During surgery, the average flow rate of the medications administered to the patient is 23 milliliters per hour.
Flow rate, denoted by Q, is defined as the amount of volume V flowing after time t. The formula for flow rate is given by:
Q = V/t
where V is volume and t is time.
For the two medication administered, given the flow rate and time, solve for the volume of each, and its total volume.
V = Q/t
1 : V1 = Q1t1 = (14ml/h)(150 minutes)(1hour/60 minutes)
V1 = 35 ml
2 : V2 = Q2t2 = (30 ml/h)(4hrs)
V2 = 120 ml
Solving for the average flow rate by dividing the sum of the volume to the sum of the time.
Qave = (V1 + V2)/(t1 + t2)
Qave = (35 + 120)ml/(2.5 + 4)hrs
Qave = 23.84615385 ml/h
Rounding off to the nearest whole number.
Qave = 23 ml/h
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Meghan needs to create a 4-digit password. The digits cannot repeat in the password and cannot start with the digit 0. What is the probability , to the nearest hundredth of a percent, the the password starts with a 9 and ends with a 6?
The probability to the nearest hundredth of a percent, the the password starts with a 9 and ends with a 6 is 1%.
A four digit password will have number ranging from 0-9.
There are four spots in total.
The first spot can not be taken by zero, so only 9 options can take the place of first spot. As the number can not be repeated, the second spot has only options a 0-8. The third spot will eventually have 8 options only. The Fourth spot will have 7 options available to fill the spot.
Hence total number of 4-digit passwords combinations can be calculated by multiplying the options,
= 9 x 9 x 8 x 7
= 10206.
A total of 10206 passwords are possible.
The number of passwords starting from nine and ending with six can be found as,
= 1 x 9 x 8 x 1
= 72
A total of 72 passwords starting from 9 and ending with 6.
The probability that a password chosen is starting from 9 and ending with 6 is,
P(E) = 72/10206
P(E) = 0.007
Probability in percent,
= 0.007 x 100
= 0.7
Rounding it off, we get nearly 1%.
So, the probability is nearly 1%.
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Find the y-intercept and x-intercept of the line.
-x+2y=2
The sum of thirty six and fourteen and divided by the sum of one and three
Written in simplest exponential form the product (3x¹)(-2x¹)
(1) –5r2
(3) x¹
(2) -6x¹0
(4)-6x²1
is?
An athlete is training for a triathlon by running each day. After 3 1/2 days, they ran a total of 12 3/5 miles. On average, how many miles did this athlete run per day? This is a division question. The mixed number 3 1 2 is the divisor. pls help asap
On average, the number of miles the athlete ran per day is; 18/5 or 3.6 miles per day
How to calculate the average distance?We are given;
Number of days the athletes ran = 3¹/₂ days = 7/2 days
Total distance ran in the given time = 12³/₅ miles = 63/5 miles
Now, the average distance will simply be given by the expression;
Average Distance = Total Distance/Number of days of running
Now, let us convert the fractions to improper fraction for easy division. Thus, we have;
Number of days the athletes ran = 7/2 days
Total distance ran in the given time = 63/5 miles
Thus;
Average Distance = (63/5)/(7/2)
Average distance = 63/5 * 2/7 = 18/5 = 3.6 miles per day
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HELP ME PLEASE
Your friend invites you to go to an indoor skateboard park. you'd like to go, but since you dont have a helmet or knee pads, you'll have to pay to rent them. You'll also need to buy a day pass to enter the park.
Write a formula that will help you determine your total cost. h=helmet rental
k=knee pad rental
p=cost of day pass
c=total cost
Answer:
C=h+k+p
Step-by-step explanation:
You just add all of the variables and it equals your total cost. if it was by hour the equation would be slightly different
Brianna asked 45 students if they would vote for her to be student council president. She used her calculator to compare
the number of students who said yes with the total number of students. Her calculator showed the result as 0.6222....
Answer parts a and b.
Write this number as a fraction.
Brianna would receive 28 votes from students.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The terms with a numerator and a denominator are called fractions.So, a recurring decimal at the number "2" is "0.6222.
Let x = 0.62222....
Multiplying by 10 to keep the repeating digits after the decimal point, x by 10x equals 6.2222.Multiplying by 100 allows us to once more leave the recurring digit after the decimal point, so multiplying x by 100 results in 62.2222.Subtract 10x from 100x as follows:
100x - 10x = 62.2222... - 6.2222... 90x = 56x = 56/90x = 28/45Therefore, Brianna would receive 28 votes from students.
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The correct question is given below:
Brianna asked 45 students if they would vote for her to be student council president. She used her calculator to compare the number of students who said yes with the total number of students. Her calculator showed the result as 0.6222...
1. Write this number as a fraction (Steps)
2. How many students said they would vote for Brianna?
lily’s age is 2 years and 4 months hugo’s age is 1 year and 8 months
write lily’s age in months as a fraction of hugo’s age in months
give your fraction in its simplest form
Step-by-step explanation:
lily's in months=4/12
hugos in months=8/12
4/12+8/12
1/3+2/3
lily's month in simplest form=1/3
hugos month in simplest form=2/3
Find all the zeros of each function. f(x)=x⁴-5 x²+6
According to the question, to calculate the zeros of each function. The given function is f(x) = [tex]x^{4}-5x^{2} +6[/tex]
Now, let us assume [tex]a=x^{2}[/tex]. Therefore, the above equation can be written as:
[tex]f(x)=a^{2}-5a+6[/tex]
Calculate the factors of the given equation and it can be re-written as:
[tex]f(x) = (a+2)(a+3)[/tex]
To calculate the final solution, equate it to zero.
[tex](a+2)(a+3)=0\\a=-2,-3[/tex]
Now, substitute these values in the original assumed equation:
The zeros function values are [tex]-\sqrt{2i};\sqrt{2i},-\sqrt{3i} ,\sqrt{3i}[/tex]
What is zero functions?
A zero function is a function which is almost zero everywhere on the graph. It is also known as a constant function.
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A nutrition label indicates that one serving of apple crisp
oatmeal has 2.5 grams of fat. How many grams of fat are t
there in 3.75 servings? Justify your answer. (Example 5) Ex
9.375 grams of fat are there in 3.75 servings.
A Nutrition Facts label lists the nutritional content, the serving size, and the calories for a recommended serving of a food product. This helps consumers make the best decision on how much to eat, maybe when they want to eat this food, or how they can better balance their food choices throughout the day.
Given the statement:
A nutrition label indicates that one serving of Apple crisp oatmeal has 2.5 grams of fat.
Determine the grams of fat in 3.75 servings.
In order to determine the grams of fat in 3.75 servings, we simply needed to multiply 2.5 grams by 3.75.
= (2.5 grams)×( 3.75)
= 9.375 grams of fat.
Thus , 3.75 servings contain 9.375 grams of fat ,if 1 serving contain 2.5 grams of fat .
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The value of an industrial machine has a decay factor of 0.75 per year. After six years, the machine is worth $ 7500 . What was the original value of the machine?
The original value of the machine is $ 30 , 720 , 000 .
Given : Decay factor = 0.75 per year
Present value of machine ( after 6 yrs . ) = $ 7500 .
According to ques .
The original value of machine be worth $ x .
After nth yr. the present value of machine will be
( x - 0.75 x ) [ [tex]( 1 - 0.75 ) ^{n-1}[/tex] ] .
Therefore , after 6 yrs. the present value of machine will be
( x - 0.75 x ) [ [tex]( 1 - 0.75 ) ^{5}[/tex] ] = 7500
0.25 x * ( [tex]0.25 ^{5}[/tex] ) =7500
Hence , x = 30 , 720,000
Therefore , the original value of the machine is $ 30 , 720 , 000 .
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the length of time for $5000 to earn $1000 if invested at 10% per annum
100 points top anyone who can answer these questions.
in the given figure the value of x is 45°.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given:
<PQR= x+7
<SQR=x+3
<PQR+<SQR=<PQS=100°
According to given question we have
<PQR+<SQR=<PQS
Put the value we get
x+7+x+3=100
Compare like terms we get
2x+10=100
Substract 10 from both sides we get,
2x=90
Divide 2 on both sides we get,
x=45°
Therefore, in the given figure the value of x is 45°.
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Rationalize the denominator of each expression. Assume that all variables are positive. ∛x / ∛y
The rationalization of the given expression is (xy²)¹/³ /y .
Rationalization can be thought of as the process used to remove the base or imaginary number from the denominator of an algebraic fraction. That is, remove the radical of the fraction so that the denominator contains only rational numbers.Radicals are expressions that use roots such as: B. Square root or cube root. For example, an expression of the form: √(a + b) is a root.The mathematical conjugate of any binomial means another exact binomial with opposite signs between the two terms.We have to rationalize the denominator of the expression ∛x / ∛y ,
where x and y are positive.
∛x / ∛y
= (∛x / ∛y) × (∛y / ∛y)
= ∛(x × y) / ∛(y × y)
= (∛xy)/ ∛y²
= (∛xy)/∛y²
= (xy²)¹/³ /y
The answer is (xy²)¹/³ /y .
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Jaycee has already saved $75 for an upcoming vacation. Every week, she adds another $15 to her vacation savings. The relationships between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings, is a linear relationship. Write an equation to describe the linear relationship.
Answer:
it adding
Step-by-step explanation:
Suppose that x and y vary inversely. Write a function that models each inverse variation and find y when x=-5 . x=2 when y=12
A function that models each inverse variation is y = 24. 1/x and y when x=-5 is -24/5
What precisely is the inverse of a function?Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.
Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.
Inverse variation is y = k. 1/x
given y = 12
x = 2
So, 12 = k. 1/2
So, the value of k = 24
We can conclude that the value of constant variation is 24
when x = -5, the value of y will be -
y = k.1/x
y = 24 . 1/-5
y = -24/5
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Aubrey is flying a kite, holding her hands a distance of 2.5 feet above the ground and
etting all the kite's string play out. She measures the angle of elevation from her
and to the kite to be 25°. If the string from the kite to her hand is 150 feet long, how
many feet is the kite above the ground? Round your answer to the nearest hundredth
of a foot if necessary.
The distance of kite above the ground is 65.33 feet.
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
We are given that;
Distance = 2.5 feet
Now,
Using this function, you can write an equation for the height of the kite, h:
sin(25°) = h / 150
Solving for h, you get:
h = 150 × sin(25°)
h = 62.83 feet
However, this is not the final answer, because you also need to add Aubrey’s hand height above the ground, which is 2.5 feet. Therefore, the total height of the kite above the ground is:
h + 2.5 = 62.83 + 2.5
h + 2.5 = 65.33 feet
Rounding to the nearest hundredth of a foot, you get:
h + 2.5 = 65.33 feet
Therefore, by trigonometric ratios the answer will be 65.33 feet .
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Answer:
The kite is 65.89 feet above the ground.
Step-by-step explanation:
which statement is true about the system of linear equations graphed in the coordinate plane below
Answer:
Step-by-step explanation:
The system of equations does not have one solution because the lines will never intersect.
Write an equation in slope-intercept form of the line that passes through (-9, -3) and (-7, 5)
The slope-intercept form of the line passing through the two points is
y = 4x + 33
Slope-intercept equation is one of the special forms of the linear equation.
To find the slope,
The point-slope formula is used to find the slope
y₂-y₁ = m (x₂-x₁)
where (x₁,y₁) and (x₂,y₂) are (-9,-3) and (-7,5), Then
5 - (-3) = m [-7 - (-9)]
5 + 3 = m (-7+9)
8 = m(2)
m = 8/2
m = 4
Therefore, the slope of the line passing through two points is 4
To find the intercept,
We can use the slope intercept formula to find the intercept
y = mx + b
where (x,y) be (-9,-3) abd m = 4 , Then
-3 = 4(-9) + b
-3 = -36 = +b
b = 36-3
b = 33
Therefore, the intercept of the line passing through two points is 33
Thus, the slope intercept form of the line passing through the two points
(-9, -3) and (-7, 5) can be written as
y = 4x + 33
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Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total of
$
1215
.
$
445
was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?
Joy was charged the labor of 11 hours
Joy was charged a total of $1215 from the landscaper for listed parts and labor
He was charged $445 for listed parts
He was charged the rest for labor
The hourly rate for labor is $ 70
Let the number of hours worked by labor be x
so, we can form a linear equation here as 445 + 70x = 1215
Now we have to solve this linear equation
445 + 70x = 1215
70x= 1215 - 445
70x = 770
x = 770/ 70
x = 11
Therefore, 11 hours of labor was needed to complete the job.
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if g(x)=x^2-7x find g(-2)
The value of the function at g(-2) is 18.
A function is defined a relation between two variables in such a way that the dependent variable y is related to the independent variable x.
Functions are normally denoted by f, g or h and g(x) denotes a function whose independent variable is x.A value of x is called the domain The resultant value of y for every x in the domain is called the range of the function.To calculate a specific value of a function we substitute the given value in the expression of x thereby calculating the value of the function at that point.
Given function : g(x)=x²-7x
At x=-2 , written as g(-2) we put the value -2 in the expression of x.
∴g(-2)=(-2)²-7(-2)
or, g(-2)=4+14
or, g(-2)=18
Hence the value of the function at g(-2) is 18.
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PLEASE HELP ME MARKING BRAINLYYYYY
Answer:
i think it c im not sure though I tried my best to figure the answer out. pls dont get mad if its wrong.
Answer:
A
Step-by-step explanation:
20xday will help determine how many she reads, the +52 will allow us to account for the 52 she a;ready read.
A 99-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
Answer: 8.25 inches per hour
Step-by-step explanation: 99/12 = 8.25
Find the degree measure of an angle of 3 π/4 radians.
Answer: 135°
Step-by-step explanation:
Since π = 180°
(3 × π)/ 4
Substitute 180° for π
= (3 × 180)/4
Simplify
= 540/4
= 135°
Yong Quan was trying to access his email account when he could not remember the 4 digit password to the email account. He clicked on the button to reveal a hint. The hint: The biggest even number which can be formed by the numbers 1, 3, 8, 6. What was Yong Quan's password to the email account?
what is nine plus ten
The value of nine plus ten is 19
What are Mathematical operations?Mathematical operations are simply known as arithmetic operations used in solving algebraic problems and other mathematical calculations.
These operations include;
AdditionSubtractionMultiplicationDivisionBracketExponents, etcIn this case, we have;
nine plus ten
This is expressed as;
9 + 10
The sum is 19
Thus, the value of nine plus ten is 19
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Patrick grated 2/3 of a block of cheese to make macaroni. What fraction of the block is left
ppppppllllllssss hhhhheeeeellllppppp
The exponent -6⁻⁴ is -(1/6⁴) which simplifies to -(1/1296).
What is exponent?Exponents represent how many times a number is multiplied by itself. Numbers written in exponent form are more compact for a large number of repetitive multiplications.
We know moving an exponent from numerator to denominator or vice versa changes the sign of the exponent.
∴ -6⁻⁴ can be written as -(1/6⁴) which is,
-(1/1296).
Now, simplifying (-6)⁻⁴ which is 1/(-6)⁴,
= (1/1296).
So, their numerical value is the same but they are of different signs as (-6) multiplied 4 times gives a positive number.
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Four-thirds of a number is decreased by 12. The result is eight
Answer:
The number is 15
Step-by-step explanation:
x = a number
4/3 x - 12 = 8
Rearrange the equation so that the integers are on one side - in the format Ax = B
4/3 x - 12 = 8
4/3 x = 8 + 12
4/3 x = 20
Simplify the equation - in the format x = A - then solve for x
4/3 x = 20
4 x = 20 * 3
4 x = 60
x = 60 / 4
x = 15
[tex] \large \bf \implies{A\: number\: is\:15}[/tex]
Step-by-step explanation:A number is x
then we have [tex]\frac{4}{3}[/tex]x - 12 = 8
[tex] \bf \longrightarrow \frac{4}{3}x - 12 = 8 \\ \\ \bf \longrightarrow \frac{4}{3}x = 8 + 12 \\ \\ \bf \longrightarrow \frac{4}{3}x = 20 \\ \\ \bf \longrightarrow 4x = 20 \times 3 \\ \\ \bf \longrightarrow4x = 60 \\ \\ \bf \longrightarrow x = \frac{ \cancel{60}}{ \cancel{4} } \\ \\ \bf \longrightarrow \: x = 15[/tex]
'Four thirds of the number is [tex]\frac{4}{3}x[/tex] then decreased by 12 is [tex]\frac{4}{3}x - 12[/tex] then gives the result 8. That is [tex]\bf\frac{4}{3}x - 12 = 8[/tex]'
What percent of
140 is 175?
Answer:
125%
this is the answer in percent form
if we take 140 as the 100%, what is 175 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 140 & 100\\ 175& x \end{array} \implies \cfrac{140}{175}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{4}{5}=\cfrac{100}{x}\implies 4x=500\implies x=\cfrac{500}{4}\implies x=125[/tex]