Maria has added 2 liters of pure alcohol to 8 liters of a 48% alcohol solution. What is the alcohol concentration of the resulting solution.

Answer:

375

Step-by-step explanation:

Answer:

36 twelfths.

Step-by-step explanation:

We are asked to find number of twelfths are in 3.

We can write 3 as a fraction as:

[tex]\frac{3}{1}[/tex]

To convert our given number to twelfths, we will multiply numerator and denominator of our fraction by 12 as:

[tex]\frac{3}{1}\times \frac{12}{12}[/tex]

[tex]\frac{3\times 12}{1\times12}[/tex]

[tex]\frac{36}{12}[/tex]

Therefore, there are 36 twelfths in 3.

The object will take 2.5 seconds to reach its maximum height. The maximum height attained by the object will be 42.375 meters.

To find how long it takes for the object to reach its maximum height, we can use the projectile motion formula

h(t) = -4.9t² + v0t + h0.

The maximum height is achieved when the vertical velocity component is zero. This happens midway through the flight.

The time to reach maximum height can be found using the formula

t = v0 / g,

where v0 is the initial velocity and

g is the acceleration due to gravity (9.8 m/s²).

In this case, v0 = 24.5 m/s and g = 9.8 m/s², so the time (t) to reach maximum height is

t = 24.5 m/s / 9.8 m/s² = 2.5 s.

The maximum height (H) can be calculated as the initial height plus the displacement due to the initial velocity upwards before it starts coming down.

Since we know the time to reach the maximum height, we can plug it into the original equation h(t) to find the maximum height:

H = -4.9(2.5)² + 24.5(2.5) + 11

We then find that

H = 42.375 m.

To convert the slope-intercept form equation y = -3/8x - 7 into standard form, mulitply by 8 to remove the fraction, then rearrange to form 3x + 8y = -56, making sure the 'A' coefficient is positive.

The student's question asks about rewriting the slope-intercept form equation y = -3/8x - 7 into standard form. To do so, we need to rearrange the equation so that all variables and constants are on one side and the equation is set equal to zero. In standard form, the equation should be written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Let's convert the given equation to standard form step by step:

Multiply both sides of the equation by 8 to clear the fraction: 8y = -3x - 56.

divide 630 by 18

630/18 = 35

so unit rate would be 35 meters per second

Answer:

30 weeks

Step-by-step explanation:

Given : Dakota runs a half-marathon every 6 weeks,

            Madison runs a half-marathon every 15 weeks

To Find : . If they start now, in how many weeks will they again be running a half marathon at the same time?

Solution :

Since Dakota runs a half-marathon every 6 weeks, Madison runs a half-marathon every 15 weeks

So, to calculate  If they start now, in how many weeks will they again be running a half marathon at the same time

We will take the LCM (lowest common factor) of 6 and 15

3 | 6,15

2 | 2,5

5 | 1,5

  | 1,1

LCM = 3*2*5 =30

The LCM of 6 and 15 is 30

So, If they start now, in 30 weeks they will again be running a half marathon at the same time

how to equate: to add 12.8 to -15 subtract 12.8 from 15

15-12.8 =2.2

 since 15 is negative and is larger than 12.8 the answer would be negative so 2.2 becomes -2.2

-15 + 12.8 = -2.2

-15 + 12.8 equates to -2.2 by subtracting the smaller absolute value from the larger one and considering the sign of the number with the larger absolute value. The solution involves basic arithmetic with negative and positive numbers.

Solving the Equation -15 + 12.8

To solve the equation -15 + 12.8, follow these steps:

So, -15 + 12.8 equates to -2.2.

Answer:

D.The vertex form is f(x) = −(x +3)^2 + 4. The standard form is f(x) = −x2−6x−5.  

Step-by-step explanation:

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The length of the given rectangular field is 120 yd while the width is 70 yd.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's say the length of a rectangle is L while the width is W

So,

Perimeter 2(L + W) = 380

And,

L = W + 50

By substitution,

W + 50 + W = 190

2W + 50 = 190

2W = 140

W = 70

And

L = 70 + 50 = 120

Hence "The length of the given rectangular field is 120 yd while the width is 70 yd.

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The cases can be categorized by comparing the means as follows: 'B. Two proportions' apply to situations like income bracket and voter likelihood comparison, 'C. Matched pairs, dependent groups' apply to dependent groups like a math test given to third graders, 'D. exclusive groups' represent separate unaffected and experimental groups, and 'A. Two independent means, normal distribution' refers to situations where two separate groups are compared.

From the details given, we can classify the cases by comparing the means as follows:

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The probability of a 1, 2, or 3 is 3/6 = 1/2. There are C(11,4) = 11!/(4!(11-4)!) = 330 ways the desired outcome can show up in the 11 rolls. The probability is

... 330×(1/2)⁴(1/2)⁷ = 330/2048 ≈ 0.1611

The tax on $95 will be equal to $8.08 at the rate of 8.5%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the tax rate is 8.5% the tax on $95 will be calculated as,

Sales tax = 8.5% of 95

Sales tax = 0.085 x 95

Sales tax = $8.08

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