A pharmaceutical company sells bottles of 500 calcium tablets in two dosages: 250 milligram and 500 milligram. Last month, the company sold 2,200 bottles of 250-milligram tablets and 1,800 bottles of 500-milligram tablets. The total sales revenue was $39,200. The sales team has targeted sales of $44,000 for this month, to be achieved by selling of 2,200 bottles of each dosage.
Assuming that the prices of the 250-milligram and 500-milligram bottles remain the same, the price of a 250-milligram bottle is $
and the price of a 500-milligram bottle is $

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x-----> the number of snacks

we  know that

The inequality that represent this situation is

[tex]9.50+3.50x\leq 35[/tex]

Solve for x

[tex]3.50x\leq 35-9.50[/tex]

[tex]3.50x\leq 25.50[/tex]

[tex]x\leq 7.3\ snacks[/tex]

The maximum number of snacks is 7

The solution for the inequality is all real numbers less than or equal to 7.3 snacks

The solution for the problem situation is all whole positive numbers less than or equal to 7 snacks

Verify each case

case 1) 4 snacks

Is a solution to both the inequality and the problem situation

case 2) 314 snacks

Is not a solution

case 3) 912 snacks

Is not a solution

case 4) 4.25 snacks

Solution to the inequality ONLY

Answer:

solution to both: 2,4

solution to inequality ONLY: -2,4.25,3 1/4

NOT a solution: 9 1/2

Step-by-step explanation:

yw ;)

Answer:

Step-by-step explanation:

By my definition, no. There's a continuity up to and including just before 1 approaching from the left, and there's a continuity just after 1 going to the right. But 1 itself has a special definition h(x) = 4 when x = 1 and that makes it discontinuous.

Answer: Derrick’s mean test score= 74.4

Derrick’s median test score = 81.5

Better picture of his scores is given by Median.

Step-by-step explanation:

The given data : 25, 40, 68, 85, 95, 98, 70, 78, 85, 100

[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}\\\\\Rightarrow\ \text{Mean}=\dfrac{744}{10}=74.4[/tex]

For Median , Arrange the data in order

25, 40, 68, 70, 78, 85, 85, 95, 98, 100

Median = Mean of two middle most value

[tex]\text{Median}=\dfrac{78+85}{2}=81.5[/tex]

Since the data set has outlier (25) and mean is affected by outlier.

So the better picture of his scores given by median value.

Answer:

(A) 74.4 (B) 81.5 (C) Median  (Look below or dont)

Step-by-step explanation:

Answer:

The result [tex]6x^4-x^3-19x^2+2x+12[/tex].

is a polynomial.

Step-by-step explanation:

The first polynomial is [tex]3x^2-2x-4[/tex].

The second polynomial is [tex]2x^2+x-3[/tex]

The closure property of multiplication states that if we multiply two polynomials the result must be a polynomial.

The product of these two polynomials is :

[tex](3x^2-2x-4)(2x^2+x-3)=6x^4-x^3-19x^2+2x+12[/tex].

We can see that the result is still a polynomial.

Answer: I believe the answer is C) The result 6x4 − x3 − 19x2 + 2x + 12 is a polynomial. !!!!!!!!

Answer:

Step-by-step explanation:

"opposite" and "opposites" are confusing when encountered in algebra and arithmetic.

In this case, the correct description of graphs of functions and their inverses follows:  the graphs are reflections of each other in the line y = x.  To call these graphs "opposites" would be misleading and incorrect.

Answer:

2/3 cup

Step-by-step explanation:

Add 1/6 cup and 3/6 cup, obtaining 4/6 cup of sugar, total.

4/6 reduces to 2/3.

The total amt of sugar in the recipe is 2/3 cup.

Answer:D

Step-by-step explanation:

The function g(x) = x + 8 is the result of the linear parent function f(x) = x shifting 8 units to the left. The addition of a positive constant to x corresponds to a leftward shift on the graph. Hence correct option A.

The student's question pertains to the transformation of a linear parent function, which is f(x) = x, to the function g(x) = x + 8. In analyzing the transformation, we must identify what changes were made to the parent function to obtain the new function. The addition of 8 to the independent variable x in the function indicates that there should be a shift along the x-axis.

Shifting the graph of a function parallel to the x-axis is denoted by the form f(x - a). If a positive constant is subtracted from x, the graph shifts to the right. Thus, f(x - 8) would represent a shift of 8 units to the right. Conversely, adding a positive constant to x, which is the case in g(x) = x + 8, signifies a shift of 8 units left. Therefore, the correct answer is:

A. Shift: 8 units left.

Answer:

A) left 6 units, up 4 units, reflection about the x-axis  

Step-by-step explanation:

The given absolute value function is

ƒ(x) = –|(x + 6)| + 4

The base function is

[tex]g(x)=|x|[/tex]

There is a transformation of the form;

[tex]-g(x+b)+c[/tex]

The base function is shifted left 6 units. (+b means left shift) and shifted up 4 units (+4 means upward vertical shift), and reflected in the x-axis , (-g(x)) means reflection in the x-axis.

The correct choice is A.

Answer:

A) left 6 units, up 4 units, reflection about the x-axis

Step-by-step explanation:

[tex]f(x) = -|x + 6| + 4[/tex]

For absolute function , the parent function is [tex]f(x)=|x|[/tex]

f(x) ---> f(x+a) , the graph will be shifted 'a' units to the left

6 is added with x so, we move graph 6 units left.

f(x) ---> f(x)+a , the graph will be shifted 'a' units up

4 is added with x. So, we move graph 4 units up

f(x) ---> -f(x) , the graph will be reflected over x-axis

we have negative sign in the front of the equation, so there will be a reflection about the x-axis

The order of transformation is

moving left 6 units, moving up by 4 units and a reflection about x-axis

To simplify negative 5 minus the square root of negative 44, you need to use imaginary numbers. The expression simplifies to -5 minus 2i√11. Hence, the correct answer is Option B.

To simplify
negative 5 minus the square root of negative 44, we need to work with imaginary numbers. Recall that the square root of -1 is defined as i, which is the imaginary unit. Using this, we can simplify the given expression step-by-step:

Recognize that
√-44 can be written as
√(-1 × 44).

Since
√(-1 × 44) = √(-1) × √44, and
√(-1) = i, we get
i × √44.

Now, we simplify
√44:
√44 = √(4×11) = 2√11.

Therefore,
i × √44 = 2i√11.

Putting it all together,
-5 - √-44 becomes
-5 - 2i√11.

Hence, the correct answer is
Option B. negative 5 minus 2 i times the square root of 11.

The fully simplified form of the expression is [tex]-25 - 14i \sqrt{11}[/tex]

To simplify the expression [tex]-5 - \sqrt{-44} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \cdot \sqrt{11} - 5 - 2 \cdot \sqrt{11} i[/tex], we will follow these steps:

Understanding Square Roots of Negative Numbers:
The square root of a negative number can be written using the imaginary unit [tex]i[/tex], where [tex]i = \sqrt{-1}[/tex].

Thus, we can rewrite [tex]\sqrt{-44}[/tex] as follows:
[tex]\sqrt{-44} = \sqrt{-1 \cdot 44} = \sqrt{-1} \cdot \sqrt{44} = i \cdot \sqrt{44}[/tex]
Note that [tex]\sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11}[/tex].

Thus,
[tex]\sqrt{-44} = 2i \sqrt{11}[/tex]
Now substituting this into the expression gives us:
[tex]-5 - 2i \sqrt{11} - 5 - 4 \cdot \sqrt{11} i - 5 - 4i \cdot \sqrt{11} - 5 - 2i \sqrt{11} - 5 - 2\sqrt{11} i[/tex]  

Combining Like Terms:
Now combine all the real parts and the imaginary parts separately in the expression:  

Real Part:
[tex]-5 - 5 - 5 - 5 - 5 = -25[/tex]

Imaginary Part:
[tex]-2i\sqrt{11} - 4i\sqrt{11} - 4i\sqrt{11} - 2i\sqrt{11} - 2i\sqrt{11}[/tex]
Combining these gives:
[tex]-2i \sqrt{11} - 4i \sqrt{11} - 4i \sqrt{11} - 2i \sqrt{11} - 2i \sqrt{11} = -14i\sqrt{11}[/tex]

Final Result:
Combining the real and imaginary parts, we get:
[tex]-25 - 14i \sqrt{11}[/tex]

Answer:

D.64

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Givens

A = 8 square meters.

B = 1/4 meter

h = ?

Formula

A = 1/2 B * h

Solution

8 = 1/2 1/4 * h     Combine

8 = 1/8 * h           Multiply by 8

8*8 = 1/8 * 8 * h

h =64 m

D answer

==============

I had to edit this to get it. Give the brainliest to the other responder.

First combine the roots:

[tex]\sqrt[7]{x^5}\cdot\sqrt[7]{x^5}=\sqrt[7]{x^5\cdot x^5}=\sqrt[7]{x^{10}}[/tex]

Now use the fact that [tex]\sqrt[n]{x^n}=x[/tex] (for odd [tex]n[/tex]):

[tex]\sqrt[7]{x^{10}}=\sqrt[7]{x^7\cdot x^3}=\sqrt[7]{x^7}\cdot\sqrt[7]{x^3}=x\sqrt[7]{x^3}[/tex]

Answer:

hope it helps you!!!!!!!!

The volume of a cylinder with a height of 8 and a radius of 3.8 is 115.52π cubic units, and with a height of 14 and a radius of 5, it is 350π cubic units.

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height of the cylinder.

For question 4 with a height of 8 and a radius of 3.8, the volume would be: V = π(3.8)²(8) = 115.52π cubic units.

For question 5 with a height of 14 and a radius of 5, the volume would be: V = π(5)²(14) = 350π cubic units.

These calculations illustrate how to determine the volume of cylinders using their respective dimensions, providing a fundamental understanding of geometric principles and applications.

Answer:

Here's what I get.

Step-by-step explanation:

9. (6, -8)

The reference angle θ is in the fourth quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = 6² + (-8)² = 36 + 64 = 100

OB = √100 = 10  

[tex]\sin \theta = \dfrac{-8}{10} = -\dfrac{4}{5}\\\\\cos \theta =\dfrac{6}{10} = \dfrac{3}{5}\\\\\tan \theta = \dfrac{-8}{6} = -\dfrac{4}{3}\\\\\csc \theta = \dfrac{10}{-8} = -\dfrac{5}{4}\\\\\sec \theta = \dfrac{10}{6} = \dfrac{5}{3}\\\\\cot \theta = \dfrac{6}{-8} = -\dfrac{3}{4}[/tex]

10. cot θ = -(√3)/2

The reference angle θ is in the second quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = (-√3)² + (2)² = 3 + 4 = 7

OB = √7

[tex]\sin \theta = \dfrac{2}{\sqrt{7}} = \dfrac{2\sqrt{7}}{7}\\\\\cos \theta = \dfrac{-\sqrt{3}}{\sqrt{7}} = -\dfrac{\sqrt{21}}{7}\\\\\tan \theta = \dfrac{2}{-\sqrt{3}} = -\dfrac{2\sqrt{3}}{3}\\\\\csc \theta = \dfrac{\sqrt{7}}{2} \\\\\sec \theta = \dfrac{\sqrt{7}}{-\sqrt{3}} = -\dfrac{\sqrt{21}}{3}\\\\\cot \theta = -\dfrac{\sqrt{3}}{2}[/tex]

Answer:

 2 a^4 -2a^2b^2 -6b^4

Step-by-step explanation:

C = 7a^4 + 5a^2b^2 -3b^4

D = 5a^4 +7a^2b^2 +3b^4

C-D = 7a^4 + 5a^2b^2 -3b^4 - ( 5a^4 +7a^2b^2 +3b^4)

Distribute the minus sign

   7a^4 + 5a^2b^2 -3b^4 -  5a^4 -7a^2b^2 -3b^4

I like to line them up vertically

 7a^4 + 5a^2b^2 -3b^4

-  5a^4 -7a^2b^2 -3b^4

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

 2 a^4 -2a^2b^2 -6b^4

Answer:

Step-by-step explanation:

There's only 1 '6' on an ordinary die with 6 sides, so the probability of rolling a 6 is 1/6.

That of NOT rolling a 6 is the complementary probability:  1 - 1/6 = 5/6.

To solve the inequalities by graphing, transform each inequality into an equation form, plot the lines on the graph, and identify the overlapping region that satisfies both inequalities. The lines are 5x + 2y ≥ 3 and y ≥ x, with appropriate slopes and y-intercepts.

To solve the inequalities by graphing, we need to transform each inequality into a graphable equation form and then use the properties of the lines to find the solution set. The inequalities in question are:

Let's graph each inequality one by one:

The solution to the system of inequalities will be the region on the graph where both conditions are satisfied, typically above the lines in this case because both inequalities are greater than or equal to.

Always label your graph with f(x) and x, and select an appropriate scale for the x and y axes to ensure all important points and lines are visible on the graph.

The provided figures and instructions on slope and graphing help us understand how to plot each line based on their equations. Using the slope-intercept form, we graph the lines and identify the intersection or overlapping regions that satisfy both inequalities.

Answer:

(x+5)^2-20

(-5,-20)

Step-by-step explanation:

Use the formula (b/2)^2 in order to create a new term to complete the square.

Answer:

7

Step-by-step explanation:

The full solution is:  

1 |...1.....3.....-5.....7  

.............-1....-2......7  

__________________  

.......1.....2.....-7.....14  

So the answer is 7

The question doesn't provide enough information to answer it properly, as it doesn't specify the polynomial or the divisor necessary for synthetic division. Synthetic division involves dividing a polynomial by a linear divisor, but without the set polynomial and divisor, the number that would belong in the place of the question mark can't be determined.

Unfortunately, the information provided doesn't clearly indicate the format or context of a synthetic division problem. Synthetic division typically involves dividing a polynomial by a linear divisor. The elements of the polynomials are numbers, specifically the coefficients of the polynomial terms. The repetition in your question about various Car X, Car Y and dots at various hash marks appears to be irrelevant data as it does not correlate with the synthetic division problem.

However, to apply synthetic division, we would need a specific polynomial to carry out the process. In synthetic division, a box is drawn, the coefficients of the polynomial are written in that box, and then the divisor is placed outside the box. From there, the numbers inside the box are manipulated, in a step-by-step manner, based on the divisor. The numbers derived from this process are the coefficients of the answer. Without this specific data, we cannot accurately determine what number belongs in the place of the question mark.

https://brainly.com/question/31409612

#SPJ11

Answer:

The trigonometric equation  (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:Using x for Θ: (sinx - cosx)^2 - (sinx + cosx)^2 = (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) = - 2 sinx cosx - 2 sinx cosx = - 4 sinx cosx = - 2sin(2x)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Expand (sinΘ + cosΘ)²

= sinΘ - cosΘ - (sin²Θ + 2 sinΘcosΘ + cos²Θ)

= sinΘ - cosΘ - sin²Θ - 2sinΘcosΘ - cos²Θ

= sinΘ - cosΘ - 2sinΘcosΘ - (sin²Θ + cos²Θ)

= - 2sinΘcosΘ - cosΘ + sinΘ - 1 → D

Answer:

12%

Step-by-step explanation:

We are informed that the heights of men in the U.S are normally distributed with a mean of 70 inches and a standard deviation of 4 inches. We need to determine the percent of men whose height falls between 65 and 67 inches. We would first evaluate the probability that the height of a randomly selected individual would fall between 65 and 67 inches;

This can be done in stat-crunch;

Click Stat, highlight on Calculators then click Normal

In the pop-up window that appears click Between

Enter the given values of mean and standard deviation; 70 and 4 respectively

Enter the values 65 and 67 in the next set of boxes in that order

Finally, click on compute;

Stat-Crunch returns a probability of 0.12097758. Therefore, the percent of men whose height falls between 65 and 67 inches is 12.10%. Therefore, the solution is 12%.

Answer:

The area of each section of the circle is [tex]A=25\pi\ m^{2}[/tex]

Step-by-step explanation:

we know that

Each section represent a quarter of circle

The area of a quarter of circle is equal to

[tex]A=\frac{1}{4}\pi r^{2}[/tex]

we have

[tex]r=10\ m[/tex]

substitute

[tex]A=\frac{1}{4}\pi (10)^{2}[/tex]

[tex]A=25\pi\ m^{2}[/tex]

Answer:

The best dimension to use to have the least cost to make 100 boxes is 5 x 5 x 4. It only costs $6.50 to make 100 boxes.

Step-by-step explanation:

120/2=60

160/4=40

60+40=100

100 boxes/1 hour=600 boxes/x

x= 6 hours

Answer:

(-7 , 7/2)

Step-by-step explanation:

Given in the question,

point E(-4,14)

x1 = -4

y1 = 14

point G(-8,-2)

x2 = -8

y2 = -2

Location of point F which is 3/4 of the way from E to G

which means ratio of point F from E to G is 3 : 1

a : b

3 : 1

xF = [tex]x1+\frac{a}{a+b}(x2-x1)[/tex]

yF = [tex]y1+\frac{a}{a+b}(y2-y1)[/tex]

Plug values in the equation

xF = -4 + (3)/(3+1) (-8+4)

xF = -7

yF = 14 + (3)/(3+1)(-2-14)

yf = 7/2

Answer:  d) Easton

Step-by-step explanation:

Let's evaluate Round 1 (blue) for each bowler:

Jimmy --> the lowest score is 0.5 SD below the mean

Claudia --> the lowest score was the mean

Easton --> the lowest score is 0.75 SD below the mean

Cynthia --> the lowest score was the mean

The person that had the worst game is: Easton

Answer:

easton

Step-by-step explanation:

I did the test

[tex]\sin\theta=\dfrac13>0[/tex], so

[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}<0\implies\cos\theta<0[/tex]

Recall that

[tex]\cos^2\theta+\sin^2\theta=1[/tex]

for all [tex]\theta[/tex], and knowing that [tex]\cos\theta<0[/tex] we have

[tex]\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{2\sqrt2}3[/tex]

Answer:

[tex]Area=121\pi ft^2[/tex] in terms of [tex]\pi[/tex].

Step-by-step explanation:

A 360 degree rotating sprinkler will water a full circular region of the lawn.

The area of this circular region is calculated using the formula:

[tex]Area=\pi r^2[/tex]

where r=11 feet is the radius of the circular region covered.

We substitute the value of the radius into the formula to get:

[tex]Area=\pi \times 11^2[/tex]

[tex]Area=121\pi ft^2[/tex] in terms of [tex]\pi[/tex].

This is approximately [tex]380.1 ft^2[/tex] to the nearest tenth

ANSWER

The area of the floor is 696 square feet.

EXPLANATION

It was given that, the volume inside a rectangular storage room is 2,088 cubic feet.

The rectangular room is a rectangular prism.

The volume of a rectangular prism is

[tex]V = floor \: area \times height[/tex]

The height of the room is 3 ft.

This implies that,

[tex]2088= floor \: area \times3[/tex]

Divide both sides by 3.

[tex] \frac{2088}{3} = floor \: area [/tex]

[tex]floor \: area = 696 {ft}^{2} [/tex]

The area of the floor is 696 square feet.

the radius of this question 25pi

Answer:

Step-by-step explanation:

(1) The formula for the area of a circle of radius r is A = πr².

If the radius is 5 units, then the exact area of the circle is A = π(5 units)², or A = 25π units².

The third possible answer is the correct one.

(2) To solve -2x > -10, we must isolate x.

Divide both sides by -2, remembering that if we divide an inequality by a negative number, we must reverse the direction of the inequality sign:

-2x > -10

-----   -------  →  x < 5

 -2      -2

The first possible answer is the correct one:  Divide both sides by -2.

Answer:

24 π

Step-by-step explanation:

First step is to determine the radius of the base.  We have the area, so we can easily determine the radius.  The base is a circle, and the area of a circle is given by A = π * r² , so r² = A / π

r² = (36 π) / π = 36

So, r = 6

The lateral surface of a cylinder is given by the following:

L = 2* π * r * 2

Now that we have r, we can easily calculate it:

L = 2 * π * 6 * 2 = 24π, second choice listed