at time , a tank contains oz of salt dissolved in gallons of water. then brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. (a) how much salt is in the tank at an arbitrary time? 200-140e^(-t/25) oz. (b) how much salt is in the tank at time min?

Answer:

Step-by-step explanation: I do these in 2 steps:

1. isolate the y term ----- 4y = -2x + 16

2. divide each term by the coefficient of the y-term

y = (-2/4)x + 4

y = (-1/2)x + 4

Eva will earn $10.50 interest.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P(1 + r/n[tex])^{nt}[/tex]

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

Given:

Eva deposited $50 in an account earning 10% interest compounded annually.

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n[tex])^{nt}[/tex]

A = 50.00(1 + 0.1/1[tex])^{2}[/tex]

A = $60.50

Therefore, she will earn $10.50 of interest.

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Answer:

T < 5

Step-by-step explanation:

High School A: A(t) = 800 + 35t

High School B: B(t) = 550 + 85t

To find the interval of years in which High School A will have more students than High School B, we need to find the years in which A(t) > B(t).

So, we need to solve the inequality A(t) > B(t)

800 + 35t > 550 + 85t

250 > 50t

t < 5

Therefore, High School A will have more students than High School B for the first five years.

The interval of years, t, for which High School A will have more students than High School B is t < 5

The solution to the mixed fraction 4 3/4 - 6/4 is 3 1/4

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

To solve the question

Convert the mixed fractions into improper fractions

4 3/4 - 6/4

= 19/4 -6/4

we can simplify, since the denominators are the same

19-6/4

=13/4

converting to mixed fractions, we have

3 1/4

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The solution of the absolute value equation:

|x-2|=|4+x|

is  x = -1

Here we want to solve the following equation:

|x - 2| = |4 + x|

A general absolute value function can be rewritten into two equations, in this case these are:

x - 2 = 4 + x

x - 2 = -(4 + x)

The first one has no solution, but the second one does.

x - 2 = -(4 + x)

x - 2 = -4 -x

2x = -4 + 2

2x = -2

x = -2/2 = -1

That is the solution.

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Answer:8

Step-by-step explanation:

dd

The sheet metal should have a total area of 12.9 x 12.9 = 166.41 square feet.

The sheet metal must be large enough to form a cube with a volume of 300 cubic feet, so the side length of the sheet must be the cube root of 300, which is approximately 6.9 feet. To find the dimensions of the sheet metal, we must take into account the four 3 foot squares that will be removed from each corner. Therefore, the sheet metal should have a length of 6.9 feet + 6 feet (4 times the 3 foot squares) = 12.9 feet and a width of 12.9 feet. This will give the box a volume of 300 cubic feet, and the sheet metal should have a total area of 12.9 x 12.9 = 166.41 square feet.

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Answer: 16x^38y^22

Step-by-step explanation:

Re-order terms so constants are on the left
(−xy)2(2x9y5)4(−)2(295)4

Distribute exponent

(−xy)2(2x9y5)4(−)2(295)4

Evaluate the exponent

(−1)2(xy)2⋅(2x9y5)4(−1)2()2⋅(295)4

The value of cos v in simplest terms in fraction form is 17/18

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The triangle ΔXWV with WV=17 , XV=18,

We know cos ∅= base/hypotenuse

here hypotenuse is XV as it is opposite to the right angle. and the base of the triangle is 17

∴ Cos v=17/18

We can also find the measure of the third angle by using the pythogarean theorm as

WX=√18²-17²

   =√35

Hence, The value of cos v in simplest terms in fraction form is 17/18

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For geometric shape no.4,∠1=26°,∠2=154°,∠3=26°,∠4=26°,

∠5=154°,∠6=154°,∠7=26°.

What are geometric shapes?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now,

∠1+154°=180° -->∠1=26°   (supplementary angles)

∠1=∠3  (opposite angles) -->∠3=26°

∠2+∠3=180°

∠2=154°

∠1=∠7 --->∠7=26°

∠7+∠6=180° (supplementary angles)

∠6=154°

∠5+∠7=180° (supplementary angles)

∠5=154°

∠4+∠5=180° (supplementary angles)

∠4=26°

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Answer:(x+3)=2x

Step-by-step explanation:

Answer:

This equation makes no sense post in better quality

Step-by-step explanation:

Leia's ending balance after 5 years will be $3245.41. The solution has been obtained by using the concept of compound interest.

What is compound interest?

Both the principal and the interest that has accumulated over the previous period are used to compute interest. Compound interest accounts for the principal when calculating the interest for the subsequent month, in contrast to simple interest, which does not. In mathematics, compound interest is frequently denoted by the letter C.I.

We know that formula for compound interest is

[tex]A= P(1 + \frac{r}{n} )^{nt}[/tex]

So, here P = $2658 , n=12, t=5 and r = 0.04

Thus, we get

[tex]A= 2658(1 + \frac{0.04}{12} )^{60}[/tex]

[tex]A= 2658(1.00333})^{60}[/tex]

A = 2658*1.2207

A = $3245.41

Hence, Leia's ending balance after 5 years will be $3245.41.

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Answer: 0.81

Step-by-step explanation:

       We will look at the thousands place to round to the hundredth. If the thousands place is at or above 5, we will round up. If it is 4 or below, we will round down.

[tex]\displaystyle 0.814\\0.81\boxed{4}\\\\4 < 5\\\\0.81[/tex]

15 x 14 x 13 x ... x 3 x 2 x 1 is the possible batting orders.

A baseball coach can create 15! (15 factorial) different batting orders for a team of 15 players if there are nine positions to fill in the lineup. This is because, for the first spot in the lineup, there are 15 options, for the second spot there are 14 options, and so on, leading to 15 x 14 x 13 x ... x 3 x 2 x 1 possible batting orders.

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

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The statement "7x5-4x5+16+4-26 when

(select) (select) (select) (select)+(select)=(select)-26", with the values in the same order, but with parentheses such that the statement is true is 7x(5-4x+4)-26 = (7x)(1) - 26

Factorization is the process of finding the factors, or integers that multiply together to give a specific number. It is also known as factoring or prime factorization when the factors are prime numbers. For example, factorization of 12 is 2x2x3, which are the prime factors that multiply to give 12. The process of factorization is used in a variety of mathematical and scientific fields, such as number theory, algebra, and computer science.

It can also refer to a mathematical expression where an algebraic expression can be written as a product of two or more expressions.

In general, factorization is a way of breaking down a number or an expression into smaller parts that can be used to understand or simplify it.

Therefore, when plugged in those values in the same order, the statement become true.

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Answer:

a. The result is always an integer because integers are not fractions or decimals.

b. Sorry I don't have an answer for b i don;t know what that means. :(

The expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.

What exactly is a phrase?

It is described as blending mathematical operators, constants, and variables.

It follows that:

The sentence is:

hD = m

To account for D Declare D as the subject.

As we know, an arithmetic operation can be defined as an operation in which we add, subtract, multiply, and divide integers. It has four basic operators that are +, -, ×, and ÷.

By dividing both sides by h:

hD/h = m/h

Here h ≠ 0

D = m/h

As a result, if the statement is hD = m, then the expression in terms of m and h is D = m/h, and the solution is D = m/h.

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The function that matches the description is given as follows:

f(x) = 2x - 5.

The parent function for this problem is given as follows:

f(x) = x.

The first transformation is a multiplication by two, hence the function is defined as follows:

f(x) = 2x.

The final transformation is a subtraction by 5, then the function is defined as follows:

f(x) = 2x - 5.

Meaning that the last option is the correct option.

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A measure computed from the entire population is called​ parameter.

A limit is a parameter. A parameter is a constant in an equation in mathematics, however today, any system can include parameters that control how it functions. You can provide guidelines for your class discussion.

Greek words para-, which means "beside," and metron, which means "measure," are combined to form the term parameter. Gravity and time are two boundaries that the natural world establishes. The law establishes the boundaries of appropriate conduct in court. While parameters and perimeters are similar, a parameter can contain or define something that is either physically present or abstractly defined, whereas a perimeter is the physical space that surrounds an entity.

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Answer: Your answer would be −2x⁴y²

Step-by-step explanation: I hope this helps!

Answer:

The third question

Step-by-step explanation:

Hope this helps!

Answer: To obtain a mixture that is 50% orange juice, you must find the amount of 60% orange juice needed to bring the overall concentration of orange juice to 50%.

We can start by using the formula:

(amount of 60% orange juice) / (amount of 60% orange juice + amount of 30% orange juice) = desired concentration

Let's call the amount of 60% orange juice that we need to add x.

So the equation will look like this:

(x) / (x + 5 gallons) = 0.5

We can then solve for x:

x = (0.5 * x + 0.5 * 5 gallons)

x = 2.5 gallons

So, 2.5 gallons of 60% orange juice must be mixed with 5 gallons of 30% orange juice to obtain a mixture that is 50% orange juice.

Step-by-step explanation:

a) The value of x from the proportion is x = 2/5

b) The value of x from the proportion is x = 8

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

a)

3 / ( x + 2 ) = ( 5 / 4 )   be equation (1)

On simplifying the equation , we get

Multiply by ( x + 4 ) on both sides of the equation , we get

( 5/4 ) ( x + 2 ) = 3

Multiply by 4 on both sides of the equation , we get

5 ( x + 2 ) = 12

On further simplification , we get

5x + 10 = 12

Subtracting 10 on both sides of the equation , we get

5x = 2

Divide by 5 on both sides of the equation , we get

x = 2/5

Therefore , the value of x is 2/5

b)

( x + 2 ) / 5 = ( x - 2 ) / 3   be equation (2)

On simplifying the equation , we get

Multiply by 5 on both sides of the equation , we get

( x + 2 ) = 5( x - 2 ) / 3

Multiply by 3 on both sides of the equation , we get

3 ( x + 2 ) = 5 ( x - 2 )

On further simplification , we get

3x + 6 = 5x - 10

Subtracting 3x on both sides of the equation , we get

2x - 10 = 6

Adding 10 on both sides of the equation , we get

2x = 16

Divide by 2 on both sides of the equation , we get

x = 8

Therefore , the value of x is 8

Hence , the proportion is solved

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Answer: Let x be the fare of the train, and y be the fare of the bus.

We know that:

x + y = 400 (the total fare of the journey)

And, on the return journey the fare of the bus is hiked by a half of what Talia paid initially, so the fare of the bus on the return journey is:

y * 1.5 = y + (y/2)

And the total fare of the return journey is hiked to 4800, so:

x + y + (y/2) = 4800

We can substitute the first equation into the second equation:

x + (y + (y/2)) = 4800

x + y + (y/2) = 4800

x + (y + (y/2)) = 4800

So, we can solve the system of equations by substituting the first equation into the second equation and solving for x.

x + y = 400

x = 4800 - (y + (y/2))

x = 4800 - y - (y/2)

x = 4800 - y - (1/2)y

x = (4800 - y) - (1/2)y

x = 4800 - (3/2)y

Now we have an equation for x in terms of y. To solve for x, we can use the value of y from the first equation

x = 4800 - (3/2)(400)

x = 4800 - 600

x = 4200

So the train fare is 4200 sh

Step-by-step explanation:

The statement is true, the point (8, 7) is a solution to the inequality.

Here we have the following statement:

"(8, -7) is a solution to the inequality y < 12x − 9"

To check if that is true, we just need to replace the values of the point on the inequality and check if the ienquaity becomes true.

We will get:

-7 < 12*8 - 9

-7 < 87

This is true, 87 is a number larger than -7, then the statement is true, (8, -7) is a solution of the inequality.

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Answer:

The answer is 351

Step-by-step explanation:

Hope this helps!

As per the 95% confidence interval, the true proportion of the professor's students who were registered to vote is between 57.3% and 82.7%

The term called confidence interval is defied as  the mean of your estimate plus and minus the variation in that estimate.

Here we know that  sample of 50 of her students randomly sampled from her 700 students, 35 said they were registered to vote.

Here we have to calculate the true proportion of the professor's students who were registered to vote with 95% confidence interval is,

Here we have a random sample of less than 10% of the professor's students with 35 expected successes and 15 expected failures

Here we have know that both of which are at least ten, so a Normal model applies.

Then the value of n = 50,

=> P =35/50 = 0.70

Then the value of q = 1 - p = 1 - 0.70 = 0.30

Then the value of SE is

=> √(0.70 0.30)/ 50 = 0.065

Then with 95% confidence interval is calculated as,

=>  p± SE(p)

Apply the values on it, then we get

=> 0.70±1.96 (0.065)=0.70±0.127

=> 0.573 to 0.827

hence the 95% confident that between 57.3% and 82.7% of the professor's students are registered to vote.

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Answer:

a) La temperatura ambiente es -1/3.