A vial of medicine contains 60oz of medicine. If a dose is 3oz how many ounces does the vial contain

Final answer:

To calculate the arc length of a circle with a radius of 5 feet and a central angle of 42 degrees, convert the angle to radians and multiply by the radius to get the arc length, which is 7π/6 feet or approximately 3.665 feet.

Explanation:

To find the arc length s subtended by a central angle of 42 degrees in a circle with a radius of 5 feet, first convert the angle from degrees to radians. Since there are 2π radians in 360 degrees, you multiply the angle in degrees by π/180 to get radians. Therefore, the central angle in radians is 42 * (π/180) = 7π/30 radians. The arc length s is then found by multiplying the central angle in radians by the radius of the circle (s = rθ).
Using the formula s = rθ, you have:
s = 5 * (7π/30) = 35π/30 = 7π/6 feet.
Therefore, the arc length s is 7π/6 feet, or approximately 3.665 feet.

Answer:

Option A. [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex]

Step-by-step explanation:

Recursive formula of the geometric sequence is given as [tex]a_{1}=(-7)[/tex]

and [tex]a_{n}=\frac{1}{3}(a_{n-1})[/tex]

From these formulas it is clear that first term of the sequence a1 = -7

and common ratio of the sequence = [tex]\frac{1}{3}[/tex]

Since explicit formula of any geometric sequence is represented by

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Therefore, [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex] will be the explicit formula of the given geometric sequence.

total cards = 30 + 25 + 45 = 100

25 are basket ball

25/100 = 0.25

0.25 = 25%

 25% are basketball

Answer:

25%

Step-by-step explanation:

0.2x+4-3>-7-6.2x

0.2x+1>-7-6.2x

0.2x+0.6x>-8

0.8x>-8

the correct answer is: x>-1.25

Answer:

Refer the attached graph.

Step-by-step explanation:

Given : Equation [tex]2x-y=2[/tex]

To find : What is the graph of the equation ?

Solution :

To plot the graph of the equation we have to determine the x and y-intercept of the equation as  [tex]2x-y=2[/tex] is a linear equation.

For x-intercept, put y=0

[tex]2x-0=2[/tex]

[tex]x=\frac{2}{2}[/tex]

[tex]x=1[/tex]

Point is (1,0).

For y-intercept, put x=0

[tex]2(0)-y=2[/tex]

[tex]-y=2[/tex]

[tex]y=-2[/tex]

Point is (0,-2).

So, The graph passing through (1,0) and (0,-2) with linear line.

Refer the attached figure below.

The graph of the equation 2x - y = 2 will be a straight line passing through the points (0, -2), (1, 0), and (-1, -4).

We have,

To graph the equation 2x - y = 2, we can start by rearranging it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Rearranging the equation:

2x - y = 2

y = -2x + 2

y = 2x - 2

Now we have the equation in slope-intercept form, where the slope (m) is 2 and the y-intercept (b) is -2.

To graph this equation, you can plot the y-intercept at (0, -2), and then use the slope to find additional points.

The slope of 2 means that for every 1 unit increase in x, y will increase by 2.

So, from the y-intercept (0, -2), you can move 1 unit to the right and 2 units up to get another point (1, 0).

Similarly, you can move 1 unit to the left and 2 units down to get another point (-1, -4).

Now you can plot these points and draw a straight line through them to represent the graph of the equation.

Thus,

The graph of the equation 2x - y = 2 will be a straight line passing through the points (0, -2), (1, 0), and (-1, -4).

Learn more about equation of a line here:

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The length of the shorter leg of the right triangle is 14 feet.

Let's denote the length of the shorter leg as x. According to the given information, the longer leg is 7 feet more than the shorter leg, so the length of the longer leg is x + 7. The hypotenuse is 7 feet less than twice the shorter leg, making the hypotenuse 2x - 7.

By applying the Pythagorean Theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a) and b in a right triangle ([tex]\(c^2 = a^2 + b^2\)[/tex]), we can set up the equation:

[tex]\[(2x - 7)^2 = x^2 + (x + 7)^2\][/tex]

Solving this quadratic equation provides the value of x, representing the length of the shorter leg. After solving, we find x = 14, so the length of the shorter leg is 14 feet.

Understanding and applying the Pythagorean Theorem is crucial in solving problems related to right triangles. In this scenario, the theorem helps establish a relationship between the lengths of the sides, allowing us to find the length of the shorter leg based on the given conditions.

In the context of measurements, 3 inches is equivalent to 1/4 or 0.25 of a foot because 1 foot is composed of 12 inches.

The student is asking about the fraction that represents 3 inches in relation to a foot. In order to answer this, we need to know that 1 foot equals 12 inches. Therefore, we can represent 3 inches as a fraction of a foot by dividing 3 (the number of inches) by 12 (the number of inches in a foot). So, 3 inches is 1/4 or 0.25 of a foot.

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Final answer:

Compound probability problems use 'and' or 'or', applying multiplication or addition rules respectively, and can be visualized with Venn or tree diagrams.

Explanation:

Probability problems containing the words and or or are considered compound probability problems. The word and typically indicates the use of the multiplication rule, implying that you need to find the likelihood of both events occurring together, which is the product of their individual probabilities. Conversely, when you encounter the word or, it suggests the need for the addition rule, implying that you should add the probabilities of each event and subtract the probability of both events occurring together to find the total probability of either event happening. This can be visualized through Venn diagrams, which are useful in representing the different events and their intersections, as well as tree diagrams which provide a visual way of breaking down compound probabilities.

Answer:

5

Step-by-step explanation:

A total of 90 people were interviewed in the survey, which was determined by setting up a proportion based on the information that 7 out of 10 people prefer coffee and the remaining prefer tea, with 27 people preferring tea.

To solve the problem, we need to determine the total number of people surveyed based on the information given about their preferences for coffee and tea in the morning.

According to the survey, 7 out of 10 people prefer coffee. The rest, which is 3 out of 10, prefer tea. We are told that 27 people prefer tea. To find the total number of people surveyed, we set up a proportion where 3 people out of 10 is equivalent to 27 people out of the total number of people interviewed:

So, a total of 90 people were interviewed.

divide 3/4 by 1/16

3/4 / 1/16 =

3/4 * 16/1 =

48/4 = 12

he can write 12

Final answer:

Amy needs to cover 23 feet through 7 full cycles of climbing and slipping, followed by a final climb of 5 feet without slipping. It takes her 15.17 minutes for the cycles and an additional 2 minutes for the final climb, summing up to a total of 17.17 minutes to reach the top.

Explanation:

Amy is learning how to rock climb and faces a challenge of climbing a 26 ft wall by moving up 5 ft in 2 minutes, then slipping back 2 ft in 10 seconds. To calculate the total time it will take her to reach the top, we can start by finding the net distance she covers in each cycle of climbing and slipping.

During each cycle, Amy climbs 5 ft but then slips back 2 ft, making her net gain per cycle 3 ft (5 ft up - 2 ft back). To reach the top of the 26 ft wall, she doesn't slip back after the final climb, so the last part of the climb she only needs to cover the distance that takes her to 26 ft without slipping back.

Let's consider the entire climb except the final push to the top:

Total distance to cover without the last climb: 26 ft - 3 ft = 23 ft.

Number of full cycles to cover 23 ft: 23 ft / 3 ft per cycle = 7.67 cycles. Since she can't do a partial cycle, we round down to 7 full cycles, covering 21 ft (7 cycles * 3 ft/cycle).

Remaining distance after 7 cycles: 26 ft - 21 ft = 5 ft, which she covers in her last climb.

Each cycle takes 2 minutes and 10 seconds (2 minutes for climbing up 5 feet and 10 seconds for slipping back 2 feet). Since 10 seconds is 1/6 of a minute, each cycle takes 2 + (1/6) = 2.167 minutes. For 7 cycles, the time is 7 cycles * 2.167 minutes/cycle = 15.17 minutes. The final climb of 5 ft takes an additional 2 minutes, resulting in a total time of 17.17 minutes to reach the top.

The amount of money the person will have is [tex]\fbox{\begin\\\ \bf \$454,800\\\end{minispace}}[/tex].

Further explanation:

In the question it is given that the amount of money invested per month is [tex]\$100[/tex].

So, the total amount of money invested in [tex]1[/tex] year or [tex]12[/tex] months is calculated as follows:

[tex]\fbox{\begin\\\ 100\times 12=1200\\\end{minispace}}[/tex]

This implies that the total amount of money invested in [tex]1[/tex] year is [tex]\$1200[/tex].

Amount of money invested grows at a rate of [tex]7\%[/tex] per year.

A person started investing the money at an age of [tex]21[/tex] years and decided to withdraw the money at the age of [tex]70[/tex] years.

So, the total time for which the money was invested is calculated as follows:

[tex]\fbox{\begin\\\ 70-21=49\\\end{minispace}}[/tex]

The formula to obtain the future value of the invested money is as follows:

[tex]\fbox{\begin\\\ FV=PV\left[\dfrac{(1+r)^{t}-1}{r}\right]\\\end{minispace}}[/tex]

Substitute [tex]1200[/tex] for [tex]PV[/tex], [tex]0.07[/tex] for [tex]r[/tex] and [tex]49[/tex] for [tex]t[/tex] in the above equation.

[tex]\begin{aligned}FV&=1200\left[\dfrac{(1+0.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{(1.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{26.53}{0.07}\right]\\&=1200\times379\\&=454800\end{aligned}[/tex]

Therefore, the future value of the invested money is [tex]\$454,800[/tex].

Thus, the amount of money the person will have is [tex]\fbox{\begin\\\ \bf \$454,800\\\end{minispace}}[/tex].

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Answer details:

Grade: College

Subject: Mathematics

Topic: Time value of money

Keywords: Future value, present value, interest, time period, investment, money, 7 percent, $100, amount, invested money, formula.

9 inches

The volume of a cylinder is given by ...

... V = πr²h

The least height will be the height that makes the volume exactly that which is necessary.

... 324π in³ = π·(6 in)²·h . . . . . . fill in the given information

... (324π in³)/(36π in²) = h = 9 in . . . . . divide by the coefficient of h

The least possible container height is 9 inches.