Two electric resistors, RyandR, are tested with
currents and voltages such that:
7R, + 8R2 = 57.3
5R, + 6R2 = 41.7 Find the inverse of the coefficient matrix. Then use it to find R, andR, (inS2) to the nearest
tenth.

The equation representing total cost of the shirt is c = 1.06p.

As per the question, we are representing the total cost of the shirt as c and price of the shirt as p.

Calculating sales tax on the shirt -

Sales tax = p × 6%

Converting percentage to fraction and hence decimal form

Sales tax = p× 6/100

Sales tax = 0.06p

Forming the equation now -

Total cost = price of the shirt + sales tax on the shirt

c = p + 0.06p

Performing addition on Right Hand Side of the equation to find the equation representing total cost

c = 1.06p

Therefore, the equation representing the total cost of the shirt is c = 1.06p.

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The differential equation for the velocity v of a falling mass m subjected to air resistance proportional to the square of the instantaneous velocity is m dv/dt = mg-kv2, where k > 0 is a constant of proportionality. The positive direction is downward.

a) Solve the equation subject to the initial condition v(0) = v0.  Therefore, v(t) = sqrt(mg/k) * sqrt(1-e^(-kt/k1)) where k1 = (mg/k-v0^2)^(1/2)/m.

b) To find the limiting or terminal velocity of the mass, we need to find lim v(t) as t approaches infinity.The terminal velocity of the mass is v∞ = sqrt(mg/k). Therefore, lim v(t) = v∞ = sqrt(mg/k).

c) If the distance s, measured from the point where the mass was released above ground, is related to velocity v by ds/dt = v(t), find an explicit expression for s(t) if s(0) = 0. s(t) = m/(k^2) * (mg-kv0^2)^(1/2) * (π/4 - (mg/k-v0^2)^(1/2)t/2m - sin[(mg/k-v0^2)^(1/2)t/m]/4) where the integral is from 0 to π/2.Therefore, s(t) = m/(k^2) * (mg-kv0^2)^(1/2) * (π/4 - (mg/k-v0^2)^(1/2)t/2m - sin[(mg/k-v0^2)^(1/2)t/m]/4) if s(0) = 0.

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Answer:

123 if your going to the nearest whole number

Step-by-step explanation:

Since

6 : 7 = X : 143

Then we know

6/7 = X/143

Multiplying both sides by 143 cancels on the right

143 × (6/7) = (X/143) × 143

143 × (6/7) = X

Then solving for X

X = 143 × (6/7)

X = 122.57142857143

Therefore

6 : 7 = 122.57142857143 : 143

Answer:

x =4  &  y=0

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation

Answer:

X=4, Y=4

Step-by-step explanation:

First Solve for y

y= 4-x

Sub that in for y on the other equation.

2x-4-x=8

x=4

Answer:

40%

Step-by-step explanation:

20/50 = 40/100 = 40%

1. A division equation that finds the total number of apple pieces that Mrs. Miller has after cutting the apples into halves is P = 7 ÷ ¹/₂, and 14 is the solution.

2. A division equation that finds the total number of apple pieces that Mrs. Miller has after cutting the apples into fourths rather than halves is P = 7 ÷ ¹/₄, and 28 is the solution.

3. When a whole number is divided by a unit fraction, the quotient is always greater than the whole number because the denominator of the fraction multiples the whole number.

A division equation is an equation with the division operand (÷).

An equation has been defined as a mathematical statement that shows that two algebraic expressions are equal or equivalent.

The total number of apples brought by Mrs. Miller = 7

The division of the apples = Halves (¹/₂)

1) The total number of pieces = 14 (7 ÷ ¹/₂)

The division equation is P = 7 ÷ ¹/₂.

2) The total number of pieces = 28 (7 ÷ ¹/₄)

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My age is 2 years from the given condition.

Given that, if you square my age and subtract 28 times my age, the result is 60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x be my age.

Now, square my age is x²

28 times my age =28x

The square of my age and subtract 28 times my age, the result is 60.

x²-28x=60

⇒ x²-28x-60=0

⇒ x²+30-2x-60=0

⇒ x(x+30)-2(x+30)=0

⇒ (x+30)(x-2)=0

⇒ x=2

Hence, my age is 2 years from the given condition.

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Answer:

Step-by-step explanation:

we are given that one angle is 40 degrees. The right angle below that is 90 degrees. Right angles will always equal 90 degrees. with the two angles how do we solve. Triangles no matter what will always be 180 degrees so,

40+90+x=180

130+x=180

-130     -130

x=50 degrees

Answer:

b

Step-by-step explanation:

..........................................

Answer:

I think r=2.55

Step-by-step explanation:

The size of the sample that she would have to get a margin of error less than 0.03 is 752

We have the margin of error E = 0.03

The confidence interval C I = 90 percent

p = 1 - p = 0.5

z α / 2 = 1.645

The formula for the sample size is given as

(z α / 2 / E)² * p * (1 - p)

(1.645 /  0.03)² * 0.5 * 0.5

= 54.833² * 0.5 *0.5

= 752

Hence n is given as 752. The size of the sample would have to be 752.

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Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

it goes into five 0 times

Answer:

0 Times

Step-by-step explanation:

The answer is 0 times!

This is due to the concept in which 8 is a bigger number than 5.

They should use 6 cup of Noah's measuring cup

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the number of cup the should use:

Number of cup = Recipe call / Noah's cup

Number of cup = (3/4) / (1/8)

Number of cup = 3*8 / 4*1

Number of cup = 24/4

Number of cup = 6

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Correctly written question:

Melanie and Noah are baking a birthday cake for Francesca. The recipe call for 3/4 measuring cup and Noah has a 1/8 measuring cup. Which cup should they use?

Answer:

x=-9ln(1/2)/[ln(4)-ln(1/2)]

Step-by-step explanation:

4^{x}=(1/2)^{x-9}

ln(4^{x})=ln((1/2)^{x-9})

xln(4)=(x-9)ln(1/2)

xln(4)=xln(1/2)-9ln(1/2)

xln(4)-xln(1/2)=-9ln(1/2)

x[ln(4)-ln(1/2)]=-9ln(1/2)

x=-9ln(1/2)/[ln(4)-ln(1/2)]

Answer: 75.2

Step-by-step explanation:

Well, if it isn't the most confusing question ever.

First of all, what is P?

I'll assume its the perimeter...

2*(1.2*2)+4*(8.8*2)

Or

2*2.4+4*17.6

75.2

The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Then the equation is given as,

(x + 12) / (x + 5) = (x + 5) / x

Simplify the equation, then we have

(x + 12) / (x + 5) = (x + 5) / x

x² + 12x = (x + 5)²

x² + 12x = x² + 10x + 25

12x - 10x = 25

Further, simplify the equation, then we have

2x = 25

x = 25/2

x = 12.5

The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.

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Answer:

It’s in between 95 and 100

Step-by-step explanation:

Not sure where though

Answer:

n(n - m)

Step-by-step explanation:

n² - mn ← factor out n from each term

= n(n - m)

Answer:

n(n-m)

Step-by-step explanation:

We are given the quadratic expression:-

\( \displaystyle \large{ {n}^{2} - mn}\)

To factor this expression, do you notice that there are two n's in the expression? Yes, since in the expression, the whole terms have n-term; what we are going to do is to common factor n out!

So how do we do that? Simple, just pull n out.

\( \displaystyle \large{n( {n} - m)}\)

From above, you might be wondering how does it turn out like this. Do not worry, I've got you!

When we pull n out of the expression, we just divide the expression by n.

Don't get it? Let me show you!

Step 1 - Form the expression:

\( \displaystyle \large{ {n}^{2} - mn}\)

Step 2 - Pull n out and bracket the expression.

\( \displaystyle \large{n( {n}^{2} - mn)}\)

Step 3 - Divide the expression by n.

\( \displaystyle \large{n( \frac{ {n}^{2} - mn}{n})} \\ \displaystyle \large{n( n - m)}\)

Still not get it? Well, let's demonstrate another method.

Let's say we have the expression again!

\( \displaystyle \large{ {n}^{2} - mn}\)

Since n^2 comes from n•n.

\( \displaystyle \large{ n \cdot n - mn}\)

Bracket the expression:

\( \displaystyle \large{ (n \cdot n - mn)}\)

Now let's imagine that these two brackets are the doors.

m-term: There are so many of you in this bracket house! If this keeps continuing, this bracket house might be collapsed!

3 n-terms were shocked! They had to find the ways to protect their bracket house, the legacy that their cases parents gave.

But then the 2 n-terms did an unexpected! They decided to help them by going outside of the bracket house and stand there!

m-term: Why there is only one n-term outside when two of them left?

another n-term: Well, the another n-term finds food for themselves and the another one there guards our bracket house.

The End!

As we get:

\( \displaystyle \large{n ( n - m)}\)

Not clearing all your doubts? Let me know or ask your doubts under my comment!

The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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A positive correlation coefficient signifies that when the value of x changes, the value of y changes in the same direction.

The correct answer is:

When x increases, y increases, and when x decreases, y decreases.

When the correlation  has a positive value, it indicates a positive linear relationship between the two variables being measured, denoted by x and y.

In other words, as the value of x increases, the value of y also increases, and vice versa.

This positive correlation suggests that there is a tendency for the variables to move in the same direction.

For example, let's consider a study that examines the relationship between study time (x) and test scores (y) of students.

If the correlation coefficient is positive, it means that as the study time increases, the test scores tend to increase as well.

On the other hand, when the study time decreases, the test scores also tend to decrease.

It's important to note that the strength of the correlation is determined by the magnitude of the correlation coefficient.

A correlation coefficient closer to +1 indicates a strong positive correlation, while a value closer to 0 indicates a weaker positive correlation.

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Answer:

what is that my guy what are you learning

Step-by-step explanation:

some very very hard stuff

Answer:

10x - 15

Step-by-step explanation:

5(2x-3) = 10x - 15

Answer:

20-(4+2)

Step-by-step explanation:

So since they are eating, they are taking away, or subtracting.

Answer:

20 - (4 + 2)

Step-by-step explanation:

The original amount is 20.

The number of cookies left is the original amount minus the amount that was eaten.

Amy ate 4 cookies.

Her brother ate 2 cookies.

Amount that was eaten: 4 + 2

Amount left = original amount - amount that was eaten

amount left = 20 - (4 + 2)

Answer:

Suppose you earned extra money by having a part-time job. You open up a bank account in order to save your money. Your body acts similar to a bank account—you can “deposit” and “store” energy.

\

Step-by-step explanation:

Answer:

x = 19 and TV = 27

Step-by-step explanation:

Given 2 secants drawn from an external point to the circle, then the product of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant.

(1)

8(8 + x) = 9(9 + 15) = 9 × 24 = 216 ( divide both sides by 8 )

8 + x = 27 ( subtract 8 from both sides )

x = 19

---------------------------------------------------------------------

(2)

VU × VT = VW × VQ

8(8 + 5x - 1) = 9(9 + 15) = 9 × 24 = 216

8(7 + 5x) = 216 ( divide both sides by 8 )

7 + 5x = 27 ( subtract 7 from both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Then

TV = 5x - 1 + 8 = 5x + 7 ( substitute x = 4 )

TV = 5(4) + 7 = 20 + 7 = 27

yes, it's a scaled version of a triangle with side lengths 3, 4 and 5.

by a factor of 20

a triangle with side lengths 3, 4 and 5 is a right triangle and it holds true for a²+b²=c², because 9+16=25

the 3,4,5-triangle is the simplest right triangle to calculate it's numbers seem somehow elegant.

the triangle in your problem is just a bigger version of it (wich means all angles stay the same).

My reasoning is lacking, but I'm sure

The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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Answer:

x = number of students tickets = 1,000

y = number of adults tickets = 250

Step-by-step explanation:

Let

x = number of students tickets

y = number of adults tickets

x + y = 1,250 (1)

2x + 3y = 2,750 (2)

Multiply (1) by 2

x + y = 1,250 (1) * 2

2x + 2y = 2,500 (3)

2x + 3y = 2,750 (2)

Subtract (3) from (2) to eliminate x

3y - 2y = 2,750 - 2,500

y = 250

Substitute y = 250 into (1)

x + y = 1,250

x + 250 = 1,250

x = 1,250 - 250

x = 1,000

x = number of students tickets = 1,000

y = number of adults tickets = 250

Answer:

Jason is incorrect.

The caterpillar's rate is 2 ft/min

Step-by-step explanation:

The rate of motion is defined as the quotient between the distance covered (in our case 16 feet) divided by the time it took to cover that distance (in our case 8 minutes)

Then, the rate is:

\(rate=\frac{distance}{time} = \frac{16\,\,ft}{8\,\,min} = 2\,\frac{ft}{min}\)

As a result, k is roughly equal to 0.0462 as where P(15) is the population after 15 years, and P(0) is the initial population.

what is derivative ?

Depending on the situation, the derivative may be represented using the notations f'(x), \(d_{f}\)/\(d_{x}\), or \(d_{y}\)/\(d_{x}\). It can be used to simulate rates of change in a variety of domains, including physics, economics, and engineering, as well as to estimate the slope of either a tangent line to the function graph at a specific point and determine the maximum and minimum values of the function.

The derivative is a key idea in calculus and is employed frequently in a variety of contexts, such as optimisation, differential equations, and rate-related problems. It also has a lot of links to assimilation, which is how differentiation is reversed.

given

Given that the population increases using the following formula:

\(k_{p}\) = \(d_{p}\)/\(d_{t}\) where t is expressed in years and k is a constant.

We can write this as: if the population triples every 15 years.

where P(15) is the population after 15 years, and P(0) is the initial population.

Using the exponential growth formula, we can find k:

When we replace t = 15 with P(15) = 3P(0), we obtain:

3P(0) = P(0) \(e^{^(15k)}\)) (15k)

By multiplying both sides by P(0), we obtain:

When we take the natural logarithm of both sides, we obtain:

ln(3) = 15k

After finding k, we obtain:

k = ln(3) / 15

As a result, k is roughly equal to 0.0462 as where P(15) is the population after 15 years, and P(0) is the initial population.

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