What are the exact values of a and b?

0 a =7/2,

The sequence -19, -11, -3, 5,... is arithmetic with a common difference of 8.

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant value, called the common difference (d), to the preceding term. To determine if the given sequence is arithmetic, we can find the differences between consecutive terms.

The difference between the second and first terms is 11 - (-19) = 30, and the difference between the third and second terms is -3 - (-11) = 8. The difference between the fourth and third terms is 5 - (-3) = 8. Since the differences between consecutive terms are the same, the sequence is arithmetic.

The common difference can be found by subtracting any term from the term that follows it. For example, the common difference can be obtained by subtracting the second term (-11) from the third term (-3), or by subtracting the third term (-3) from the fourth term (5).

In both cases, we get a common difference of 8. Therefore, the common difference of the given sequence is 8.

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Answer:

Step-by-step explanation:

[tex]\frac{n}{n-1}+\frac{2}{n+1} = 2\\\frac{n^2+n + 2n-2}{n^2-1} = 2\\ n^2+3n-2 = 2n^2-2\\n^2=3n\\n^2-3n= 0\\n(n-3) = 0\\n = 0 \\or\\ n = 3[/tex]

a. The concentration would be 0.5 mg/L at approximately t = 40 hours.

b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.

c. A reasonable domain for this function is t ≥ 0.

d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.

e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.

In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);

c(t) = 20t/(t² + 4)

0.5 = 20t/(t² + 4)

0.5(t² + 4) = 20t

0.5t² + 2 = 20t

0.5t² + 2 - 20t = 0

t² + 4 - 40t = 0

t² - 40t + 4 = 0

Time, t = 38.8998 ≈ 40 hours.

Part b.

In this context, we would complete the table of values at various time (t) as follows;

t        0    2      4     6       8           10        12        14     16        18      20

c(t)    0    5      4      3     2.35      1.92     1.62     1.4    1.23     1.10    1.00

Part c.

Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

Part d and e.

Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.

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Answer:

3.5 feet

Step-by-step explanation:

To determine whether you can jump a fence that is 7/6 of a yard tall, we need to convert the height to feet and compare it to your own jumping ability.

1 yard = 3 feet

So, 7/6 yards = (7/6) x 3 feet = 3.5 feet

Since a horse can jump a fence that is 4 feet tall and 4 feet is greater than 3.5 feet, it is likely that the horse can jump the fence while it may be more challenging for you to do so.

(a) The value of h in the right triangle is 5.8.

(b) The value of a in the right triangle is 9.9.

Right triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e, in which two sides are perpendicular.

(a) To find the value of h in the right triangle, we use the formula below

Formula:

Where:

Susbtituet these values into equation 1

(b) Also, to calculate the value of a in the right triangle, we us the formula below

Where:

Substitute these values into equation 2

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Natalie owes $18 at the end of every two weeks.

To find the weekly payment amount, we can use the given data to write a system of equations. Let's assume that Natalie borrowed x amount from her parents.

From the given table, we can write the following equations:

At the end of 2 weeks, Natalie still owes:

x - 2d = 180 ...(1)

At the end of 4 weeks, Natalie still owes:

x - 4d = 144 ...(2)

Solving equations (1) and (2), we get:

2d = 36

d = 18

Therefore, Natalie owes $18 at the end of every two weeks.

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Answer:

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

Find the slope of the line passing through the given points:

Perpendicular lines have negative- reciprocal slopes, so the perpendicular bisector has a slope of m = 4.

Find the midpoint of the segment with the endpoints  (7, - 1) and (- 9,3).

Now, we need to find the line with a slope of 4 and passing through the point (- 1, 1). Use point-slope form and find the equation:

The correlation coefficient between the year and high temperature is approximately 0.9604,

To calculate the correlation coefficient between x (representing the year) and y (representing the high temperature), we can use the following steps:

1. Find the means of x, y, and their products.

   - Mean of x,  ¯  = (1+2+3+..+14)/14 = 7.5

   - Mean of y,  ¯    = (17.17+22.14+24.61+...+51.98)/14 ≈ 32.05

   - Mean of , ¯ = [(1* 17.17)+(2* 22.14)+...+(14* 51.98)]/14 ≈ 1312.925

2. Calculate the sample standard deviations of x and y.

  - Standard deviation of x, = √([∑(−¯)[tex]^2[/tex]]/(−1)) ≈ 4.3205

  - Standard deviation of y, = √([∑(−¯)^2]/(−1)) ≈ 10.8629

3. Calculate the covariance of x and y.

  - Covariance of x and y, cov(x,y) = [∑(−¯)(−¯)]/(−1) ≈ 51.7874

4. Calculate the correlation coefficient, r.

  - Correlation coefficient, r = cov(x,y) / ( ) ≈ 0.9604

Therefore,  indicating a strong positive linear relationship between x and y. The value of r being close to 1 suggests that as the year increases, so does the high temperature.

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Answer:

V = 25 cm³

Step-by-step explanation:

the volume (V) of a rectangular prism is calculated as

V = Ah ( A is the area of the base and h the height )

V = 15 × 5 = 75 cm³

the volume of the pyramid is one third the volume of the prism , then

V = 75 × [tex]\frac{1}{3}[/tex] = 25 cm³

Answer: 1507.84ft^2

Step-by-step explanation:

Semicircle r = 16ft

Rectangle width = 22ft (because the radius of the semicircle is 16 and there are two of them, 2 x 16 = 32, 54 - 32 = 22)

Rectangle height = 32ft

Area of rectangle:

22 x 32 = 704ft^2

Area of circles:

16^2 x 3.14 = 803.84ft^2

No need to half the area for a semicircle because there are 2 of them

Therefore:

803.84 + 704 = 1507.84ft^2

Every adult's meal costs $26, and every child's meal costs $17.

Let

cost of adults = x

Cost of child = y

78x + 78y = $3,354

58x + 76y = $2,800

From (1)

Divide through by 78

x + y = 43

x = 43 - y

Substitute into (2)

58x + 76y = $2,800

58(43 - y) + 76y = 2800

2494 - 58y + 76y = 2800

- 58y + 76y = 2800 - 2494

18y = 306

y = 306/18

y = 17

Substitute the value of y into

x = 43 - y

x = 43 - 17

x = 26

Therefore, the cost of adults meal is $26 and child's meal is $17

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She will need to use 4 bottles of plant food in 12 weeks.

To feed one plant, Juba mixes 15ml of plant food with 1 liter of water. She will therefore require the following to feed nine plants in the greenhouse once a week:

9 plants × 15 ml plant food every week = 135 ml plant food.

To feed 11 plants in the vegetable plot twice a week, she will need:

11 plants x 15 ml plant food x 2 times = 330 ml plant food per week

Juba will therefore require a total of 135 ml + 330 ml = 465 ml of plant food per week.

She will require: 465 ml  x 12 weeks = 5580 ml.

Plant food comes in bottles of 1500 ml each. Juba will therefore require:5580 ml ÷ 1500 ml/bottle = 3.72

Therefore, She will need to use 4 bottles of plant food in 12 weeks.

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For the second week of November, Donald Miller earned $754.

Let's calculate Donald Miller's earnings for the second week of November using the given information:
1. Determine the number of regular and overtime hours:
Donald worked 52 hours in total, with overtime paid for hours above 40. So he worked 40 regular hours and 12 overtime hours (52 - 40 = 12).
2. Calculate regular pay:
Donald earns $13 per hour for the regular hours. To find his regular pay, multiply the hourly rate by the number of regular hours worked: 40 hours * $13/hour = $520.
3. Calculate overtime pay:
The overtime rate is 1.5 times the hourly rate, so the overtime pay is $13 * 1.5 = $19.5 per hour. To find the total overtime pay, multiply the overtime rate by the number of overtime hours worked: 12 hours * $19.5/hour = $234.
4. Calculate the total pay for the second week of November:
Add the regular pay and overtime pay together: $520 (regular pay) + $234 (overtime pay) = $754.
So, for the second week of November, Donald Miller earned $754 (rounded to the nearest cent if necessary).

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Answer:

Slope that is perpendicular to y=-2/3x+5: 3/2

y-11=3/2(x-2)

Step-by-step explanation:

have a great day and thx for your inquiry :)

The graph of function is shown in image.

We have to given that;

The Function is,

f (x) = ∛ (x + 1)

Now, We can find the domain and range as;

Since, We know that the set of all inputs of the function is called Domain of set.

Hence, Domain of function is,

D = (- ∞,∞)

And, Range is,

R = (- ∞,∞)

Here, In the function there is no inflection point in present.

And The end behavior of the function y =∛ (x + 1) is as x approaches negative infinity, y approaches negative infinity, and as x approaches positive infinity, y approaches positive infinity.

Thus, The graph of function is shown in image.

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There are 6,000,000 different license plates possible given the given conditions of 2 letters followed by 5 Digits, with the first letter being C, F, J, or K, and the first digit being less than 7.

The number of different license plates possible given the given conditions, we need to consider the choices available for each position.

For the first letter, we are given that it must be either C, F, J, or K. So, we have 4 options for the first letter.

For the second letter, any letter can be chosen except the one already used in the first position. Since repetition is not permitted, we have 25 options for the second letter (26 letters in the alphabet minus 1 used in the first position).

For the first digit, it must be less than 7. So, we have 6 options (0, 1, 2, 3, 4, 5).

For the second digit, we have 10 options (0-9).

For the third digit, we also have 10 options.

Similarly, for the fourth and fifth digits, we have 10 options each.

the total number of possible license plates, we need to multiply the number of choices for each position.

Total number of license plates = Number of choices for the first letter * Number of choices for the second letter * Number of choices for the first digit * Number of choices for the second digit * Number of choices for the third digit * Number of choices for the fourth digit * Number of choices for the fifth digit

Total number of license plates = 4 * 25 * 6 * 10 * 10 * 10 * 10 = 6,000,000

Therefore, there are 6,000,000 different license plates possible given the given conditions of 2 letters followed by 5 digits, with the first letter being C, F, J, or K, and the first digit being less than 7.

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The standard form of the equation of a circle is,

⇒ (x - 3)² + (y + 1)² = 13

Given that;

a circle that has a center at (3, -1) and a point on the circle at (5, 2).

Hence, The value of radius is distance between (3, - 1) and (5, 2).

So, We get;

Radius = √(5 - 3)² + (2 - (- 1))²

Radius = √4 + 9

Radius = √13

So, the standard form of the equation of a circle is,

⇒ (x - 3)² + (y + 1)² = (√13 )²

⇒ (x - 3)² + (y + 1)² = 13

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We can use the binomial probability formula to solve this problem.

P(X≥3) = 1 - P(X<3)

First, we need to find P(X<3), which means finding the probability of getting 0, 1, or 2 successes in 7 trials with a probability of success of 0.1.

P(X<3) = P(X=0) + P(X=1) + P(X=2)

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

P(X=0) = (7 choose 0) * 0.1^0 * 0.9^7 = 0.4783

P(X=1) = (7 choose 1) * 0.1^1 * 0.9^6 = 0.3830

P(X=2) = (7 choose 2) * 0.1^2 * 0.9^5 = 0.1144

P(X<3) = 0.4783 + 0.3830 + 0.1144 = 0.9757

P(X≥3) = 1 - P(X<3) = 1 - 0.9757 = 0.0243

Therefore, the probability of getting at least 3 successes in 7 trials with a probability of success of 0.1 is 0.0243.

The area for the figure in this problem is given as follows:

A = 1216 ft².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The figure in this problem is composed as follows:

Hence the area of the figure is calculated as follows:

A = 55.75 x 17.5 + π x 8.75²

A = 1216 ft².

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The value of the missing angle obtained using the Cosine Formula is 28.2°

The Cosine Formula can be expressed thus ;

CosB = (a²+c²-b²) / 2ac

b = 11

a = 12

c = 20

Substituting the values into the equation

CosB = (12² + 20² - 11²) / 2(12×20)

CosB = (144-400-121)/480

CosB = 423/480

CosB = 0.88125

B =

[tex] {Cos}^{ - 1} (0.88125)[/tex]

B = 28.2°

Therefore, the value of the missing angle is 28.2°

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The amount of time it will take to completely fill the pool would be = 18 hours.

To determine the amount of time it will take to fill the pool, the volume of the pool is first calculated by dividing the figure to obtain two regular shapes of a trapezoidal prism and a square prism.

The volume of a trapezoidal prism = 1/2(a+b)×h×l

where;

a = 3m

b = 1m

h = 18-6 = 12m

l = 9m

Volume of the trapezoidal prism = 1/2(3+1)×12×9

= 4×12×9 = 432m³

Volume of square prism = length×width×height

where;

length = 6m

width = 9m

height = 1 m

Volume = 6×9×1 = 54m³

Therefore the volume of the pool = 432+54 = 486m³

If 4 hours = 2 m up from the deepest part

The volume filled for 4 hours = 1/2×2×12×9 = 108m³

If 4 hours = 108

X hours = 486

make X the subject of formula;

X = 4×486/108

= 1944/108

= 18 hours.

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Answer: x = [tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

       To show your work for this problem, you will write out every step that you take to solve for x.

Given:

     3x - 5 = x + 2 - 10 - 7x

Combine like terms:

     3x - 5 = - 6x - 8

Add 5 and 6x to both sides of the equation:

     9x  = - 3

Divide both sides of the equation by 9 and simplify the fraction:

     x = [tex]-\frac{3}{9}=-\frac{1}{3}[/tex]

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

The domain of the function is all real numbers (x ∈ R) and the range is all positive real numbers (y > 0).

The set of all values of the independent variable for which the function is defined is known as domain.

The function is defined for all real values of x so domain is R.

Domain: x ∈ R

The range of a function is the set of all values of the dependent variable (usually denoted as 'y') that the function can take as x varies over its domain.

For this function, the base of the exponent is 2, which means that the function grows exponentially as x increases.

As such, the range of this function is all positive real numbers.

Range: y > 0

Therefore, the domain of the function is all real numbers (x ∈ R) and the range is all positive real numbers (y > 0).

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The required probability of randomly selecting a white marble, replacing it, then randomly selecting another white marble is 4/25.

The probability of randomly selecting a white marble from the bag is 8/20, or 2/5, since there are 8 white marbles out of a total of 20 marbles (5 red, 8 white, and 7 green).

After replacing the first marble, there are still 8 white marbles and a total of 20 marbles in the bag. Therefore, the probability of randomly selecting another white marble is also 2/5.

To find the probability of both events happening (selecting a white marble, replacing it, and then selecting another white marble), we multiply the probabilities of the two events:

The probability of selecting a white marble and replacing it, then selecting another white marble = (2/5) x (2/5) = 4/25

Therefore, the probability of randomly selecting a white marble, replacing it, then randomly selecting another white marble is 4/25.

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The side lengths of RS and RT are 4 and 5 units

From the question, we have the following parameters that can be used in our computation:

The right triangles (See attachment)

The side lengths of RS and RT are calculated using

RT = KS = 4

Then we apply the pythagoras theorem for RS as follows

RS² = RK² + KS²

substitute the known values in the above equation, so, we have the following representation

RS² = 3² + 4²

So, we have

RS = 5

Hence, the side lengths of RS and RT are 4 and 5 units

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a.) The concentration of the drug after 8 hours in the blood would be = 24 mg/L.

b.) The concentration increases over the interval of 0-2 hours.

c.) The maximum concentration of the drug is at 2 hours after intake which is 64 mg/L.

d.) After the drug reaches its maximum concentration, it will take 8 hours to decrease to 16mg/L.

e.) The concentration of the drug in the blood after one week will be zero.

f.) In summary, the concentration of the drug in the blood stream after the first 20 hours will be done below.

Drug blood concentration is defined as the amount of drug that is absorbed into the blood stream that contains a particular quantity per liter of blood.

The graph above represents the relationship between the concentration of a drug in the blood and the time it was taken.

For a ) The concentration of the drug after 8 hours in the blood would be = 24 mg/L.

For b.) The concentration increases over the interval of 0-2 hours.

For c.) The maximum concentration of the drug is at 2 hours after intake which is 64 mg/L.

For d.) After the drug reaches its maximum concentration, it will take 8 hours to decrease to 16mg/L.

For e.) The concentration of the drug in the blood after one week will be zero.

For f.) In summary, the concentration of the drug in the blood stream after the first 20 hours is not the same as observed in the graph above. There is a spike increase after the first two hours of intake after which a decrease in concentration was observed through our the remaining hours.

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