Va doctor prescribes 10 mg of cough syrup. available is 5 mg/5 ml. how many teaspoons would you give?

Answer:

C

Step-by-step explanation:

Answer:

The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

If np >= 15 and n(1-p) >= 15

Can be approximated to the normal distribution, with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

So

The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

To divide the given polynomial by x + 2, use polynomial long division, which involves dividing the leading term, multiplying the divisor, subtracting, and repeating the process until all dividend terms are addressed.

To divide the polynomial -2x^3 - 5x^2 + 4x + 2 by x + 2, we can use the process of polynomial long division. This method is similar to long division with numbers, where we divide, multiply, subtract, bring down the next term, and repeat the process until we have gone through all terms of the dividend.

The process would look like this:

The final result would be the quotient of the division, which may or may not have a remainder.

x = sqrt(17^2 + 15^2)

x = 8

 missing side = 8

Answer:

a x n

Step-by-step explanation:

There are a pounds in n identical boxes. That means you would have to multiply to get the answer.

Final answer:

To find the weekly wage for someone working 40 hours at an hourly rate of $9.75, multiply the number of hours by the hourly rate, which equals $390.

Explanation:

The weekly wage for a person who works 40 hours at an hourly rate of $9.75 can be calculated by multiplying the number of hours worked per week by the hourly wage. Here's the calculation:

Therefore, the answer required for the weekly wage for this person is $390.

The correct order is [tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex].

To list the values ln, rn, mn, tn and i in increasing order for any value of n, we need to understand the relationship between these variables.

The variables ln, rn, mn, and tn likely represent different measures, such as left endpoint, right endpoint, midpoint, and trapezoid point in numerical methods, while i often represents the imaginary unit iota in mathematics.

Commonly, if we assume these have increasing values when ordered, they would be listed as:

Therefore, the values in increasing order are:

[tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex]

The area of a circle is calculated with the formula A = πr², where pi is the mathematical constant approximately equal to 3.14159 and r represents the circle's radius. Considering significant figures is crucial for maintaining precision, as demonstrated in rounding the calculated area of a circle with radius 1.2 m to 4.5 m², based on the initial data's precision.

The area of a circle is calculated using the formula A = πr², where π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. When calculating the area with a given radius, it's important to consider the significance of figures in your final answer. For instance, if a circle's radius is given as 1.2 meters (with two significant figures), and you calculate the area to be 4.5238934 square meters using a detailed value of pi, you need to round your final answer to maintain the precision of your initial data, resulting in an area of 4.5 m².

It's also valuable to note how ancient civilizations, like the Greeks, approximated mathematics related to circles and how such estimations have evolved into our modern understanding, where the concept of significant figures plays a critical role in ensuring accuracy across varying fields of study and applications.

Final answer:

The given function f(x) = x3 – 5x2 + 9x – 45 has rational roots ±1, ±3, ±5, and ±9.

Explanation:

To determine the number of roots and identify them for the function f(x) = x3 – 5x2 + 9x – 45, we can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation, then p must divide the constant term (in this case, 45) and q must divide the leading coefficient (in this case, 1). By trying all possible combinations of p and q, we can find the rational roots of the equation. In this case, the rational roots are ±1, ±3, ±5, and ±9.

The number of real roots is 1, and it is ( x = 5 ).

To determine the number of roots and identify them for the function[tex]\( f(x) = x^3 - 5x^2 + 9x - 45 \)[/tex], we can use various methods such as the Rational Root Theorem, Descartes' Rule of Signs, or graphing techniques. In this case, since the degree of the polynomial is 3, we know that there will be 3 roots in total.

We'll start by checking for rational roots using the Rational Root Theorem. According to this theorem, if a rational root [tex]\( \frac{p}{q} \)[/tex] exists for the polynomial [tex]\( f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 \), then \( p \)[/tex] is a factor of the constant term [tex]\( a_0 \) and \( q \)[/tex] is a factor of the leading coefficient [tex]\( a_n \)[/tex].

The constant term of [tex]\( f(x) \) is \( -45 \)[/tex]and the leading coefficient is ( 1 ). The factors of ( -45 ) are [tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]. The factors of \( 1 \) are \( \pm 1 \)[tex]\( 1 \) are \( \pm 1 \)[/tex].

By trying all possible combinations of these factors, we can find the rational roots of the polynomial. We'll then use synthetic division or polynomial long division to check if these roots are actually roots of the polynomial.

Let's proceed with the calculations:

1. Possible rational roots:

[tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]

2. Testing these roots using synthetic division or polynomial long division:

Testing [tex]\( x = 1 \)[/tex]:

[tex]\[ f(1) = (1)^3 - 5(1)^2 + 9(1) - 45 = 1 - 5 + 9 - 45 = -40 \][/tex]

Testing [tex]\( x = -1 \)[/tex]:

[tex]\[ f(-1) = (-1)^3 - 5(-1)^2 + 9(-1) - 45 = -1 - 5 - 9 - 45 = -60 \][/tex]

Testing [tex]\( x = 3 \)[/tex]:

[tex]\[ f(3) = (3)^3 - 5(3)^2 + 9(3) - 45 = 27 - 45 + 27 - 45 = -36 \][/tex]

Testing [tex]\( x = -3 \)[/tex]:

[tex]\[ f(-3) = (-3)^3 - 5(-3)^2 + 9(-3) - 45 = -27 - 45 - 27 - 45 = -144 \][/tex]

Testing ( x = 5 ):

[tex]\[ f(5) = (5)^3 - 5(5)^2 + 9(5) - 45 = 125 - 125 + 45 - 45 = 0 \][/tex]

[tex]\[ \Rightarrow \text{Root: } x = 5 \][/tex]

Testing ( x = -5 ):

[tex]\[ f(-5) = (-5)^3 - 5(-5)^2 + 9(-5) - 45 = -125 - 125 - 45 - 45 = -340 \][/tex]

Testing ( x = 9 ):

[tex]\[ f(9) = (9)^3 - 5(9)^2 + 9(9) - 45 = 729 - 405 + 81 - 45 = 360 \][/tex]

Testing ( x = -9 ):

[tex]\[ f(-9) = (-9)^3 - 5(-9)^2 + 9(-9) - 45 = -729 - 405 - 81 - 45 = -1260 \][/tex]

Testing ( x = 15 ):

[tex]\[ f(15) = (15)^3 - 5(15)^2 + 9(15) - 45 = 3375 - 1125 + 135 - 45 = 2340 \][/tex]

Testing ( x = -15 ):

[tex]\[ f(-15) = (-15)^3 - 5(-15)^2 + 9(-15) - 45 = -3375 - 1125 - 135 - 45 = -4680 \][/tex]

Testing ( x = 45 ):

[tex]\[ f(45) = (45)^3 - 5(45)^2 + 9(45) - 45 = 91125 - 10125 + 405 - 45 = 81060 \][/tex]

Testing ( x = -45 ):

[tex]\[ f(-45) = (-45)^3 - 5(-45)^2 + 9(-45) - 45 = -91125 - 10125 - 405 - 45 = -102705 \][/tex]

From these tests, we see that ( x = 5 ) is a root of the polynomial. The other roots are irrational or complex.

So, the number of real roots is 1, and it is ( x = 5 ).

Answer:

The area if this figure is 35cm2

Step-by-step explanation:

There are 9 ways to choose eight coins from a piggy bank.

Total number of ways =

(Combinations of 8 pennies) + (Combinations of 7 pennies and 1 nickel) + ... + (Combinations of 0 pennies and 8 nickels)

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9 ways

Answer:

Option 3 - [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.

Step-by-step explanation:

To find : Which statement is true?

Solution :

As the function defined in all statement is logarithmic function.

So, The definition of logarithmic function is defined as

[tex]y=\log_bx\Rightarrow b^y=x[/tex] where, b>0 and b ≠ 1.

Now, The following statement

1) [tex]y=\log_{10}x[/tex] is not a logarithmic function because the base is greater than 0.

The statement is False as by definition, the base of a log must be greater than zero but cannot equal one.

2) [tex]y=\log_{\sqrt3}x[/tex] is not a logarithmic function because the base is a square root.

The statement is False as by definition, the base [tex]\sqrt3[/tex]  is a positive number not equal to one.

3) [tex]y=\log_{1}x[/tex] is not a logarithmic function because the base is equal to 1.

The statement is True as by definition log cannot have a base of one.

4)  [tex]y=\log_{\frac{3}{4}}x[/tex] is not a logarithmic function because the base is a fraction.

The statement is False, as 3/4 is a legitimate base, just like any other positive number other than one.

Therefore, Option 3 is true.

Answer:

HI!

Your spinner has 5 colors, and if you spin it, the probability of landing in each color will be the same ( because the spiner has 5 equal sections).

So for every spin, the probability on landing on each color will be 20%.

If i spin it 200 times, then the 20% of 200 is 0.2*200 = 40.

It means that if you spin it 200 times, then each colour shows 40 times theoretically. The question is: how many times should Alina expect the spinner to land on either purple or orange?

you have 40 for purple and 40 for orange, then the total times that the spinner lands on either purple or orange is 80.

Answer: The required function formula is,

S(t) = 2 - 0.25 t

Step-by-step explanation:

Here, the initial thickness of the ice sheet = 2 meters,

After 3 weeks, the thickness of ice sheet = 1.25 meters

Total changes in the thickness in 3 weeks = 2 - 1.25 = 0.75 meters,

⇒ Total changes in the thickness in 1 weeks = 0.75/3 = 0.25 meters,

Since, the ice is melting with the constant rate.

⇒ The rate of ice decreasing = 0.25 meters per week.

⇒ Total changes in t weeks = 0.25 t meters

The new thickness of ice after t weeks = Initial thickness - Total changes in t weeks.

⇒ S(t) = 2 - 0.25 t

Which is the required function's formula.

The function's formula for the ice sheet's thickness as a function of time is S(t) = -0.25t + 2.

To write the function's formula, we can use the slope-intercept form of a linear equation, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope represents the rate at which the ice thickness decreases over time. From the given information, we know that the thickness decreases by 0.75 meters over 3 weeks. Therefore, the slope is -0.75/3 = -0.25 meters per week.

Since the ice thickness is 2 meters in the beginning, the initial point on the graph is (0, 2). Using the slope-intercept form, we can write the formula for the ice sheet's thickness as a function of time as:

S(t) = -0.25t + 2

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