0.70

The cost of one magazine = $2.50

The sales tax = 6.5%

The money spend = $20

We have to find the number of each item bought;

Here,

Let x be the number of magazines Tom purchased.

Then number of protein bars purchased = 3x

So,

Total rate of items = 2.5x + 3x × 0.7 = 2.5x + 2.1x = 4.6x

Add sales tax  = 4.6x (1 + 0.065) = 4.899x

This must be less than 20

So,

4.899x < 20

x < 20/4.899

x < 4.082

Then,

x = 4

3x = 3 x 4 = 12

Therefore,

Tom bought 4 magazines and 12 protein bars

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Answer:

whole

Step-by-step explanation:

add the whole numbers first, then the fractions

Answer:

\(you \: add \: the \: whole \: number \: then \\ the \: fraction\)

Step-by-step explanation:

\(this \: helps \: to \: make \: the \: addition \\ more \: easier\)

Answer:

false

Step-by-step explanation:

Answer:

The fraction equivalent to 2/11 and the numerator is 8 will be 8/44.

In Fechner's Law, as one variable increases arithmetically, the other variable increases geometrically.

In Fechner's Law, as one variable increases arithmetically, the other variable increases: b. geometrically.

Fechner found in his research that different people have different sensitivities to certain stimuli. For example, the ability to see differences in light can affect the quality of a person's vision. It has also been noted that people are sensitive to changes in stimuli due to emotional impact. He used this to create another version of Weber's law, which he called die Maß formel, or "measurement formula." Fechner's law states that the force of thought is proportional to the logarithm of the force.

If the intensity of the stimulus is tripled (eg 3×1), the sensitivity doubles from its original value (eg 1+1).

If the intensity of the stimulus is tripled again (eg 3×3×1), the corresponding sensitivity will be three times its original value (eg 1+1+1).

So, for the stimulus intensity to double, the perceived intensity only increases.

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The distance of 40 lb will be 5ft, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

The fulcrum be located from the 40 lb.

The weight of bar is 9ft long.

Now, we will calculate the distance,

40x = 50(x-1)

40x = 50x - 50

40x - 50x = -50

-10x = -50

x = 5

Therefore, the required answer is 5ft.

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(a) To identify the type of control system being used, you can look for certain characteristics and components within the system: Open-loop Control ,Feedback Control,Feedforward Control

1. Open-loop Control: In an open-loop control system, the output is not measured or compared to the desired reference input. It relies solely on the input command to produce the output. It does not use feedback to adjust or correct the output. Examples include a simple timer or an automatic door that opens for a fixed duration when a button is pressed.

2. Feedback Control: In a feedback control system, the output is measured and compared to the desired reference input. Feedback is used to continuously monitor and adjust the output to match the desired input. The system makes corrections based on the feedback signal. Examples include a thermostat regulating room temperature or a cruise control system maintaining a constant speed in a vehicle.

3. Feedforward Control: In a feedforward control system, the system anticipates disturbances or changes in the input and adjusts the control output accordingly, without relying on feedback. It aims to compensate for known disturbances before they affect the system output. Examples include a temperature control system that adjusts heating based on external weather conditions or a robotic arm compensating for anticipated load changes.

4. Cascade Control: Cascade control is a combination of feedback and feedforward control. It uses multiple control loops, where the output of one control loop is used as the setpoint or reference input for another control loop. It allows for better disturbance rejection and improved control performance. Examples include a temperature control system where one loop controls the primary heating and another loop controls the secondary heating.

5. Ratio Control: Ratio control is used when maintaining a fixed ratio between two variables is critical. It adjusts the manipulated variable in proportion to changes in the controlled variable to maintain the desired ratio. Examples include controlling the fuel-to-air ratio in a combustion system or maintaining a constant mixing ratio of ingredients in a chemical process.

(b) Here are five examples with appropriate symbols:

1. Open-loop Control: A simple timer that turns on a light for a fixed duration when a switch is pressed can be represented as:

```

Switch -----> [ Timer ] -----> Light

```

2. Feedback Control: A room temperature control system with a thermostat can be represented as:

```

Setpoint -----> [ Controller ] -----> [ Heater ] -----> [ Temperature Sensor ] -----> [ Comparator ] -----> Error

                                             |

                                             v

                                        Temperature

```

3. Feedforward Control: A temperature control system adjusting heating based on external weather conditions can be represented as:

```

Weather Conditions -----> [ Feedforward Controller ] -----> [ Heater ] -----> [ Temperature Sensor ] -----> [ Comparator ] -----> Error

                                                              |

                                                              v

                                                         Temperature

```

4. Cascade Control: A temperature control system with primary and secondary heating loops can be represented as:

```

Setpoint -----> [ Primary Controller ] -----> [ Primary Heater ] -----> [ Secondary Controller ] -----> [ Secondary Heater ] -----> [ Temperature Sensor ] -----> [ Comparator ] -----> Error

                                                                                   |

                                                                                   v

                                                                              Temperature

```

5. Ratio Control: A system maintaining a constant fuel-to-air ratio in a combustion process can be represented as:

```

Fuel Flow -----> [ Ratio Controller ] -----> [ Fuel Valve ] -----> [ Air Flow ] -----> [ Air Valve ]

```

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The system of equations 12x + 51y = 156 and -8x - 34y = -104 has infinitely many solutions

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Given the equation:

12x + 51y = 156

Dividing by 3:

4x + 17y = 52       (1)

Also:

-8x - 34y = -104

Dividing by 2:

-4x - 17y = -52    (2)

To solve both equation by elimination, add equation 1 and 2:

0 = 0

The equation has infinitely many solutions

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The volume of the reservoir with an isosceles triangle surface and trapezoid cross-sections is 375,000 cubic meters.

To find the volume of the reservoir with an isosceles triangle surface and trapezoid cross-sections, we'll follow these steps:

1. Identify the dimensions of the trapezoid: Given that the top side (base) of the trapezoid is 100 m, its bottom side (smaller base) will be half of that, so 50 m. Similarly, the height of the trapezoid is half the length of the top side, so 50 m.

2. Calculate the area of the trapezoid cross-section: To find the area of a trapezoid, we use the formula A = (1/2)(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the two bases, and h is the height. In our case, A = (1/2)(100 + 50)(50) = (1/2)(150)(50) = 3750 square meters.

3. Determine the length of the reservoir: The length of the reservoir is given as 100 m.

4. Calculate the volume of the reservoir: Finally, to find the volume, we multiply the area of the trapezoid cross-section by the length of the reservoir. V = A * L = 3750 * 100 = 375,000 cubic meters.

So, the volume of the reservoir with an isosceles triangle surface and trapezoid cross-sections is 375,000 cubic meters.

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The p-value for the test is 0.006, which is less than the commonly used significance level of 0.05. This suggests that there is a significant association between COVID-19 and life expectancy in the 15 states tested.

To obtain the p-value for the null hypothesis that the slope is zero (i.e., no significant association between COVID-19 and life expectancy), we need to use the t-distribution.

The formula for calculating the t-statistic is:

t = (b - 0) / SE

where b is the estimated slope coefficient, 0 is the hypothesized value of the slope coefficient under the null hypothesis, and SE is the standard error of the slope coefficient.

In this case, b = 32.55, 0 = 0, and SE = 10.5. Therefore, the t-statistic is:

t = (32.55 - 0) / 10.5 = 3.1 (rounded to one decimal place)

To find the p-value, we need to look up the t-distribution table with n-2 degrees of freedom (where n is the sample size, which is 15 in this case) and find the probability of getting a t-value greater than or equal to 3.1 or less than or equal to -3.1 (since we are conducting a two-tailed test).

Using a t-distribution table or calculator, we find that the probability of getting a t-value of 3.1 or greater (or less than -3.1) with 13 degrees of freedom is approximately 0.006.

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Answer:

3.8

Step-by-step explanation:

Answer:

A = 45 cm²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = \(\frac{1}{2}\) h( b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases

Here h = 5, b₁ = 10 and b₂ = 8 , then

A = 0.5 × 5 × (10 + 8) = 0.5 × 5 × 18 = 45 cm²

Answer: 189 teens

Step-by-step explanation:

Given

- There are 19% of teens who like to volunteer at animal shelters

- There are in total 995 teens

Solve

19% × 995= 189.05

189.05≈189 (Since people must be in whole numbers, we need to round)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

8

Step-by-step explanation:

A is at -6

B is at 2

The distance between the two numbers is 8 Units

Answer:

326.5

Step-by-step explanation: