(a) Complete this synthetic division table.
-2) 3
-1
-11
8 7

The nurse should administer 6 tablets per dose.

To calculate this, divide the total daily dose (300 mg) by the dose per tablet (50 mg):

300 mg / 50 mg = 6 tablets

Since the dose is divided equally every 6 hours, the nurse should administer 6 tablets every 6 hours.

It's important for the nurse to double check the medication order and dosing calculations before administering any medication to ensure the safety and well-being of the client. In addition, the nurse should monitor the client's response to the medication and report any adverse effects to the healthcare provider.

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Answer: The value of the variable x in this exponential equation is 4.

The problem simply asks to solve the following exponential equation on the set of reals:

\(\begin{gathered} \bold{\dfrac{27^x~-~3^x}{9^x~-~3^x}~=~82}\\\\\\ \bold{\dfrac{\left(3^3\right )^x~-~3^x}{\left(3^2\right)^x~-~3^x}~=~82}\\\\\\ \bold{\dfrac{3^{3x}~-~ 3^x}{3^{2x}~-~3^x}~=~82}\end{gathered}\)

To solve this exponential equation in a much simpler way, what we're going to try to do is factor. Note that if we take \(\bold{ 3^x3}\)

x as a common factor what we will get is:

\( \bold{\dfrac{\not\!\!3^x\cdot\left(3^{2x}~-~1\right)}{\not\!\!3^x\cdot\left( 3^{x}~-~1\right)}~=~82}\\\\\\ \bold{ \dfrac{3^{2x}~-~1}{3^x~-~1}~=~82}\)

We can see that factoring the first part of our exponential equation resulted in a much easier exponential equation to solve. Note that \(\sf 3^{2x}~-~13\)

− 1 by the laws of exponents can be written as \(\sf \left(3^x\right)^2~-~1^ 2\)

by definition \(\sf x^2~-~y^2~=~\left(x~+~y\right)\cdot\left(x~-~y\right)\) so we have:

\(\begin{gathered} \bold{\dfrac{\left(3^x\right)^2~-~1}{3^x~-~1}~=~82} \\\\\\ \bold{ \dfrac{\left(3 ^x~+~1\right)\cdot\left(3^x~-~1\right)}{3^x~-~1}~=~82\\\\\\ 3^x~+~ 1~=~82}\\\\\\ \bold{3^x~=~81 }\end{gathered}\)

The exponential equation we now have is not at all difficult to solve. If you repeat the powers of the number 3, you can see that \(\sf 3^4\)

Is the same as 81, so we have:

\(\begin{gathered} \bold{\not\!\!3^x~=~\not\!\!3^4} \\\\\\ \boxed{\sf \bold{\therefore~x~=~4}}~~ \bold{\Rightarrow ~Answer}\end{gathered}\)

\(\sf{\dfrac{27^x\:-\:3^x}{9^x\:-\:3^x} = 82}\)

\(\sf{\dfrac{9^x(3^x)\:-\:3^x}{3^x(3^x)\:-\:3^x} = 82}\)

\(\sf{\dfrac{3^x(9^x-1)}{3^x(3^x-1)} = 82}\)

\(\sf{\dfrac{\cancel{3^x}(9^x-1)}{\cancel{3^x}(3^x-1)} = 82}\)

\(\sf{\dfrac{(9^x-1)}{(3^x-1)} = 82}\)

\(\sf{\dfrac{(3^x-1)(3^x+1)}{(3^x-1)} = 82}\)

\(\sf{(3^x+1)= 82}\)

\(\sf{(3^x)= 81}\)

\(\sf{(3^x)= 3^{4}}\)

\(\boxed{\bold{x= 4}}\)

Answer:

blue i think good luck

The power series for f(x) centered at 0 is:

6 ln(x) + ∑[n=1 to ∞] (-1)^(n+1) / (n x^(6n))

To find a power series for the function f(x) = ln(x^6 + 1), we can use the formula for the Taylor series expansion of the natural logarithm function:

ln(1 + x) = x - x^2/2 + x^3/3 - x^4/4 + ...

We can write f(x) as:

f(x) = ln(x^6 + 1) = 6 ln(x) + ln(1 + (1/x^6))

Now we can substitute u = 1/x^6 into the formula for ln(1 + u):

ln(1 + u) = u - u^2/2 + u^3/3 -  ...

So we have:

f(x) = 6 ln(x) + ln(1 + 1/x^6) = 6 ln(x) + 1/x^6 - 1/(2x^12) + 1/(3x^18) - 1/(4x^24) + ...

Thus, the power series for f(x) centered at 0 is:

6 ln(x) + ∑[n=1 to ∞] (-1)^(n+1) / (n x^(6n))

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The total weight of the liquid in the tank, to the nearest full pound, is calculated to be 3,012 pounds.

The volume of a hemisphere with diameter 6 feet is (2/3) x π x (6/2)³ = 56.55 cubic feet.

The weight of the liquid in the tank can be found by multiplying the volume of the liquid by its density:

Weight = Volume x Density = 56.55 x 53.3 = 3,012.32 pounds.

Rounding this to the nearest full pound gives a total weight of 3,012 pounds. Therefore, the total weight of the liquid in the tank is 3,012 pounds (to the nearest full pound).

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Answer:

3014

Step-by-step explanation:

I just did it

Answer:

£4860

Step-by-step explanation:

\(\sf 10\%\: of \:6000\: =\:6000 * 0.10 = 600\)

£6000 - £600 = £5400

\(\sf10\% \:of\: 5400 \:= 5400 * 0.10 = 540\)

£5400 - £540 = £4860

Therefore, the value of the van after 2 years would be £4860.

Answer:

1

Step-by-step explanation:

Hello :)

So to answer this problem, we can use the rise over run formula.

The rise is the difference of any two y values.

The run is the difference of the x values from the same two y values.

This question gives us 1,-2 and 3,0

We can use them for the formula:

-2 - 0 divided by 1 - 3

-2/-2 = 1

Answer:

\(m=1\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (1, -2)

Point (3, 0)

Step 2: Find slope m

Finding the mode of each data-set, the bimodal city's data is given by:

C. City C.

It is the value that appears the most times in the data-set. If two values appear the same number of sets, the data-set is called bimodal.

Hence, looking at the table:

Hence option C is correct.

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Answer:

45.5

Step-by-step explanation:

i passed

Answer:

1) Total cost is $27.84

2) a)You first have to divide the product price by their price per pound to find the pound value

2)b) Find their values

2)c) Yolanda bought 3.2 pounds of mixed fruit and 2.8 pounds of dried fruit

3) a) We made a linear equation

3)b) Found the value of x where x is representing the value of pounds

5) She used 6.72 of shampoo

Step-by-step explanation:

1) Total cost = 2.32(3.50)+(2.32)(2)(4.25)

=8.12+(2.32)(2)(4.25)

=8.12+(4.64)(4.25)

=8.12+19.72

=27.84

Total cost is $27.84

2)a) You first have to divide the product price by their price per pound to find the pound value

2)b) find their values

2)c) 21.60/6.75=x

11.90/4.25=y

where, y = value of dried fruit pound value

x= value of mixed fruit value

calculate

Rewrite equations:

3.2=x;2.8=y

Step: Solve3.2=xfor x:

3.2=x

3.2+−x=x+−x(Add -x to both sides)

−x+3.2=0

−x+3.2+−3.2=0+−3.2(Add -3.2 to both sides)

−x=−3.2

−x/−1 = −3.2/−1

(Divide both sides by -1)

x=3.2

Step: Substitute3.2forxin2.8=y:

2.8=y

2.8=y

2.8+−y=y+−y(Add -y to both sides)

−y+2.8=0

−y+2.8+−2.8=0+−2.8(Add -2.8 to both sides)

−y+0=−2.8

−y+0/−1 = −2.8/−1

(Divide both sides by -1)

y+0=2.8

y = 2.8

Yolanda bought 3.2 pounds of mixed fruit and 2.8 pounds of dried fruit

3) a) We made a linear equation

Let's make an equation

3.50x+0.40=20.00

3)b) 3.5x+0.4=20

Step 1: Subtract 0.4 from both sides.

3.5x+0.4−0.4=20−0.4

3.5x=19.6

Step 2: Divide both sides by 3.5.

3.5x/3.5 = 19.6/3.5

x=5.6

Mario bought 5.6 pounds of trail mix

5) 4.8 + 5.4 + 6.6

=10.2+6.6

=16.8

Since she used 2/5 of shampoo we will multiply 2/5 by 16.8

= (16.8)(2)/5

= 33.6/5

=6.72

She used 6.72 of shampoo

Then, substract 6.72 from 16.8

=16.8-6.72

=16.8−6.72

=16.8+−6.72

=10.08

10.08 is the remaining ounces

Therefore, she used 6.72 ounce

Step-by-step explanation:

The Amplitude is 4

The period is 2π

The midline is y=1.5

OPTION 1, 3,6

Answer:

See below ~

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the inscribed angle intersects an arc that twice the measure of the arc interested by the central angle. The inscribed angle's arc measures 144° and the central angle's arc measures 72°

>central angle and the arc the intersected arc are equal i.e they are both 72°

>the inscribed angle is half of the measure of the intersected arc i.e since the inscribed angle is 72° the arc interested is 144°

Answer:

20

Step-by-step explanation:

1 hour = 60 minutes

1200 riders = 60 minutes: divide by sixty to set equal to 1

20 riders = 1 minute

Just divide 1,200 by 60 because there are 60 minutes in 1 hour.

Just think about it this way: If you eat 1 banana a minute, you eat 60 bananas an hour. The amusement park ride goes around once a minute. In one hour it goes around 60 times. Each time it carries the same amount of people.

1,200 divided by 60 is...

20!

The ride can carry 20 riders each ride, and each ride lasts a minute.

1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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To prove that the limit of 1/x as x approaches 5 is 1/5, we manipulate the expression |1/x - 1/5| < epsilon. By introducing the absolute value of x - 5 and setting |x - 5| < 5 * epsilon, we can choose delta = 5 * epsilon. Therefore, for any epsilon > 0, we have |f(x) - L| < epsilon whenever |x - 5| < delta, confirming that lim(x->5) 1/x = 1/5.

Starting with the function f(x) = 1/x, we want to find a value of delta such that |f(x) - L| < epsilon, where L = 1/5 and epsilon > 0.

To do this, we begin by manipulating the expression |f(x) - L| < epsilon:

|1/x - 1/5| < epsilon

Next, we introduce the absolute value of x - 5:

|1/x - 1/5| = |1/x - 1/5| * |x - 5| / |x - 5|

Here, we multiply both sides of the inequality by |x - 5|, which is positive for x > 0.

Simplifying further:

|1/x - 1/5| * |x - 5| / |x - 5| = |(1 - x/5)/(5x)| * |x - 5|

We notice that 1 - x/5 is less than 1, so we have:

|(1 - x/5)/(5x)| * |x - 5| < |1/(5x)| * |x - 5|

Now, we choose a value for delta such that:

|1/(5x)| * |x - 5| < epsilon

For this to hold, we set |x - 5| < 5 * epsilon, which implies:

|x - 5| < delta = 5 * epsilon

Therefore, for any epsilon > 0, we can choose delta = 5 * epsilon such that |f(x) - L| < epsilon whenever |x - 5| < delta.

In other words, as x approaches 5, the limit of 1/x is indeed 1/5.

Mathematically, we can express this as:

lim(x->5) 1/x = 1/5

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Answer:

y=6x-1

Step-by-step explanation:

Answer:

\(\bold{-6x + y = -1}\)

Step-by-step explanation:

The slope form is \(y=mx+b\). So, convert this to a slope form:

Answer:

Kunie is 25

Step-by-step explanation:

Let's make Yemi's age y, and Kunie's age k.

Because Yemi is 5 years older that Kunie, k + 5 = y.

Because the product of their ages is 750, k * y = 750.

With substitution, we can determine that k * (k + 5) = 750.

Then with distributive property we can simplify the equation to get k^2 + 5k = 750.

Then we bring all the terms to one side of the equation to get k^2 + 5k - 750 = 0.

Then with quadratics, we can factor the equation to get (k + 30)(k - 25)=0.

Thus, either k + 30 must equal 0, or k - 25 must equal 0.  Thus, k must equal 25 or -30, and because someone cannot be -30 years old, k = 25.

Then, because Yemi is 5 years older than Kunie, y = 30.

Hope it helps <3

Kunle's age is marked as k.

Yemi's age is therefore k + 5.

The product of k and k + 5 equals 750.

What is k?

Now that we have tought this through...

Here is the equality:

\(k(k+5)=750\)

Expanding the parentheses and subtracting 750 from both sides gives you

\(k^2+5k-750=0\)

Which is a second degree polynomial (ie. quadratic equation).

That means there are two solutions of what Kunle's age might be.

\(k^2+5k-750=0\)

\(k^2+30k-25k-750=0\)

\(k(k+30)-25(k+30)=0\)

\((k+30) (k-25) =0\implies k_1=-30, k_2=25

\)

So we got two results and since age cannot be negative that leaves us with one result and that is 25.

TL;DR The answer is: Kunle is 25 years old.

Hope this helps.

Answer:

3\sqrt(5)

or 6.71

Step-by-step explanation:

Answer:

According to search result [1], the Biblical account of Joshua's long day is a miracle of "all of these": timing, intervention of natural laws, and visible appearance.

Step-by-step explanation:

Explanation:

We're given that

Note that P(A)*P(B) = 0.53*0.17 = 0.0901 which is somewhat similar to 0.901 but not entirely the same. We have an extra zero between the decimal point and the nine. So this indicates that \(P(A)*P(B) \ne P(\text{A and B})\). Therefore, events A and B are not independent. We consider them dependent.

A dotted shape is a type of shape that can be suggested by dots or dashes that don't connect. A shape that can be suggested by dots or dashes that do not connect is known as a Dotted shape.

The term "dotted shape" refers to the shapes that are created by drawing dots or dashes that don't connect. The idea behind this technique is to suggest the shape of an object without drawing its entire outline.The dotted shape technique is commonly used in drawing and graphic design to add a decorative touch to a design. It is also used in children's books and educational materials to teach children about shapes and how to draw them.

There are different types of dotted shapes, including circles, squares, triangles, and rectangles, to name a few. The dotted shape technique can be used to create a variety of designs, from simple to complex, depending on the desired effect.

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Answer:

So, A

22 divided by 5

Reduce the expression, if possible, by cancelling the common factors.

Exact Form:

22 /5

Decimal Form:

4.4

Mixed Number Form:

4  and 2 /5

Next, B

Reduce the expression, if possible, by cancelling the common factors.

Exact Form:

7 /8

Decimal Form:

0.875

Step-by-step explanation:

I hope this helps! Have a great day!

Answer:

I have boxed and highlighted the answer. Sorry for the ink to make the answers a bit messy, but the answers are :-

a. 22 ÷ 5 = 4.4

b. 7 ÷ 8 = 0.875

Hope this helps, thank you :) !!

Answer:

A = 2, B = 3 and C = 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y = 2 ( subtract 2x from both sides )

3y = - 2x + 2 ( divide all terms by 3 )

y = - \(\frac{2}{3}\) x + \(\frac{2}{3}\) ← in slope- intercept form

with slope m = - \(\frac{2}{3}\)

Parallel lines have equal slopes, thus

y = - \(\frac{2}{3}\) x + c ← is the partial equation

To find c substitute (2, 0) into the partial equation

0 = - \(\frac{4}{3}\) + c ⇒ c = \(\frac{4}{3}\)

y = - \(\frac{2}{3}\) x + \(\frac{4}{3}\) ← in slope- intercept form

Multiply through by 3

3y = - 2x + 4 ( add 2x to both sides )

2x + 3y = 4 ← in standard form

with A = 2, B = 3 and C = 4

Answer:

(-127)-62-(-15)

Open the bracket

-127-62+15

Bodmas rule(addition first)

-127-47=-174

Answer:

-32

Step-by-step explanation:

Michael is now (B) 6 years old.

Let's start by defining variables for the current ages of Norman and Michael.

Let N be Norman's current age, and M be Michael's current age.

From the problem statement, we know that N = M + 12 (Norman is 12 years older than Michael).

We also know that in 6 years, Norman will be twice as old as Michael.

So we can set up the following equation:

N + 6 = 2(M + 6)

Substituting N = M + 12 into the equation, we get:

M + 12 + 6 = 2(M + 6)

Simplifying:

M + 18 = 2M + 12

M = 6

Therefore, Michael is currently 6 years old.

Answer: (B) 6

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9514 1404 393

Answer:

  (B)  306

Step-by-step explanation:

The chart says 17% of the 1800 cars sold were Mazdas. That number is ...

  17% × 1800 = 0.17 × 1800 = 306

The dealership sold 306 Mazdas.

To find the probability that Alice and Bob will have different outcomes when tossing their coins once, we need to consider the possible combinations of outcomes.

Alice's coin can result in two outcomes: heads (H) with a probability of 1/2 and tails (T) with a probability of 1/2.

Bob's coin can also result in two outcomes: heads (H) with a probability of 1/3 and tails (T) with a probability of 2/3.

The possible combinations of outcomes are:

1. Alice gets H (1/2) and Bob gets T (2/3)

2. Alice gets T (1/2) and Bob gets H (1/3)

The probability that they will have different outcomes is the sum of the probabilities of these two cases.

Probability of different outcomes = (1/2) * (2/3) + (1/2) * (1/3)

                                 = 2/6 + 1/6

                                 = 3/6

                                 = 1/2

Therefore, the probability that Alice and Bob will have different outcomes when tossing their coins once is 1/2 or 50%.

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