Step-by-step explanation:
sol;
l=5w
area=l*w
or,45=5w*w
or,45=5w2
or,45\5=w2
0r[tex]\sqrt{9}[/tex]=w
or,3=w
again,
l=5w
l=5*3
l=15
Therefore, length is 15 inch and width is 3 inch.
11.
An IV of D5W 1000 mL was ordered to infuse over 8 hr at a rate of 42 gtt/min (42 macrogtt/min). Drop
factor: 20 gtt/mL. After 4 hr, you notice that only 400 mL has infused.
Recalculate the rate in gtt/min for the remaining solution
The rate is 50gtt per minutes.
How to calculate the growth rate?From the information, out of the total hours of 8 hours, four hours were used.
The volume will be:
= 1000 - 400
= 600ml
Time = 4 × 60 = 240 minutes
Drop factor = 20
Therefore, the growth rate will be:
= 600/240 × 20
= 50gtt/min
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A movie theater has a seating capacity of 167. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 1198, How many children, students, and adults attended?
Child attend:
Student attend:
Adult attend:
Answer:
Child attend: 58
Studen attend: 80
Adult attend: 29
Step-by-step explanation:
a + c + s = 167 Eq. 1
12a + 5c + 7s = 1198 Eq. 2
a = c/2 Eq. 3
a = adult attend
c = children attend
s = students attend
Replacing Eq, 3 in Eq. 2:
12(c/2) + 5c + 7s = 1198
6c + 5c + 7s = 1198
11c + 7s = 1198
7s = 1198 - 11c
s = (1198 - 11c) / 7 Eq, 4
Replacing Eq, 3 and Eq, 4 in Eq, 1
c/2 + c + (1198-11c) / 7 = 167
7c/14 + 14c/14 + 2(1198-11c)/14 = 2338/14
7c/14 + 14c/14 + 2396/14 - 22c/14 = 2338/14
7c + 14c + 2396 - 22c = 2338
7c + 14c - 22c = 2338 - 2396
-1c = -58
c = -58/-1
c = 58
from Eq. 3
a = c/2
a = 58/2
a = 29
from Eq. 4
s = (1198-11c)/7
s = (1198 - 11*58)/7
s = (1198 - 638) / 7
s = 560/7
s = 80
Check:
from Eq, 1
58 + 29 + 80 = 167
A bacteria culture starts with 1000 bacteria and the number doubles every 40 minutes. (a) find a formula for the number of bacteria at time (b) find the number of bacteria after one hour (c) after how many minutes will there be 50000 bacteria?
The formula for the number of bacteria at time t is 1000 x (2^t).
The number of bacteria after one hour is 2828
The number of minutes for there to be 50,000 bacteria is 324 minutes.
What is the number of bacteria after 1 hour?The exponential function that can be used to determine the number of bacteria with the passage of time is:
initial population x (rate of increase)^t
1000 x (2^t).
Population after 1 hour : 1000 x 2^(60/40) = 2828
Time when there would be 50,000 bacteria : In(FV / PV) / r
Where:
FV = future bacteria population = 50,000PV = present bacteria population = 1000r = rate of increase = 100%In (50,000 / 1000)
In 50 / 1 = 3.91 hours x 60 = 324 minutes
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In how many ways can 3 cards be chosen from a standard deck of 52 cards?
[tex]\displaystyle\\\binom{52}{3}=\dfrac{52!}{3!49!}=\dfrac{50\cdot51\cdot52}{2\cdot3}=22100[/tex]
b) Some economists in the cOuntry are proposing mandatory wage and price controls to combat inflation, but others claim such controls are ineffective. Suppose it is established that 40% of all adults in the country favour wage and price controls. If 5 adults are selected at random, find the probability that: i. At least 3 favour wage and price controls?
Answer:
3/5
Step-by-step explanation:
40% of all adults favor wage and price controls, that means that 4 out of every 10 adults favor them. Therefore, if 5 adults are selected at random, the probability that at least 3 of them favor wage and price controls is 3/5 or 60%.
Please Answer! It is a emergancy! SUPER EASY
Answer:
x^-3
Step-by-step explanation:
1 / (x^3) = x^(-3)
At a sale, coats were sold for $184 each. If the coats originally cost $200 each, what percentage of its original price was a coat sold for?
Answer:
92%
Step-by-step explanation:
sale price is 184.
original price was 200.
184/200 = 0.92
Multiply by 100 to change to a percent.
0.92 × 100 = 92
184 is 92% of 200.
The coat was sold for 92% of its original price.
Answer:
92%
Step-by-step explanation:
What percentage of 200 is 184 ?
184 / 200 * 100% = 92%
Median weekly earnings for women with some college for an associate degree.
1980.......$231
2013.............$657
Using today's dollars, the data in the bar graph can be described by the mathematical model
W = 13n + 231,
Where W represents median weekly earnings n years after 1980.
Does the formula underestimate or overestimate the median weekly earnings in 2013? By how much?
Using the given linear function, the formula underestimates the median weekly earnings in 2013 by $3.
What is the linear function for the estimate?The function that estimates the median weekly earnings n years after 1980 is given by:
W = 13n + 231.
2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by:
W = 13 x 33 + 231 = 660.
Since 657 < 660, the formula underestimates the median weekly earnings in 2013 by $3.
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If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer: x-7
Step-by-step explanation:
[tex]f(x)+g(x)=-3x-5+4x-2=\boxed{x-7}[/tex]
Suppose that an individual has a body fat percentage of 15.9% and weighs 159. How many pounds of her weight is made up of fat? Round to the nearest tenth
Answer:
25.3 lb
Step-by-step explanation:
We can multiply the whole by the percentage to find the part. Since 15.9% is equal to 0.159, the weight of fat is 159*0.159 = 25.281. Round this to the nearest tenth, and we get 25.3 pounds.
The amount of trash, in tons per year, produced by a town has been growing linearly, and is projected to
continue growing according to the formula P(t) = 75 + 4t. Estimate the total trash that will be produced
over the next 8 years by interpreting the integral as an area under the curve.
tons
The total trash that will be produced over the next 8 years will be 107 trash
Functions and valuesGiven the function that represents the amount of trash, in tons per year, produced by a town has been growing linearly, and is projected to
continue growing according to the formula P(t) = 75 + 4t
The total trash that will be produced over the next 8 years is expressed as:
p(8) = 75 + 4(8)
p(8) = 75 + 32
p(8) = 107
Hence the total trash that will be produced over the next 8 years will be 107 trash
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How do I Expand (2x − 1)^6
Answer:
well if u do this
(2x-1)(2x-1)(2x-1)(2x-1)(2x-1)(2x-1)
it would be the expanded form for (2x-1)^6
Step-by-step explanation:
i um learned it before so...
Which shows an equation in point-slope form of the line shown?
y−4=43(x−2)
y−2=34(x+6)
y−4=34(x−2)
y+2=43(x+6)
Number graph ranging from negative ten to ten on the x and y axes. A line passes through the labeled points (negative six, negative two) and (two, four).
Answer: Option (3)
Step-by-step explanation:
The slope of the given line is
[tex]\frac{-2-4}{-6-2}=\frac{-6}{-8}=\frac{3}{4}[/tex]
Thus, the answer must be Option (3)
If you are driving at a rate of 55 miles per hour, about how many feet per second are you traveling?
290400 feet per second
0.015 feet per second
4840 feet per second
80.67 feet per second
The function g(x) = -2x +3 compare the slopes and y-intercepts
The slope of the function in discuss is -2 and the y-intercept of the function is; 3.
What is the slope and y-intercept of the function?The slope which is simply a measure of the rate of change can be obtained by comparison of the function given to the slope-intercept form of a linear function.
f(x) = mx + c
Hence, the slope of the function is -2 and it's y-intercept (point of intersection with the y-axis) is; (0,3).
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A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 56 feet. If the material used to build the pen is $1.50 per foot for the longer sides and $2.75 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.
The cost of the shorter and longer side of the rectangular pen is $19.25 and $31.50 respectively.
Perimeter of rectangleWidth = xLength = 3xPerimeter = 56 feetPerimeter = 2(length + width)
56 = 2(3x + x)
56 = 2(4x)
56 = 8x
x = 56/8
x = 7
So,
Width = x
= 7 feet
Length = 3x
= 3(7)
= 21 feet
Cost of material used for the shorter side = $2.75 × 7
= $19.25
Cost of material used for the longer side = $1.50 × 21
= $31.50
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1) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino. What would you expect to be true for all expected values for these seven games? In your discussion, also state whether the expected value is positive or negative. 1 ) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino . What would you expect to be true for all expected values for these seven games ? In your discussion , also state whether the expected value is positive or negative.
As per the question seems, the expected value can be positive, negative or zero.
The given question is of probability, which cannot be negative so don't get confused between expected values and probability, expected value and be negative, positive or zero.
What is probability?
Probability can be defined as the ration of favorable outcomes to the total number of events.
If person playing different games in casino , the probability of that person winning could be varying from 0/7 to 7/7 which implies that person can win from zero games to all games. If that person wins all the 7 games that mean he the gain in values, but if the loses 1 games or more games there than he supposed have gain or have loosen expected values so it can be positive, negative or zero. however the person loosen every game their is certain negative expected values.
Thus, The expected value can be positive, negative or zero.
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A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $80 million after 4 years, as shown in the graph:
There is a graph of a line with Years on the x axis and Profits in millions on the y axis that passes through 1, negative 100 and 4, 80.
Which equation most closely represents the line depicted in the graph?
f(x) = 60x − 160
f(x) = −60x + 160
f(x) = −80x + 4
f(x) = 80x − 4
The equation that most closely represents the line depicted in the graph is; f(x) = 60x − 160
How to find the equation of a Graph?We're given a point of the graph (4, 80).
From the complete question seen online, we see that the profits increased $60 million per year. Thus, slope = 60.
Let us write the equation and find x and y intercepts.
y = 60x + b
Thus;
80 = 60*4 + b
80 = 240 + b
b = -160
Thus, the equation that most closely represents the line depicted in the graph is; f(x) = 60x − 160
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Which represents the inverse of the function
f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = =x
h(x) =÷x
please please out of certain people of all locality 50% speak Nepali language 55% speak English language and 5% speak not if 40 people speak both the language find total number of people,people who speak nepali language only english language only.Show the result in a venn diagram.
The given pics are your answers... Thank you
PLS HURRRYYYyyyyyyyydhsbsbd
Answer:
116.5027
Step-by-step explanation:
degree/360 *pie * radius^2
Which expressions represent purely real numbers and which expressions represent non-real complex numbers?
All rights reserved.
-289
i9
√(-18)
4- 321² 2 √-49
3 +2i
Purely Real Number
Non-real Complex Number
An expression is defined as a set of numbers, variables, and mathematical operations.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
From the given expression the numbers can be classified as,
Real Numbers
-289i⁹ = -14-32i² = 36Non-real / Complex Number
3 + 2i2 - √-49 = 2 - 7iLearn more about Expression:
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Solve the inequality −38<5x+7≤17
66877383
Step-by-step explanation:
I made a single dad be single of ⅝
3
)))
3
Tiles
31/50 42√/2
Pairs
972
448
3,528
4,050€
43/7 4√3
C
3/4
738
Submit
Answer:
I need detailed question
In what situation would you use an ANOVA statistical test over T-test?
Step-by-step explanation:
when means of more than two groups are to be compared, ANOVA is perferred
Periodic Deposit: $1000 at the end of each year Rate: 4.5% compounded annually Time: 11 years
The interest amount is $622.85
How to determine the interest amount?The given parameters are:
Principal, P =$1000 Rate, r = 4.5% compounded annually i.e. n = 1Time, t = 11 yearsThe interest amount is calculated as:
I = P(1 + r/n)^(nt) - P
This gives
I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000
Evaluate the products and the quotient
I = 1000 * (1 + 0.045)^(11) - 1000
Evaluate the sum
I = 1000 * (1.045)^(11) - 1000
Solve
I = 622.85
Hence, the interest amount is $622.85
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7)Which statement is true?
A. The radius of a given circle is longer than its diameter.
B. The length of the radius is the same in all circles.
C. The circumference is always twice the radius.
D. All circles contain 360 degrees.
Answer:
D.
Step-by-step explanation:
A. The radius of a given circle is longer than its diameter.
False. The diameter is twice the radius.
B. The length of the radius is the same in all circles.
False. Since there are circles of many sizes, there are many different sizes of the radius.
C. The circumference is always twice the radius.
False. The circumference is 2π times the radius or π times the diameter.
D. All circles contain 360 degrees.
True.
People were asked if they prefer Pepsi or Coke. The results are in the table below.
Pepsi Coke
Female 23 44
Male 28 39
a) If two people are chosen, what is the probability that they both prefer Pepsi?
b) If one person is chose, find the probability that they are Female or prefer Coke.
Using it's concept, it is found that the probabilities are given as follows:
a) 0.1431 = 14.31%.
b) 0.7910 = 79.10%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
The number of people is:
23 + 44 + 28 + 39 = 134.
The number of people that prefer Pepsi is:
23 + 28 = 51.
Hence, for the two people, the probability is:
p = 51/134 x 50/133 = 0.1431 = 14.31%.
Item b:
There are 23 + 44 = 67 females, and 39 males who prefer Coke, hence the probability is:
p = (39 + 67)/134 = 0.7910 = 79.10%.
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Let R(x)=3x^3+2x^2+x and S(x)=4+1. Find R(x) * S(x)
Pls help!!!!
3x^3 x 4x^2 = 12x^5
3x^3 x 1 = 3x^3
2x^2 x 4x^2 = 8x^4
2x^2 x 1 = 2x^2
1x x 4x^2 = 4x^3
1x x 1 = 1x
12x^5 + 3x^3 + 8x^4 + 2x^2 + 4x^3 + 1x
Simplify
12x^5 + 7x^3 + 8x^4 + 2x^2 + 1x
Thus, answer is B
Hope this helps!
Drag each graph to show which transformation was applied to the original figure.
Each graph is the result of one transformation.
Transformation is a process in which the dimensions or orientation of a given plane shape is changed. The required answers are:
Graph 1: Reflection
Graph 2: Translation
Graph 3: Rotation
Graph 4: Rotation
Graph 5: Translation
Graph 6: Reflection
Transformation is the process in which the dimensions or orientation is a given shape is changed. The major types are reflection, dilation, translation, and rotation.
Reflection is a transformation method in which a given shape is flipped over a given reference point or line. Dilation is a transformation method that involves either increasing or decreasing the length of sides of a given shape.Translation is a transformation method that requires the movement of all points of a shape with respect to a given reference point or line.Rotation is a transformation method that involves the rotation of a given shape at a certain degree clockwise or counterclockwise.Thus the transformation process that was applied to the original figure for each graph is:
Graph 1: Reflection along the y-axis
Graph 2: Translation at 4 units in the -x direction
Graph 3: [tex]90^{o}[/tex] clockwise Rotation
Graph 4: [tex]180^{o}[/tex] clockwise Rotation
Graph 5: Translation
Graph 6: Reflection along the x-axis
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