Factorize 5b2-11b+6=0​

Answer:

  0.444 µg/mL

Step-by-step explanation:

You want the maximum value of C(t) = 3(e^(−0.4t)−e^(−0.6t)) in the period 0 < t < 12. C is measured in µg/mL, and t is measured in hours.

The maximum concentration will be at the point where the derivative of C(t) with respect to t is zero.

  C' = 3(-0.4e^(-0.4t) +0.6e^(-0.6t)) = 0

  3e^(-0.6t) -2e^(-0.4t) = 0 . . . . . divide by 0.6

  3e^(-0.2t) -2 = 0 . . . . . . . . . divide by e^(-0.4t)

  e^(-0.2t) = 2/3 . . . . . . . . . add 2, divide by 3

Now, we can find the values of the exponential terms:

  e^(-0.4t) = (e^(-0.2t))^2 = (2/3)^2 = 4/9

  e^(-0.6t) = (e^(-0.2t))^3 = (2/3)^3 = 8/27

So, ...

  C(t) = 3(4/9 -8/27) = 3(4/27) = 4/9 . . . . . maximum concentration

The maximum concentration of antibiotic is 0.444 µg/mL.

__

Additional comment

The time at which the maximum occurs will be approximately ...

  t = ln(2/3)/-0.2 ≈ 2.027 . . . . hours after the tablet is taken

You might normally expect the value of t to be found first, then C(t) evaluated for that value of t. By skipping those steps, we eliminate some rounding errors and arrive at a more accurate value for the maximum concentration.

Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

First find the area of the square, then the triangle.

15 times 17 = 255 sq. yd

Triangle:

(5 times 5)/2 = 12.5 sq. yd

Your answer is 267.5 sq. yd

Hope this helps.

Answer:

Step-by-step explanation:

Determine the lengths of the sides, then apply Heron's Formula to find the area.

Answer:

C. 5/12

Step-by-step explanation:

Finding the missing side :

Taking the tan ratio :

Answer:

The answer will be x = 3, you are correct!

Step-by-step explanation:

Hope this helps!! :)))

Answer:

The answer will be x = 3, you are correct!

Step-by-step explanation:

I tried to help so sorry if I get it wrong

The random variable X represents the number of Californians in the sample of 6 who have been to Disneyland. X is a binomial random variable because each person in the sample can be classified as either having been to Disneyland or not, which is a binary outcome.The probability of success (having been to Disneyland) is constant at 0.41 for each person in the sample.  the probability that exactly 3 Californians in the sample of 6 have been to Disneyland is 0.274 or approximately 27.4%. The mean of X is 2.46.  The standard deviation of X is 1.27. The probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean is 0.767 or approximately 76.7%.

a) The random variable X represents the number of Californians in the sample of 6 who have been to Disneyland.

b) X is a binomial random variable because the following conditions are met:

Each person in the sample can be classified as either having been to Disneyland or not, which is a binary outcome.

The probability of success (having been to Disneyland) is constant at 0.41 for each person in the sample.

The individuals in the sample are independent of each other.

c) To find the probability that exactly 3 people in the sample have been to Disneyland, we can use the binomial probability formula:

P(X = 3) = (6 choose 3) * (0.41)^3 * (1-0.41)^3 = 0.274

Therefore, the probability that exactly 3 Californians in the sample of 6 have been to Disneyland is 0.274 or approximately 27.4%.

d) The mean of X is given by the formula:

mean(X) = n * p = 6 * 0.41 = 2.46

Therefore, the mean of X is 2.46.

e) The standard deviation of X is given by the formula:

stddev(X) = sqrt(n * p * (1-p)) = sqrt(6 * 0.41 * (1-0.41)) = 1.27

Therefore, the standard deviation of X is 1.27.

f) To find the probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean, we can use the normal approximation to the binomial distribution.

First, we need to find the z-scores corresponding to X = 1 and X = 4:

z1 = (1 - 2.46) / 1.27 = -1.17

z4 = (4 - 2.46) / 1.27 = 1.22

Then, we can use the standard normal distribution table to find the probabilities corresponding to these z-scores:

P(X ≤ 1) = P(Z ≤ -1.17) = 0.121

P(X ≤ 4) = P(Z ≤ 1.22) = 0.888

Finally, we can subtract these probabilities to find the probability that X is within one standard deviation of the mean:

P(1 < X < 4) = P(X ≤ 4) - P(X ≤ 1) = 0.888 - 0.121 = 0.767

Therefore, the probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean is 0.767 or approximately 76.7%.

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Answer:

417.831823 \(in^{2}\)

Step-by-step explanation:

surface area of cone ;

\(=\pi r^{2}+\pi rl\\ =\pi (7^{2}) +\pi (7)(12)=417.831823 in^{2}\)

Answer:417.831823

Step-by-step explanation:

The number of the trees that will be left after 10 years will be 2.3 billions.

A rate of change is negative when the output decreases as the input increases or when the output increases as the input decreases.

Given that, the number of trees in a rainforest decreases each month by 0.5%. The forest currently has 2.5 billion trees.

The expression will be:

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = rate

n = time

Therefore,

A = 2500000000(1-00.5)¹⁰

A = 2500000000(0.995)¹⁰

A = 2300000000

Hence, the number of the trees that will be left after 10 years will be 2.3 billions.

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Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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The series of rigid motion transformations that map polygon A to Polygon A''' are;

A rigid transformation is a transformation in which the distance between all pairs of points on the pre-image is preserved following the transformation.

The series of rigid motion transformations that map polygon A to polygon A''' are;

Transformation from A to A'

Transformation from A' to A''

Transformation from A'' to A'''

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Answer:

b. 5, 11, 6

Step-by-step explanation:

Let the sides of a triangle be a, b, and c, where a < b < c. Then, we know that a + b > c. If we use this identity to solve this problem, then we can find that answer choice b does not satisfy it. Thus, b does NOT  have the lengths of a triangle.

Answer:

\(\frac{1}{9}\)

Step-by-step explanation:

\(\frac{1}{3^2}=\frac{1}{3} *\frac{1}{3} =\frac{1}{9}\)

Answer: -4

Step-by-step explanation:

The algebraic expression for the statement the product 7 and the square of a number is 7x²

Algebraic expressions are described as mathematical expressions that consist of arithmetic terms, factors, constants, variables and coefficients.

These expressions are also composed of arithmetic operations which may include;

From the information given, we have that;

The product 7 and the square of a number

Now, let the number be x

The square of x is x²

This statement is expressed as;

7x²

Thus, the expression is 7x²

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The complete question:

The product 7 and the square of a number. Write the algebraic expression

Answer:

18.99 miles

Step-by-step explanation:

6.74 + 7.3 + 4.95 = 18.99 miles

Using distributive property, the solution to the given expression is: 50v - 40w + 20

The Distributive Property is a term which is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

For example:

4(3 + 5)

According to the distributive property, you first have to multiply out the bracket to get:

4*3 + 4*5 = 12 + 20

= 32

Thus:

5(10v - 8w + 4) = (5 * 10v) - (5 * 8w) + (5 * 4)

= 50v - 40w + 20

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Answer:

To divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

For more examples and explanatTo divide fractions, you need to follow these steps:

Flip the second fraction (the one you want to divide by) upside down (this is called taking the reciprocal).

Multiply the first fraction by the reciprocal of the second fraction.

Simplify the resulting fraction if possible.

Here is an example:

1/3 ÷ 2/5

Step 1: Flip the second fraction: 2/5 becomes 5/2.

Step 2: Multiply the first fraction by the reciprocal of the second fraction: 1/3 x 5/2 = 5/6.

Step 3: Simplify the resulting fraction if possible: 5/6 is already in its simplest form.

Step-by-step explanation:

brainliest pls

Answer:

Step-by-step explanation:

For dividing fractions:

Remember:

Keep Change Flip

Keep the first the same

Change the sign to multiplication

Flip the second fraction.

EX.

\(\frac{4}{5}\) ÷ \(\frac{1}{2}\)                           >Keep, Change Flip

=\(\frac{4}{5}\) * \(\frac{2}{1}\)                          >Now it's multiplication, reduce first if you can

                                    (nothing reduces in this problem), so mulitply

                                    across

= \(\frac{8}{5}\)

Given data:

The original cost of dinner C=$20.00.

The sale price is 80% of the original cost.

Thus, the final sale price is $16.00.

_________

\( \: \)

2½m = 2.5 × 100 = 250cm

Soo :

\( \longmapsto\frac{3}{1 \cancel0} \times 25 \cancel0\)

\( \longmapsto3 \times 25\)

\( \longmapsto \bold{75cm}\)

Answer:

whole life insurance

Step-by-step explanation:

Answer:

Term life insurance and Universal life

Step-by-step explanation:

Answer:

increase of 100%

Step-by-step explanation:

50 cents to 1 dollar is an increase.

The percent increase can be calculated by dividing the increased amount by the original amount.

$1.00 - $0.50 = $0.50 increase

% increase = 100%

Answer:

(\(1/2,1/\sqrt{6}\)),(-1/2,\(1/\sqrt{6}\)),(-1/2,\(-1/\sqrt{6}\)) and

(\(1/2,-1/\sqrt{6}\))

Step-by-step explanation:

We are given that

\(g(x,y)=2x^2+3y^2-1=0\)

\(f(x,y)=xy\)

Using Lagrange's multipliers

\(f_x(x,y)=y\)

\(f_y(x,y)=x\)

\(g_x(x,y)=4x\)

\(g_y(x,y)=6y\)

\(f_x(x,y)=\lambda g_x(x,y)\)

\(y=4x\lambda\)

\(f_y(x,y)=\lambda g_y(x,y)\)

\(x=6\lambda y\)

\(\lambda=\frac{y}{4x}\)...(1)

\(\lambda=\frac{x}{6y}\)...(2)

Equation (1) divided by (2)  Then we get

\(1=\frac{6y^2}{4x^2}=\frac{3y^2}{2x^2}\)

\(2x^2=3y^2\)

Substitute the values  in g(x,y)

\(3y^2+3y^2=1\)

\(6y^2=1\)

\(y^2=1/6\)

\(y=\pm \frac{1}{\sqrt{6}}\)

\(2x^2+2x^2=1\)

\(4x^2=1\)

\(x^2=1/4\)

\(x=\pm \frac{1}{2}\)

Therefore, the points on the ellipse are

(\(1/2,1/\sqrt{6}\)),(-1/2,\(1/\sqrt{6}\)),(-1/2,\(-1/\sqrt{6}\)) and

(\(1/2,-1/\sqrt{6}\))

a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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All tables that represent proportional relationship between x and y are:

B. table B.

E. table E.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)

Constant of proportionality, k = 1.

Therefore, the required linear equation is given by;

y = kx

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The unknown angle in the cyclic quadrilateral is as follows:

∠R = 86 degrees

The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.

Hence, let's find the unknown angle.

∠R = 1 / 2 (92 + 80)

∠R = 1 / 2 (172)

∠R = 86 degrees

Therefore, the unknown angle is 86 degrees.

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Answer:

if the mean of 4 numbers is 30 then that means that the total of all the numbers added together must add up to 120 (30 x 4)

then you subtract the three numbers that you have from the total

120-12-50-48 = 10

so the last number is 10

Step-by-step explanation:

The graph of the translated function is g ( x ) = ( x + 5 )² + 2

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x²

On simplifying , we get

The function is translated 5 units to the horizontal left direction:

And , when the function is translated 2 units in the vertical upward direction:

So , the translated function is

g ( x ) = ( x + 5 )² + 2

Now , the vertex of the function g ( x ) = ( x + 5 )² + 2 is (-5, 2)

Hence , the graph of the function is plotted and g ( x ) = ( x + 5 )² + 2

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