PLEASE HURRY WILL GIVE BRAINLIEST

c=4a+4b solve for b

There ought to be infinitely many solutions.

How many solutions can a system of 3 linear equations with 5 variables have?

There are infinitely many solutions. Assuming the 3 linear equations are linearly independent you have 2 free variables that can be chosen freely and depending on those two values you can find the 3 remaining variables as function of those two so for any choice of those two variables you can find a solution. If the equations are not linearly independent you have effectively only 1 or two equations so you can pick 4 or 3 variables freely and then the remaining variable or variables are function of these.

How do you solve a system of equations with 3 variables?
Simultaneous equations. Easy, if they are all linear. Possibly difficult otherwise. Basically pick 1 variable and 1 equation to rearrange so that variable is expressed in terms if the other 2. Then simplify. Now you have 2 equations in 2 variables. Repeat with the remaining 2 variables. When you have solved for the last variable, you can then substitute to solve for the second last. Then backtrack to the original substitution and solve that. General advice that works even for nonlinear equations.

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Distance for the anchor drop every 5 seconds is,

⇒ E = 63 meters

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

A big ship drops its anchor.

Here, E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).

E = - 2.4t + 75

Now, Distance for the anchor drop every 5 seconds is,

Put t = 5;

E = - 2.4t + 75

E = - 2.4 × 5 + 75

E = - 12 + 75

E = 63 meters

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Therefore, Pump B will have a longer average cycle time compared to Pump A.

To determine which pump will have a longer average cycle time, we need to calculate the cycle time for each pump based on the given information and compare the results. The cycle time for a single-server system can be calculated using Little's Law: Cycle Time = (1 / Arrival Rate) * (1 / (1 - Utilization))

Given:

Arrival Rate = 0.2 car per minute

Squared-Coefficient of Variation (CV^2) for Arrival Rate = 1

Utilization can be calculated as the product of the mean effective process time and the arrival rate:

Utilization = Mean Effective Process Time * Arrival Rate

For Pump A:

Mean Effective Process Time (A) = 4 minutes

Squared-Coefficient of Variation for Pump A = 0.5

Utilization (A) = 4 * 0.2 = 0.8

For Pump B:

Mean Effective Process Time (B) = 3 minutes

Squared-Coefficient of Variation for Pump B = 5

Utilization (B) = 3 * 0.2 = 0.6

Now, let's calculate the cycle time for each pump:

Cycle Time (A) = (1 / 0.2) * (1 / (1 - 0.8))

= 5 minutes

Cycle Time (B) = (1 / 0.2) * (1 / (1 - 0.6))

= 2.5 minutes

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Answer:

Number of brownies = 30

Number of cookies = 15

Step-by-step explanation:

Given:

Cost of each brownie = $2

Cost of each cookie = $1.5

Total number of treats = 45

Total amount = $82.50

Find:

Number of cookies and brownie

Computation:

Assume;

Number of brownies = b

Number of cookies = c

So,

b + c = 45........eq1

2b + 1.5c = 82.50...........eq2

Eq1 x 2

2b + 2c = 90 ..................eq3

Eq 3 - Eq 1

0.5c = 7.5

c = 7.5 / 0.5

Number of cookies = 15

Number of brownies = 45 - Number of cookies

Number of brownies = 45 - 15

Number of brownies = 30

Answer:

The answer is 1/20 or 0.05

Step-by-step explanation:

Multiply 1/4*1/5

To get 1/20

1. Equation of tangent and normal: We found the number c that satisfies the Mean Value Theorem on the given intervals.

(a)  +cos =²,  = 2 √²+1

We will use the chain rule to find the derivative of  with respect to . Differentiating both sides with respect to ,

we get;

(+cos())

=(²)− +

=2+²−, (using product rule)

We know that the slope of the tangent line at a point (,) is given by ′()and the slope of the normal line at a point (,) is given by

−1/′()

At =1, =0.

So +cos⁡()−²⁡=1+cos(0)−1sin(0)=0

The equation of the tangent line is therefore =0,

which is a horizontal line.

The normal line has a slope of −1/′(1).

So, ′()==2+²−(),

Since =1, =0,

We get

′(1)=2+²−()

=2(1)+0(1²)−0=2

So, the slope of the normal line is −1/2.The equation of the normal line is

−0=−12(−1) or

=−/2+1/2.3.

Derivatives:

(a)  ()=(√²+2)5

Let =√(²+2).

Therefore, ()=5()

Now, by the chain rule, we have;

′()=5′()′

=5′(√(²+2))(√(²+2))

=5(²+2)3/2

(b)  ℎ()=1,  =1.26

Let ℎ()=1

We are required to find ℎ′(1.26)

Here, ℎ() is a constant function of 1.

Therefore, the derivative ℎ′() of the function is 0 for all .The derivative ℎ′(1.26) is therefore equal to 0.4. Find the number of derivative of F(x) and simplify:

()=√∫²+1dt/2

For the derivative of (),

we need to use the Chain Rule.

=∫²+1

= ℎ⁡(²+1)+

We also have;

=2And,

=/

= (tan h(r²+1)+C)/2x

Now, /=1/2[(/)−(′)/²].

′=²²/√²+1²

So, /=1/2[(/)/2−(²²)/2²√²+1].

/=2/(2√²+1)=/√²+1

Therefore, /=1/2[/√²+1x−(²²)/(2²(²+1))]5.

Find the derivative of the given function:  

()= 4³+ 2²− + 3

Differentiating with respect to ,

we get; ′()=12²+4−1.

2.  Mean Value Theorem:

(a)  ()=, [0, 2]

We know that () is continuous in the interval [0,2] and differentiable in (0,2). Hence the conditions of MVT are satisfied.

Now, the MVT is given by

′()=(2)−(0)2−0

=e2−e02

=12

=12

=(1/2)2

(b)  ()=x+2, [1,]

We know that () is continuous in the interval [1,π] and differentiable in (1,π). Hence the conditions of MVT are satisfied.

Now, the MVT is given by

′()=()−(1)−1

=π+2−3π−1

=π−12

=π−12.(3/2)

= π/2 - 3

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Therefore, the price per inch of aluminum wire is $0.56.

given that

2- foot piece of aluminum wire costs $13. 44

The price per unit, such as a liter, a kilogram, a pound, etc.

There are 12 inches in a foot, so a 2-foot piece of aluminum wire is 2 x 12 = 24 inches long.

The total cost of a 24-inch piece of wire is $13.44.

To find the cost per inch, we can divide the total cost by the number of inches:

Cost per inch = Total cost / Number of inches

Cost per inch = $13.44 / 24

Cost per inch = $0.56

Therefore, the price per inch of aluminum wire is $0.56.

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To determine the point(s) at which the given function f(x) is continuous, we need to use the definition of continuity which is: A function is said to be continuous at a point a in its domain if the following three conditions are met:

1. f(a) is defined;

2. lim x → a f(x) exists; 3. lim x → a f(x) = f(a).By using this definition, we can determine the set of x-values where the function is continuous.To determine where the function is continuous, we must first find the values of x that make the function undefined. The function will be undefined when the denominator equals zero, which is when x = 6. So, we cannot include the value of 6 in our interval notation to describe the set of x-values where the function is continuous.

Now, we need to determine if the function is continuous to the left and right of x = 6 using the definition of continuity. Let's consider the left side of x = 6. We need to find if the limit exists and if it equals f(6).lim x → 6- f(x) = lim x → 6- (14 /(x - 6)) - 5x = ∞Since the limit does not exist as x approaches 6 from the left, the function is not continuous to the left of x = 6.Let's consider the right side of x = 6. We need to find if the limit exists and if it equals f(6).lim x → 6+ f(x) = lim x → 6+ (14 /(x - 6)) - 5x = -∞Since the limit does not exist as x approaches 6 from the right, the function is not continuous to the right of x = 6.

Since the function is not continuous to the left or right of x = 6, we can describe the set of x-values where the function is continuous using interval notation. The set of x-values where the function is continuous is: (-∞, 6) U (6, ∞).

In this question, we were required to determine the point(s) at which the given function f(x) is continuous. For this purpose, we used the definition of continuity which states that a function is continuous at a point a in its domain if f(a) is defined, the limit x→a f(x) exists, and lim x → a f(x) = f(a).By using this definition, we found that the function will be undefined when the denominator equals zero, which is when x = 6. So, we cannot include the value of 6 in our interval notation to describe the set of x-values where the function is continuous.

Furthermore, we considered the left side of x = 6 and the right side of x = 6 separately to determine if the limit exists and if it equals f(6). We found that the limit does not exist as x approaches 6 from the left and right, so the function is not continuous to the left or right of x = 6.As a result, we concluded that the set of x-values where the function is continuous is (-∞, 6) U (6, ∞), which means that the function is continuous for all values of x except x = 6.

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Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

Answer:

60°

Step-by-step explanation:

Complementary angles sum 90°

a + b = 90°      Eq. 1

b = a/2             Eq. 2

Replacing Eq. 2 in the Eq. 1

a + a/2 = 90

2a/2 + a/2 = 90

3a/2 = 90

a = 90*2/3

a = 60

from the Eq. 2

b = 60/2

b = 30

Check:

from the Eq. 1

60 + 30 = 90

Answer:

60>30

Then

The larger angle is:

60°

Answer:

2x + 3x^2 (4x - 5)

2x + 12x^3 - 15x^2

12x^3 - 15x^2 + 2x

Degree - 3

Terms - 3 (Trinomial)

12x³-15x²+2x is simplified equation of 2x+3x²(4x-5) and degree is 3 with three terms.

An expression is a combination of numbers, variables and operators.

The given expression is two x plus three x square times of four x minus five.

2x+3x²(4x-5)

Use distributive law and simplify

2x+3x²(4x)+3x²(-5)

2x+12x³-15x²

12x³-15x²+2x

The degree of a polynomial is the highest power of its variable. The degree of the polynomial is three.

There are three terms in 12x³-15x²+2x.

Hence 12x³-15x²+2x is simplified equation and degree is 3 with three terms.

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9514 1404 393

Answer:

Step-by-step explanation:

1. The shape of each cut surface is the same shape as the base it is parallel to: a rectangle. It is an 8" by 10" rectangle.

__

2. The area of each cut surface is the area of the rectangle:

  A = LW = (10")(8") = 80 square inches

__

3. The total area of cut surfaces is the sum of the two areas on either side of the cut:

  new surface area = 2 × 80 square inches = 160 square inches

Answer:

x= 4

Step-by-step explanation:

i dont think u need explanation but lmk if u do :)

The forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0

Given: Smoothing constant α = 0.45, Forecast for period 10 = 297

We need to calculate the forecasts for periods 11 through 15 using the essential smoothing forecast method.

The essential smoothing forecast is given by:Ft+1 = αAt + (1 - α)

Ft

Where,

At is the actual value for period t, and Ft is the forecasted value for period t.

We have the forecast for period 10, so we can start by calculating the forecast for period 11:F11 = 0.45(297) + (1 - 0.45)F10 = 162.35 + 0.45F10

F11 = 162.35 + 0.45(297) = 297.4

For period 12:F12 = 0.45(At) + (1 - 0.45)F11F12 = 0.45(297.4) + 0.55(297) = 296.7

For period 13:F13 = 0.45(At) + (1 - 0.45)F12F13 = 0.45(296.7) + 0.55(297.4) = 297.1

For period 14:F14 = 0.45(At) + (1 - 0.45)F13F14 = 0.45(297.1) + 0.55(296.7) = 296.9

For period 15:F15 = 0.45(At) + (1 - 0.45)F14F15 = 0.45(296.9) + 0.55(297.1) = 297.0

Therefore, the forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0 (All values rounded to two decimal places)

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Answer:

1.072 x 10^18

Step-by-step explanation:

(1.6 x 10^5) x (6.7 x 10^12) = 1.072e18 = 1.072 x 10^18

The probability that an adult in the city is single is 14%.

In the given city, based on the survey results, the percentages of adults with different marital statuses are provided. To find the probability of an adult being single, we look at the percentage of single individuals, which is 14%. Therefore, the probability of an adult being single is 14%.

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For a data set, half of the observations are always greater than the median. The median is the middle value in a set of data when it is arranged in order of increasing or decreasing magnitude.

It is a measure of central tendency that is more robust to outliers than the mean. The median splits the data set in half, with half of the observations being greater than it and half being less than it.

The median is a crucial measure of central tendency that helps us understand the distribution of a data set. It represents the value that separates the top half of the data from the bottom half. The median is often used as an alternative to the mean when the data set contains outliers or extreme values that can skew the mean. The median is easy to calculate and provides a clear picture of the middle of a data set. Therefore, it is a useful tool for statisticians, researchers, and analysts who need to summarize and describe data sets accurately.

In summary, the median is the value that divides a data set into two equal halves, with half of the observations being greater than it and half being less than it. It is a robust measure of central tendency that is widely used in statistics to describe the distribution of data sets.

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Answer:

140 cm^2

Step-by-step explanation:

Area of rectangular = L x W

14 times 10 = 140cm^2

Answer:

Step-by-step explanation:

Note that the question wants the chance of at LEAST one green ball. that means containing 1,2,3,4... etc is all fair game. Now calculating all of those odds by hand is a pain. But we dont have to. There's a clever little trick we can use to cut time: The sum of the odds of all the possible events (no greens, 1 green, etc) must be 100%. Knowing that, we can just calculate the odds of getting no green balls and subtract that from 100%.

The odds of no green balls are:

\(\frac{11}{20} \cdot\frac{10}{19} \cdot\frac{9}{18} \cdot\frac{8}{17} \cdot...\\\)\(\cdot \frac{4}{13}\)

Wich can be rewritten as:

\(\frac{11!12!}{20!3!} \approx 0,0013\) or 0,13%

Subtracting from 100%:

100-0,13=99,87% of at least one green

Answer: width = 27.5 feet and length = 92.5 feet

Step-by-step explanation:

Let width = x, then length = 3x+10

Perimeter of rectangle = 2 (length +width)

Given:  Perimeter of the garden = 240 feet.

Then, \(2 (x+3x+10)=240\)

\(\Rightarrow\ 2 (x+3x+10)=240\\\\\Rightarrow\ (4x+10)=120\\\\\Rightarrow\ 4x=110\\\\\Rightarrow\ x=\dfrac{110}{4}=27.5\)

i.e. width = 27.5 feet

Then, length = 3(27.5)+10= 82.5+10=92.5 feet

Hence, width = 27.5 feet and length = 92.5 feet

Answer:

C. 18

Step-by-step explanation:

Inverse of 1/3 = 3

3 x 6 = 18

18 flowerpots can be filled with these 6 bags.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have,

Brianna has 6 bags of soil.

Filling one flowerpot requires 1/3 of a bag of soil.

So, the number of flowerpots filled using 6 bags

=  6 / (1/3)

= 6 x 3

= 18 pots

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Answer:

The amount of Lauren's original deposit is $1100.

Step-by-step explanation:

The formula of the simplest interest is I = P r t, where

∵ Lauren deposited x dollars into a savings account that pays

   2.75% annual simple interest.

∴ P = x dollars

∴ r = 2.75

→ Divide it by 100 to change it to decimal

∵ 2.75 ÷ 100 = 0.0275

∴ r = 0.0275

∵ After one year, Lauren's account had earned $30.25 in interest

∴ t = 1 year

∴ I = 30.25 dollars

→ Substitute them in the rule above

∵ 30.25 = x(0.0275)(1)

∴ 30.25 = 0.0275x

→ Divide both sides by 0.0275

∴ 1100 = x

∴ The amount of Lauren's original deposit is $1100.

Answer:

Step-by-step explanation:

Write equations as you read the problem

    x -  y =  50      (1)

   5x + 2y = 950      (2)

        First  equation comes from counting persons.

        Second equation comes from counting money.

There are several different methods to solve.

For example, using the Elimination method, multiply first equation by 2 (all the terms in both sides);  

keep equation (1) as is.

   2x - 2y = 100      (3)

   5x + 2y = 950      (4)

Now add the equations. The terms  "-2y"  and  "2y"  will   cancel each other, and you will get

a single equation in only one unknown x

   2x + 5x = 100 + 950,

or

     7x    = 1050,

      x    = 1050/7 = 150.

Then from equation (1),  y = x - 50 = 150 - 50 = 100.

ANSWER.  150 adults and 100 students.

CHECK.  5*150 + 2*100 = 750 + 200 = 950  dollars   (t0tal money).    ! Correct !

Answer: 80% rent or 72 students

Step-by-step explanation:

20 percent of 90 is 18

So 18 kids own instruments

100-20=80%

So 80% of kids do rent instruments

Or

18x4= 72 kids rent

Answer:

Number of protons

Step-by-step explanation:

The atomic number represents the number of protons that are in the nucleus. This says what chemical properties something has and where it is located on the periodic table.

Best of Luck!

Answer: 34.95 rounded to the nearest tenth is 35.0.

Answer:

1st: 0.04, 0.04, 0.25, 0.4

2nd: 0.06, 0.16, 0.6, 60

3rd: 0.07, 0.7, 0.075, 0.75, 7.5

4th: 0.02, 0.18, 0.2, 200

5th: 0.009, 0.09, 0.9, 0.95

6th, 0.1, 0.12, 1, 10

Step-by-step explanation:

Step-by-step explanation:

here

f(x)=2x^2-1

Now

f(4y)=2*4y^2-1

Answer: £225

Step-by-step explanation:

Let Sarah's amount be represented by x.

Since Caroline gets three times as much as Sarah, Caroline will get: 3x

Bridget gets twice as much as Caroline, therefore Bridget will get: 2 × 3x = 6x

Sarah = x

Caroline = 3x

Bridget = 6x

Total = x + 3x + 6x = 10x

Caroline's faction is 3/10. We then multiply the fraction by £750. This will be:

= 3/10 × £750

= 0.3 × £750

= £225

Caroline will get £225