a patient suffering from a cold is given prescription for 15 mL of cough suppressant every 8 h for 10 days. how many milliliters of medication will the patients take in one day?

Answer:

2y

Step-by-step explanation:

Since 17y and 15y both have a y, you can combine it. You can subtract 17-15 to get 2, so the answer is 2y.

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

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Answer:

10

Step-by-step explanation:

For an odd number of values, the median is the middle value when you write the values in ascending order.

5, 7, 9, 10, 16, 17, 20

The median is 10.

Answer:

"Vx: if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Step-by-step explanation:

The Following statement in the form  âˆ€x ______, if _______ then _______ is a valid argument and this because any valid argument with "true premises" has a "true conclusion" as well

we will rewrite this statement in a universal condition statement form

assume x is a valid argument with true premises

then the following holds true

p(x) : x is a valid argument with true premises

q(x) : x has true conclusion

applying universal conditional statement

"Vx, if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Answer:

Your answer is: 6

84/7=12-6= 6

6 is your answer

The first step to calculate the indicated x value using synthetic division is to assemble the synthetic division table, which will be:

The first number on the top line, 1, is the coefficient of the highest degree term in the polynomial. The remaining coefficients are written in order, with 0 placeholders for any missing terms. The divisor, -4, is written to the left of the table.

Therefore, we find ƒ(-4) = -51.

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analyze problem

find apple-cost ratio

8-4

simplify ratio

2-1

find apple amount(given)

9/2=4.5

4.5*1=4.5

Answer:4.5

Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

Answer:

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

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

Answer:

C) x = 8√3 ; y = 4√3

Step-by-step explanation:

In this figure, the triangle is 30°-60° right triangle.

So x/12= 2/√3, y/12 = 1/√3

Answer:

C

Step-by-step explanation:

Answer: D

Step-by-step explanation:

The equation that represent the given situation is y = 15x + 70

When she plants 3 stalks, each plant yields 115 ounces of beans

The first point = (3, 115)

When she plants 8 stalks, each plant yields 190 ounces of beans

The second point = (8, 190)

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Substitute the values in the equation

The slope of the line m = (190-115) / (8-3)

= 75/5

= 15

The point slope form is

\(y-y_1=m(x-x_1)\)

Choose one point and substitute the values in the equation

y - 115 = 15(x - 3)

y - 115 = 15x - 45

y = 15x - 45 + 115

y = 15x + 70

Hence, the equation that represent the given situation is y = 15x + 70

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The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

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Answer:

Write a time equation, time = dist/speed

:

go time + return time = total time

d%2F16 + d%2F15 = 7.75 hrs

multiply equation by the least common multiple 240, cncel the denominators:

15d + 16d = 240(7.75)

31d = 1860

d = 1860/31

d = 60 km one way

total dist = 120 km

:

Check this, find the actual time each way

60/16 = 3.75 hrs

60/15 = 4 hrs

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

total time 7.75 hrs

Step-by-step explanation:

Answer:

Step-by-step explanation:

hold I’m going to put much elaborated steps in the comments

Answer and Step-by-step explanation:

Let's first calculate the cost of the dress.

If Ellie made a 100% profit on the scarf, that means she sold it for twice the cost, or £8. So, the cost of the scarf was £4.

To find the cost of both items, we can subtract the cost of the scarf from the total price:

Total price = £26

Cost of scarf = £4

Cost of dress = £26 - £4 = £22

Ellie made a 30% profit on the total cost, which includes the cost of both the scarf and the dress.

To calculate the total profit, we can find 30% of the total cost:

30% of £26 = 0.3 x £26 = £7.80

So, Ellie's total profit is £7.80.

To find the percentage profit on the cost of the dress, we need to compare the profit made on the dress to its cost.

Profit on the dress = Total profit - Profit on the scarf

Profit on the dress = £7.80 - £4 = £3.80

So, Ellie made a profit of £3.80 on the dress.

To calculate the percentage profit on the cost of the dress, we can divide the profit by the cost and then multiply by 100 to get a percentage:

Percentage profit on the dress = (Profit on the dress / Cost of dress) x 100%

Percentage profit on the dress = (£3.80 / £22) x 100%

Percentage profit on the dress ≈ 17.27%

Therefore, Ellie made a percentage profit of approximately 17.27% on the cost of the dress.

The addition of the given polynomials would be x³+ y³ -3x²y + 2y² + x.

What is the addition of polynomials?

Adding polynomials is defined as adding the like terms of two or more algebraic expressions while keeping their sign. It's very similar to a standard addition operation.

The given polynomials are = x³-3x²y + 3y²-y² and x + y³.

Now take addition, we get

         = x³-3x²y + 3y²-y² + x + y³

Adding like terms, we get

         = x³-3x²y + 2y² + x + y³

Arranging the terms, we get

         = x³+ y³ -3x²y + 2y² + x

Hence, the addition of the given polynomials would be x³+ y³ -3x²y + 2y² + x.

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Answer:

quadrilateral

Step-by-step explanation:

4 sides = quadrilateral

Answer:

Step-by-step explanation:

!od

7x=96

Answer:

300 packages

Step-by-step explanation:

The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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Answer:

6cd^3

Step-by-step explanation:

-48c^2d^4/-8cd

you divide the -48 by -8 and you get 6.

6c^2d^4/cd

when you divide c^2 by c, d^4 by d you get c and d^3 - this is kind of because c^2 is cxc/d^4 is dxdxdxd and when you divide it by c/d the ^ decreases.

Answer

I gotchu. The answer I got is 15.9235 or 16

Step-by-step explanation:

So the formula for circumference is Pi times diameter. (If I remember right) Now we can flip this equation to become Circumference divided by pi. This will give us our answer. I dunno if you have to round so here are my two answers.

16 (rounded) or  15.9235 :)

The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.

We have given that circle having radius of 8 units. Thus, r = 8.

Since we know that circle having the center (10,−7).

Thus, the equation of the circle, with a radius of 8 units is;

(x - h)² + (y - k)² = r²

(x - 10)² + (y + 7)² = 8²

Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

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Average = sum / total number

total game bowled by laura = 5

first 4 scores are 83, 131, 100, and 147

Let x be the fifth score

The average score = 122.2

Since average = sum / total number

122.2 = 83 + 131 + 100 + 147 + x / 5

introducting cross multiplibcation

122.2 x 5 = 83 + 131 + 100 + 147 + x

611 = 461 + x

let isolate x by collecting the like terms

x = 611 - 461

x = 150

The least score to have an average of 122.2 is 150

Therefore, the answer is 150 for the fifth score

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

The regression curve is attached with the answer and the value of x on y = 0.5 is 2.

Curve fitting in regression analysis is the process of choosing the model that best fits the particular curves in your dataset.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that an engineer is studying early morning traffic patterns at a particular intersection. The observation period begins at 5:30 am. Let X denote the time of arrival of the first vehicle from the north-south direction; let Y denote the first arrival time from the east-west direction. Time is measured in fractions of an hour after 5:30 am.

The mean value of X at y=0.5 will be calculated as,

y = 1 / X

X = 1 / y

X = (1 / 0.5)

X = 2

Therefore, the regression curve is attached with the answer and the value of x on y = 0.5 is 2.

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first thing we need to do is factorise because we can't calculate infinity/infinity

and we are left with 1^infinity this is an euler function

an euler function looks like this

Answer: B

Step-by-step explanation: