The correct dosage to be administered is 5 ml.
To calculate the correct dosage to be administered, we can use the following formula:
Dose = (Desired dose / Stock strength) x Stock volume
In this case, the desired dose is 15 mg and the stock strength is 10 mg/0.5 ml. Therefore:
Dose = (15 mg / 10 mg/0.5 ml) x Stock volume
Simplifying this expression, we get:
Dose = 3 x Stock volume
To find the stock volume needed, we can rearrange this formula as follows:
Stock volume = Dose / 3
Substituting the values we have, we get:
Stock volume = 15 mg / 3 = 5 ml
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a motorist buys a 5litre can of gear oil.she uses 800ml.what percentage of oil has she used and what remains
Step-by-step explanation:
1000ml=1 litre
800 divided by(1000 multiplied by 5)=16%
What is the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4)?
x = -5
x=4
y = -5
y = 4
The equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x = -5.
How do equations work?A mathematical statement that equates two algebraic expressions is known as an equation. The equal to (=) sign appears between the expression and an equation.
How do parallel lines work?Parallel lines are straight lines in the same plane that never cross each other.
The parallel lines have the same slope.
Given that,
Equation of the given line is x = -2
Any line parallel to this line will be in the form x = K, where K is a constant.
The line will pass through ( -5 , 4).
The line x = K will satisfy the point ( -5 , 4)
-5 = K
x = -5
Hence, the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x = -5.
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Katie is 1.62 m tall George is 3cm shorter than Katie how tall is George
Someone help with this equation please!!
The angle congruence property illustrated is given as follows:
Symmetric Property of Angle Congruence.
What is states by the Symmetric Property of Angle Congruence?The symmetric property of angle congruence states that if if one geometric shape is congruent to a second shape, than the second shape is also congruent to the first.
The shapes in this problem are given as follows:
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e
s
3
A shop sells cupcakes packed in different-sized boxes: small, medium
and large.
The table shows the number of cupcakes in each box.
Small
Medium
6 cupcakes
15 cupcakes
Large
24 cupcakes
The bakers in the shop fill 60 boxes.
40% of the boxes are medium, 35% of the boxes are small and the
rest are large.
How many cupcakes have been packed?
The total number of cupcakes packed is 846 cupcakes.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let's first find out the number of boxes of each size:
40% of 60 boxes = 24 boxes are medium
35% of 60 boxes = 21 boxes are small
The remaining 60 - 24 - 21 = 15 boxes are large
Now we can calculate the total number of cupcakes packed:
24 boxes x 15 cupcakes per medium box = 360 cupcakes in medium boxes
21 boxes x 6 cupcakes per small box = 126 cupcakes in small boxes
15 boxes x 24 cupcakes per large box = 360 cupcakes in large boxes
Therefore, the total number of cupcakes packed is 360 + 126 + 360 = 846 cupcakes.
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C. a third bond is worth $100 and grows in value by 4 percent each year, but the interest is applied continuously, at every moment. The value of this bond after years is given by 100-Order the bonds from slowest growing to fastest growing. Explain how you know
We can order the bonds from slowest-growing to fastest-growing as:
First bond: fixed growth rate of $50 per year
Third bond: growth rate of 4% per year, compounded continuously
Second bond: growth rate of 6% per year, compounded annually
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To order the bonds from slowest growing to fastest growing, we need to compare their growth rates.
The first bond grows at a fixed rate of $50 per year, regardless of how long it is held.
So its growth rate is constant and does not change with time.
The second bond is worth $500 and grows at a fixed annual rate of 6%, so its value after one year will be:
Value after one year
= $500 + 0.06 x $500
= $530
After two years, its value will be:
Value after two years.
= $530 + 0.06 x $530
= $561.80
We can see that the second bond's growth rate is increasing over time since the increase in value each year is calculated as a percentage of the new value.
The third bond is worth $100 and grows at an annual rate of 4% that is applied continuously.
The formula for the value of a continuously compounded bond after t years = $100 x e^(0.04t)
where e is the mathematical constant approximately equal to 2.718.
After one year,
The value of the third bond.
= $100 x e^(0.04 x 1) = $104.08
After two years,
Value after two years
= $100 x e^(0.04 x 2)
= $108.24
We can see that the growth rate of the third bond is also increasing over time because the interest is being compounded continuously.
Now,
We can order the bonds from slowest-growing to fastest-growing as:
First bond: fixed growth rate of $50 per year
Third bond: growth rate of 4% per year, compounded continuously
Second bond: growth rate of 6% per year, compounded annually
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the file utility contains the following data about the cost of electricity during july of a recent year for a random sample of 50 one- bedroom apartments in a large city: 96 171 202 178 147 102 153 197 127 82 157 185 90 116 172 111 148 213 130 165 141 149 206 175 123 128 144 168 109 167 95 163 150 154 130 143 187 166 139 149 108 119 183 151 114 135 191 137 129 158 a. construct a histogram and a percentage polygon. b. construct a cumulative percentage polygon. c. around what amount does the monthly electricity cost seem to be concentrated?
a) The histogram for the data is illustrated below.
b) The cumulative percentage polygon is define in the histogram
c) The amount does the monthly electricity cost seem to be concentrated is 128 - 152
A histogram is a graphical representation of a frequency distribution. It consists of a set of bars that represent the frequency of data within certain intervals, also known as bins. The height of each bar represents the frequency or count of data points that fall within that bin.
To create a histogram for the electricity cost data, we need to first decide on the number and size of the bins. One common rule is to choose the number of bins as the square root of the sample size. In this case, we have 50 data points, so we can choose about 7 bins. The size of the bins can be determined by dividing the range of the data by the number of bins.
Once we have determined the number and size of the bins, we can create the histogram by drawing a set of bars with heights proportional to the number of data points that fall within each bin. The histogram can be further enhanced by adding labels for the x and y-axes, a title, and a legend.
As per the histogram, the amount does the monthly electricity cost seem to be concentrated is 128-152
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What is the area of this compound figure?
the answer is 66
its easy... you posted this as high-school... this is 6th grade work
Area is 69 km2
………..,……….
The point A(2, 1) is a vertex of a square ABCD. M(5, 1) is the point of intersection of the
diagonals of the square. Find the coordinates of B, C and D. (Remember: The diagonals
of a square are equal in length and bisect each other at right angles.)
pls give serious answers!!
Answer:
Step-by-step explanation:
Since M is the point of intersection of the diagonals of the square, it is also the midpoint of both diagonals. This means that AM is equal to half the length of a side of the square and also bisects the angle formed by the two sides that it connects.
Let's call the length of a side of the square s. Then, the distance AM can be found using the Pythagorean theorem:
AM = sqrt((5 - 2)^2 + (1 - 1)^2) = sqrt(3^2 + 0^2) = sqrt(9) = 3
So, the length of a side of the square is 2 * AM = 2 * 3 = 6.
Next, we can use the length of a side and the coordinates of A to find the coordinates of B. Since AB is a side of the square and is 6 units long, we can find B by moving 6 units to the right of A:
B = (2 + 6, 1) = (8, 1)
We can also find the coordinates of C by moving 6 units up and 6 units to the left of A:
C = (2 - 6, 1 + 6) = (-4, 7)
Finally, we can find the coordinates of D by moving 6 units down and 6 units to the right of A:
D = (2 + 6, 1 - 6) = (8, -5)
So, the coordinates of the other vertices of the square are B = (8, 1), C = (-4, 7), and D = (8, -5).
Help ASAP.............
Answer: about 1587 cm^2
Step-by-step explanation: The equation for area of circle is A= πr^2 OR A= (pi/4)d^2
Given the diameter is 46.7, the radius would be half of that which is 23.35.
Simply plug it into the equation
A = π23.35^2
OR
A= (π/4)46.7^2
Since you are using 3 in place of pie, it would be 3(23.35)^2 OR (3/4)46.7^2
the answer i got was 1,635 cm^2 so your closest choice to that is 4
Factor out the Greatest Common Factor (GCF): 64d^(5)-24d^(2)
Answer: [tex]8d^{2} (8d^3 - 3)[/tex]
Step-by-step explanation:
8d^2 is the GCF for this binomial
LCM of x^2 -25 and x-5
Answer:10
Step-by-step explanation:
5.5 equals 25.then you subtract 25 by 25 and get zero.
a coordinator will select 4 songs from a list of 10 songs to compose an event's musical entertainment lineup. how many different lineups are possible?
There are [tex]10^{4}[/tex] = 10,000 different possible musical entertainment lineups that can be created from a list of 10 songs.
This is computed by using the formula for combinations without repetition, which is [tex]n^{r}[/tex], where n is the number of items in the list and r is the number of items to be selected. In this case, n = 10 and r = 4, which results in [tex]10^{4}[/tex] = 10,000.
It is important to note that this calculation does not take into account any repetitions of songs, so if the same song appears more than once in the list, then the actual number of possibilities could be less. For instance, if there is a list of 10 songs, but 5 of them are the same, then the number of possible lineups would be[tex]10^{4/5}[/tex]! = 800, taking into account the repetitions.
To illustrate this further, if we were to list all the possible lineups, then we would end up with 10,000 unique combinations of 4 songs. For instance, a possible lineup could be Song 1, Song 5, Song 8, Song 10. Another possible lineup could be Song 4, Song 7, Song 9, Song 10. This process could be repeated with any combination
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4/3 divided by 1/4+2/5 divided by 1/4+4/15 divided by 1/4
On solving the provided question we can say that by bodmas ((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8
what is BODMAS ?The acronym BODMAS helps children learn the hierarchy of math operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms:
B Bracket, O Degrees (Power/Exponent or Square Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also known as PDMAS in some areas. It symbolizes exponents, division, multiplication, addition and subtraction. It also represents brackets. The BODMAS rule states that parentheses must be handled first, then powers or roots (that is, of), division, multiplication, addition, and finally subtraction. Known as BODMAS in India and the UK, PEMDAS is primarily used in the US. However, they are identical to each other. The parentheses, order, and order of addition, subtraction, multiplication, and division are the same for the two rules.
by bodmas
((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8
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Use the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =
By Using the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =
Therefore, The solutions are : a = -3, b = 0, c = 6, d = 9
Equation:
In mathematics, an equation is an expression that indicates equality of two expressions by connecting them with the equal sign = . The word "equation" and related words in other languages can have slightly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English a well-formed formula consisting of two expressions connected by an equal sign is an equation.
Given:
This table;
x y = 3x+3
-3 -6
-2 a
-1 b
0 3
1 c
2 d
To Find:
Values of a, b, c and d
Consider the 2nd row,
x = -2, y = a
Putting the values in the equation,
we get,
a = 3(-2) + 3
⇒ a = -3
Consider the 3rd row,
x = -1, y = b
Putting the values in the equation,
we get,
b = 3(-1) + 3
⇒ b = 0
Consider the 5th row,
x = 1, y = c
Putting the values in the equation,
c = 3(1) + 3
⇒ c = 6
Consider the 6th row,
x = 2, y = d
d = 3(2) + 3
⇒ d = 9
The final answer is,
a = -3, b = 0, c = 6, d = 9.
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y-4=3(x+2) in slope intercept form
Answer:
y = 3x + 10
Step-by-step explanation:
slope intercept form is y = mx + b
y - 4 = 3(x+2)
y - 4 = 3x + 6
y = 3x + 10
So, the answer is y = 3x + 10
How many solutions does the following system of equations have?
a. 1
b. Infinitely many
c. 0
d. Not enough information
The correct option is B, the system of equations has infinitely many solutions.
How many solutions does the system of equations has?When we graph a system of equations, the points where the graphs of the equations intercept are the solutions.
In this case we can see a single line graphed, which only can happen when both equations of the system represent the exact same line.
Then the graphs intercept at infinite points, thus, the system of equatios has infininitely many solutions.
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8q≥– 8 I need the answer pls
Answer:
=q > - 1
Step-by-step explanation:
8q > - 8
= 8q/8 > -8/8
=q > - 1.
In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the ___________ come from a normal distribution.a. Response Variableb. Errorsc. Observationsd. Explanatory Variable
In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the errors come from a normal distribution.
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution centred on the mean, implying that data closer to the mean occur more frequently than data further away from the mean.
The normal quantile plot of the residuals in a simple linear regression model is used to establish if it is reasonable to think the errors are normal.
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HELP POLSSSSSSSSSSSSSSSSSSS
Answer:
The angle is 180°
Step-by-step explanation:
[tex]{}[/tex]
Answer: look at the image for the answer and solution
Step-by-step explanation:
What are the coordinates of the point on the directed line segment from (1, 2)to(6,7) that partitions the segment into a ratio of 2 to 3?
Coordinates of the point on the directed line segment from (1, 2) to (6,7) that partitions the segment into a ratio of 2 to 3 are (3, 4).
Using proportions, it is found that the coordinates of the desired point are (2,2).
The first point is A(1, 2)
The second point is B(6, 7)
The desired point is C(x, y)
The point C partitions the segment AB into a ratio of 3 to 2, hence:
[tex]C - A = \frac{2}{5}(B - A)[/tex]
This proportion is applied using both the x and y coordinates of the points, hence:
[tex]x - 1 = \frac{2}{5}(6 - 1)[/tex]
x - 1 = 2
x = 3
Now, [tex]y - 2 = \frac{2}{5} (7 - 2)[/tex]
y - 2 = 2
y = 4
Therefore the coordinates of the points are (3, 4).
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What is the period of the function f(x) shown in the graph?
Enter your answer in the box.
Basic
Answer:
Period is [tex]\mbox{\huge {\boxed{\pi }}}[/tex]
Step-by-step explanation:
Each gridline marker on the horizontal axis is π/4
The period of this function is the horizontal displacement at which the function starts to repeat itself
Looking at the function we see that the minimum value of the function is 1 and occurs first at -π/4 and then at 3π/4
So the period is 3π/4 - (-π/4) = 3π/4 + π/4 = (3/4 + 1/4)π = π
We could also double check this using another point of reference
let's take the peaks of the function
The first peak visible is at -3π/4 and the next peak at π/4
So the period = π/4 - (-3π/4) = π/4 + 3π/4 = π
Y less than 9 in algebra expression
Answer:
9 - y
Step-by-step explanation:
less than means Subtraction
ayuda ES URGENTE 911
Answer: B D I J M
Step-by-step explanation: you just gotta see if any of the two answers work an if they don’t it’s nethier!
A rectangle is 3/4 of a feet long and 5/12 of a feet wide. What fraction represents the area of the rectangle
The area of the rectangle can be expressed as a fraction by multiplying 3/4 and 5/12. The answer is 5/16, which represents the area of the rectangle.
1. Multiply the length and width of the rectangle: 3/4 x 5/12 = 15/48
2. Reduce the fraction to its simplest form: 15/48 = 5/16
3. The answer is 5/16, which represents the area of the rectangle.
To find the area of a rectangle, you need to multiply the length and width of the rectangle together. In this case, the rectangle is 3/4 of a foot long and 5/12 of a foot wide. To express the area as a fraction, you need to multiply the two fractions together. 3/4 x 5/12 = 15/48. Since 15 and 48 have a common factor of 3, the fraction can be reduced to its simplest form, 5/16. Therefore, the area of the rectangle can be expressed as 5/16. This fraction represents the area of the rectangle.
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The complete question is
A rectangle is 3/4 of a feet long and 5/12 of a feet wide. What fraction represents the area of the rectangle of a feet wide.
. if it is assumed that all poker hands are equally likely, what is the probability of being dealt a. a flush? (a hand is said to be a flush if all 5 cards are of the same suit.) b. one pair? (this occurs when the cards have denominations where and are all distinct.)
a) The probability of being dealt a flush is approximately 0.00198, or about 0.2%.
b) The probability of being dealt one pair is approximately 0.422, or about 42.2%.
a. To find the probability of being dealt a flush, we need to first determine how many possible flush hands there are, and then divide that by the total number of possible hands. There are 4 suits in a deck of cards, so there are 4 ways to choose which suit the flush will be in.
Once we have chosen a suit, there are 13 cards of that suit, and we need to choose 5 of them. The number of ways to choose 5 cards from 13 is given by the combination formula: C(13,5) = 1287. Therefore, there are 4 x 1287 = 5148 possible flush hands.
The total number of possible hands is given by the combination formula for choosing 5 cards from a deck of 52: C(52,5) = 2598960. Therefore, the probability of being dealt a flush is 5148/2598960, which simplifies to approximately 0.00198, or about 0.2%.
b. To find the probability of being dealt one pair, we need to first determine how many possible one pair hands there are, and then divide that by the total number of possible hands. There are 13 denominations in a deck of cards, so there are 13 ways to choose which denomination will form the pair.
Once we have chosen a denomination, there are 4 cards of that denomination, and we need to choose 2 of them. The remaining 3 cards must each be a different denomination from the pair, so there are 12 denominations left to choose from, and 4 cards of each denomination.
We need to choose 3 of these 12 denominations, and then 1 card from each of those 3 denominations. The number of ways to choose 2 cards from 4 is given by the combination formula: C(4,2) = 6. The number of ways to choose 3 denominations from 12 is given by the combination formula: C(12,3) = 220.
The number of ways to choose 1 card from each of 3 denominations is 4 x 4 x 4 = 64. Therefore, the total number of possible one pair hands is 13 x 6 x 220 x 64 = 1,098,240. Dividing this by the total number of possible hands gives us the probability of being dealt one pair, which is 1,098,240/2598960, or approximately 0.422, or about 42.2%.
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If each base angle in an isosceles triangle is 10 degrees larger then the vertex angle, find the measure of the vertex angle.Write the equation how to use to solve for the vertex angle?
The measure of the vertex angle is 53.3degrees, the equation is 3x+20=180.
What is an isosceles right angled triangle?It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.
Given;
Each base angle in an isosceles triangle is 10 degrees larger then the vertex angle.
The addition of the internal angles of triangle is 180
So, let vertex angle be x
The other two sides will be x+10,
x+x+10+x+10=180
3x+20=180
x=160/3
x=53.3
Therefore, the vertex angle of the triangle will be 53.3degrees.
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five times a number is at most 15 what are the possible values for the number
Answer:
x <= 3 represents all values such as: -∞, -100, -4, -3, -2, -1, 0, 1, 2, 3.
Step-by-step explanation:
5x <= 15
Next, we'll solve for x by dividing both sides by 5:
x <= 3
So, the possible values for the number are any value less than or equal to 3, including negative numbers.
x <= 3 represents all values such as: -∞, -100, -4, -3, -2, -1, 0, 1, 2, 3.
in a certain culture of bacteria, the number of bacteria is increased sixfold in 10 hours. how long did it take for the population to double? [use the natural growth equation.]
To double, the population must increase by a factor of 2, which would take ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.
To solve for the time it took for the bacterial population to double, we need to use the exponential growth formula:
[tex]N(t) = N_0 * e^{(kt)[/tex]
where N0 is the initial population, N(t) is the population at time t, k is the growth rate, and e is the base of the natural logarithm (approximately 2.71828).
Since the population is increased sixfold in 10 hours, we can set up the equation as:
[tex]N_0 * e^{(kt)} = 6 * N_0[/tex]
Taking the natural logarithm of both sides gives:
kt = ln(6).
Dividing both sides by k and using the fact that the natural logarithm of 2 is approximately 0.693,
ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.
So it took approximately 2.817 hours for the population to double.
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find an obtuse angle, θ, such that 0 ≤ θ ≤ 2π and has the same sine as -275° (please explain)
The obtuse angle such that has the same sine as -275° is θ = 95°
How to find the angle θ?We want to find an obtuse angle (with a measure larger than 90°) in the range 0 ≤ θ ≤ 2π (or 0 < θ < 360°, after that we can change the units from degrees to radians) such that sin(θ) = sin(-275°)
First, remember that the sine function has a periodicity of 360°, then:
sin(-275°) = sin(-275° + 360°) = sin(85°)
Now we know that the sine function is symmetric around x = 90°
Then:
sin(90° + x) = sin(90° - x)
if we take x = 5° we will get:
sin(90° + 5°) = sin(90° - 5°)
sin(95°) = sin(85°) = sin(-275°)
Thus we can conclude that θ = 95°
That is the obtuse angle.
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