The exponential function to model the situation is f(x) = 130(1.05)ˣ⁺¹⁶
How to find the exponential function?First of all, note that each variable represents number of years the price increases in each year
We are given,
The initial number of population = 130
Rate of growth = 5% = 0.05
Number of years = 16.
Thus, we get that the growth in population for 16 years is given by,
f(x) = 130(1.05)¹⁶
⇒f(x) = 130(1.05)¹⁶i
This gives us that the population after 16 years will be given by,
f(x) = 130(1.05)ˣ⁺¹⁶
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Please help me do this
Answer:
1. 5 inches in 2 days
2. y = (5/2)x. where y is rainfall and x is days.
3. Yes
4. (5/2)
5. 2.5"/day
6. 37.5 Inches
Step-by-step explanation:
See attached worksheet
.
dopamine 4 mcg/kg/min by continuous iv infusion for a client who weighs 64 kg. available is dopamine 400 mg in 250 ml of d5w. determine how many ml/hr to administer. round to the nearest tenth.
We should administer 2.05 ml/hr.
A sort of neurotransmitter and hormone is dopamine. It affects a variety of vital bodily processes, such as mobility, memory, rewarding pleasure, and motivation. Dopamine levels are linked to a number of neurological and mental health conditions.
To determine the ml/hr to administer, we first need to calculate the dose of dopamine in mg/kg/min. We can use the following formula:
dose (mg/kg/min) = 4 mcg/kg/min x 10^-3 (to convert from mcg to mg)
dose (mg/kg/min) = 0.004 mg/kg/min
Next, we need to calculate the total dose in mg/min. We can use the following formula:
dose (mg/min) = dose (mg/kg/min) x weight (kg)
dose (mg/min) = 0.004 mg/kg/min x 64 kg = 0.256 mg/min
Now we need to convert the dose from mg/min to ml/hr, using the following formula:
ml/hr = dose (mg/min) x weight (kg) / concentration (mg/ml) x 60 min/hr
ml/hr = 0.256 mg/min x 64 kg / 400 mg/250 ml x 60 min/hr
ml/hr = 2.048 ml/hr
To round to the nearest tenth, we will round 2.048 to 2.05 ml/hr. Therefore, we should administer 2.05 ml/hr.
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Given the system of equations: 5x + 2y = 3 4x − 8y = 12 solve for (x, y) using elimination.a. (−7, 5) b. (−5, −4) c. (1, −1) d. (3, −6)
(x,y) = (1, -1). Option (c) is the correct answer.
Given equations:
5x + 2y = 3 ..(1)
4x - 8y = 12 ..(2)
Solving using the elimination method:
so, 4x = 8y + 12 or x = 2y + 3 ..(3)
Now, substituting the x in equation(1) from equation(3)
so we get,
5(2y+3) + 2y = 3
10y + 15 + 2y = 3
12y = -12
y = -1
Putting the value of y in equation(3)
x = 2(-1) + 3 = 1
x = 1
Therefore, (x,y) = (1, -1)
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Answer: Option C, (-1,1)
Step-by-step explanation:
Write the values of n such that -15<3n<6
The values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.
What are inequalities?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The given expression is:
-15< 3n < 6
Divide all the sides of the equation with 3 to isolate the value of n.
-15 / 3 < 3n/3 < 6/3
-5 < n < 2
Hence, the values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.
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asserion: 997 is the largest 3 digit prime number
reason: a positive integer n is a prime number if no positive integer less than or equal to √n divides n
The assertion that 997 is the largest 3-digit prime number is correct.
What is a prime number?
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. In other words, it is a number that is divisible by only 1 and itself. To determine if a number is prime, one common method is to check if any positive integer less than or equal to the square root of the number divides the number.
In the case of the assertion that 997 is the largest 3-digit prime number, we know that 997 is a 3-digit number (999 being the largest) and we can check if any positive integer less than or equal to the square root of 997 divides 997. Since 997 is a prime number, it is not divisible by any positive integer less than or equal to 31 (the square root of 997). Therefore, we can conclude that 997 is a prime number and the largest 3-digit prime number.
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a president and vice-president for a sorority are chosen from six people. how many different president/vice-president combinations are possible?
Answer:
there is 30 ways
Step-by-step explanation:
There are 6 people who can be president x 5 other people who can be vice president. so there is 30 ways
Can you write an Orginal Oratory speech on benefits of solar energy
Throughout the solar system, solar energy is continuously emitted by the sun. The Earth is warmed by solar energy, which also affects the weather, the wind, and the survival of plant and animal life. Electromagnetic radiation, which is a kind of energy, heat, and light, is released from the sun (EMR).
What is solar system?Anything produced by the sun is considered to be solar energy.Nuclear fusion that occurs in the sun is the source of solar energy. Hydrogen atom protons clash ferociously in the sun's core, where they fuse to form helium atoms, which is the process of fusion.An large quantity of energy is released during this process, which is sometimes referred to as a PP (proton-proton) chain reaction. Around 620 million metric tons of hydrogen are fused by the sun every second in its core. Other stars, similar in size to our sun, also experience the PP chain reaction, which supplies them with ongoing heat and energy. These stars have an average Kelvin temperature of 4 million degrees (about 4 million degrees Celsius, 7 million degrees Fahrenheit).The CNO cycle is responsible for energy production in stars that are around 1.3 times larger than the sun. Carbon, nitrogen, and oxygen (C, N, and O) are required for the CNO cycle to convert hydrogen to helium. As of right now, the CNO cycle produces less than 2% of solar energy.To Learn more About solar system, refer To:
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Rick paddles a kayak 20 miles upstream in 4 hours. The return trip downstream takes him 2. 5 hours. What is the rate that Rick paddles in still water? What is the rate of the current?
For the given time taken to cover 20 miles from upstream and downstream the rate of Rick paddles in still water is 6.5mph and rate of current is 1.5mph.
Let us consider 'x' be the rate at which Rick paddles in still water
'y' be the rate of the current
Distance covered while going in upstream = 20 miles
Time taken while going 20 miles upstream = 4 hours
Rate of upstream = 20 / 4
⇒ x - y = 5 miles /hours ___(1)
Distance covered while going in downstream = 20 miles
Time taken while going 20 miles downstream = 2.5hours
Rate of downstream = 20 / 2.5
⇒ x + y = 8 miles /hours ___(2)
Solve (1) and (2) we get,
x - y = 5
x + y = 8
2x = 13
⇒ x = 6.5miles per hour
y = x - 5
⇒ y = 1.5 miles per hour
Therefore, the rate of the Rick paddles in the still water is 6.5mph and the rate of the current is 1.5mph.
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Three times the square of a number minus eight
The expression of the statement is 3x² - 8
How to determine the expression of the statementFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
Three times the square of a number minus eight
Represent the number with x
So, we have
Three times the square of x minus eight
Express as squares and numbers
This gives
3 * x² minus 8
So, we have
3x² - 8
hence. the expression is 3x² - 8
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Janine sold 428 tickets for the school play. Student tickets were $3 and adult tickets were $5.
Janine’s total ticket sales were $1674. How many student tickets and how many adult tickets were sold ?
Solve this problem using a system of linear equations. Make sure you introduce the two variables
used and explain what they represent, write two equations using the two variables you have chosen,
solve the linear system using substitution OR elimination method, showing ALL steps, and write a
concluding statement in words.
The system of the equation is written as
x + y = 428
5x + 3y = 1674
the solution:
adult tickets is 195
students tickets is 233
How to write the required equationThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
Janine sold 428 tickets for the school play
let the adult ticket be x and student ticket be yx + y = 428
Janine’s total ticket sales were $1674
Student tickets were $3 and adult tickets were $5
5x + 3y = 1674
The simultaneous equation
x + y = 428
5x + 3y = 1674
solving the equation by elimination method
x + y = 428 * 3
3x + 3y = 1284
5x + 3y = 1674
subtraction gives
-2x = -390
x = 195
substitute x = 195 into x + y = 428
195 + y = 428
y = 428 - 195
y = 233
hence adult tickets is 195, while students tickets is 233
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whats 4*4*5*10 equals the the fild of math
The expression 4× 4 × 5 × 10 = 800 in the field of math.
What is algebra?Algebra is a branch of mathematics that is used to manipulate symbols and equations in order to solve problems. Algebra helps to solve problems involving unknown quantities and to develop relationships between different variables. It is a powerful tool that can be used to solve and analyze a variety of mathematical problems and equations.
Algebra can be used to solve equations, simplify expressions, and find solutions to linear and quadratic equations. Through algebra, we can also find the slope of a line, the area of a triangle, and the volume of a cube. Algebra is an invaluable tool that is useful in many areas of mathematics and science.
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4. Xander's hedgehog weighs 0.62 pound.
Express his hedgehog's weight in grams.
Round your answer to the nearest gram.
Pls do step-by-step
The weight of the hedgehog in grams is 281 grams
What is the weight of the hedgehog in grams?The first step is to determine the unit of conversion of pounds to grams.
1 pound = 453.592 grams
In order to convert the weight of the hedgehog to grams, multiply the unit of conversion by the weight of the hedgehog in pounds. Multiplication is the product of two or more numbers,
Weight of the hedgehog in grams = 0.62 x 453.592 grams = 281 grams
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Go step by step to reduce the radical.
V 224
NOVO
try
The square root of 224 in long division is 14.96
The term square root in math is defined as a factor of a number that, when multiplied by itself, gives the original number
Here we know that we need to find the square root of √224.
In order to solve this one we have to do the following steps,
Here we have to start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 224, then we have two pairs 24 and 2.
And then we have to find a number(z) whose square is ≤ 2.
Then the value of z will be 1 as 1 × 1 = 1 ≤ 2.
Here we get the value of quotient and the remainder as 1 and now we have to add the divisor z with itself and get the new divisor 2z (2).
And then we have to drag down the next pair and find a number (n) such that 2n × n ≤ 124 here we have the value of n comes out to be 4.
Finally we have to add a decimal in the dividend (224) and quotient (14) simultaneously.
Here we have to add 2 pairs of zero in the dividend after the decimal and repeat the above step for the remaining three pairs of zero.
Complete Question:
Finale the square root of √224 and go step by step to reduce the radical.
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I NEED HELP ASAP!!! 15 POINTS
The results of the multiplications are: 1) x²+6x-16 (2) x²+8x+15 (3) x²-2x-63 (4) 6x+x-15 (5) 4x²-17x-15 (5) x²+13x+42
How to multiply the brackets?The given equations are
1) (x+8)(x-2)
Opening the brackets to have and collecting like terms to have
x²-2x+8x-16
x²+6x-16
2) (x+5)(x+3)
Opening the brackets to have and collecting like terms to have
= x²+3x+5x+15
x²+8x+15
3) (x+7)(x-9)
Opening the brackets to have and collecting like terms to have
x²9x+7x-63
x²-2x-63
4) (2x-3)(3x+5)
Opening the brackets to have and collecting like terms to have
6x²+10x-9x-15
6x²+x-15
5) (4x+3)(x-5)
Opening the brackets to have and collecting like terms to have
4x²-20x+3x-15
4x²-17x-15
6) (x+7)(x+6)
Opening the brackets to have and collecting like terms to have
x²+6x+7x+42
x²+13x+42
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Triangle ABC is dilated with the origin as the center of the
dilation. Which ordered pair could represent the image of
point C(5, 2) after the dilation?
0 (5,-2)
(-1,-4)
O (2.5, 1)
o (7.5, 4.5)
The ordered pair could represent the image of point C(5, 2) after the dilation is (2.5, 1)
Which ordered pair could represent the image after the dilation?If we have a general point (x, y) and we apply a dilation with the origin as the center of a scale factor k, then the coordinates of the image after the dilation is (k*x, k*y)
Here we want to see which point can be the image of (5, 2) after the dilation, it will must have the form (k*5, k*2)
The only point that has this form is the one on the third option, where we can write:
(2.5, 1) = (k*5, k*2)
Then we have two equations:
2.5 = k*5
1 = k*2
Solving these we should get the same value of k.
2.5/5 = k = 0.5
1/2 = k = 0.5
so that is the correct option.
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I got this problem in edmentum, and i have no idea what i should be looking for. I answered 5 as a guess. i had no idea if i should be looking for an average or something else
The box plot given by the number of students read 8 books is the centre quartile which is 5.
Define the term quartile of the data?Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each. One kind of quantile is a quantile.
Q1, or the lower quartile, is another name for the first quartile. The number that falls in the middle of the lowest and middle numbers is this one.Second quartile: Also referred to as the median or Q2. This value sits in the middle, midway between the lowest and greatest numbers.Third quartile, or the upper quartile, is also referred to as Q3. The number that falls in the middle of the middle and highest numbers is this one.Thus, for the stated question.
The box plot given by the number of students read 8 books is the centre quartile which is 5.
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you will need a straightedge for this assessment. which table represents a proportional relationship
The table that represents the proportional relationship would be table A. Option A
What is a proportional relationship?In this table we can see that in option A, there is a constant for which the values of the y are gotten. This is common on all of the values in A
For instance 2² = 4
3² = 9
4² = 16
0² = 0
The power of 2 is the constant that when applied on the values it gives the corresponding solution.
This shows the constant proportional relationship that is in existence between the values in x and the y solution
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(Simple)......Classify the transformation pls
The transformation represented by the figure is (c) translation
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have the following
A figure and its translated image
When a shape is translated to form another, then the transformation is a translation
Hence, the transformation is translation
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The values in the table represent function A and B. Which statement about the 2 functions is true?
The statement that is true about the 2 functions, in which the relationship between the x and y-values in the table of values for both functions is a linear relationship is presented as follows;
The y-intercept of the graph of A is equal to the y-intercept of the graph of BWhat is a linear relationship?
A linear relationship is a relationship that when plotted on the coordinate plane, produces a linear graph.
The first difference of the y-values in the data contained in the table for Function A are the same and equal to 6, therefore, the data for Function A is a linear relationship.
The slope of the graph of the values in Function A, [tex]m_A[/tex] is found as follows;
Slope of Function A, [tex]m_A[/tex] = (18 - 12)/(3 - 2) = 6
The slope of the graph of A is 6
The equation representing the relationship in function A in point-slope form is therefore;
y - 12 = 6·(x - 2)
y - 12 = 6·x - 12
y = 6·x - 12 + 12 = 6·x
The equation in slope-intercept form, y = m·x + c, where c is the y-intercept is therefore; y = 6·x
The value c in the equation is 0 (c = 0). The y-intercept intercept of the graph of Function A is therefore, c = 0
The y-intercept of the graph of Function A is 0
The first difference of the data in the table of Function B is also a constant
The slope of Function B, [tex]m_B[/tex] = (5 - 1)/(1 - 0) = 4
The slope of the graph of B is 4
From the values in the table, the y-value at the y-intercept, which is the point where x = 0, is y = 1
The y-intercept of the graph of Function B is 1
The true statement is therefore;
The y-intercept of the graph of A is less than the y-intercept of the graph of B
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10v + 11v I NEED HELP PLSSS
Answer:
21v
Step-by-step explanation:
Since it is the same variable you would just add them!!
10+11=21
10v+11v+21v
PLEASE HELP!
Using the geometric probability distribution after 500 trials, determine the following probabilities. Type your answer in the blank space below.
I AM ABSOLUTELY GOING INSANE IN THE MEMBRANE.
As per the asked equation the value of P(x<6) will be c=1
How to find the probability?The probability of an event is always between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Given the information provided, P(x-1)=0.178, P(x>1)=0.822, it's not possible to calculate P(x<6) because the information provided doesn't give us the complete picture of the probability distribution function, also we don't know the type of distribution used to calculate the probabilities. So we can't infer anything about P(x<6) from the information given.
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if light travels exactly 1 meter in 1/299,772,458 of a second, how many kilometers does it travel in 4.00 years? for this question, 1 year
The light travels 3.784 x 10 ^13 kilometers in 4 years .As Given that, light travels 1 meter in 1/299,772,458 of a second.
In 4 years how many kilometers it will travel?
covert 4 years into seconds.
since it is given that 1 year = 365.25 days.
4 years in seconds = 4 x 365.25 x 24 x 60 x 60
= 126230400 sec
1 m in 1/299,772,458 sec
x km in 126230400 sec
(let x be the distance travelled)
x = 126230400 x 299,772,458
= 3.784 x [tex]10^13\\[/tex] km.
Therefore , The light travels 3.784 x 10 ^13 kilometers in 4 years .
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The complete question :
if light travels exactly 1 meter in 1/299,772,458 of a second, how many kilometers does it travel in 4.00 years? for this question,
1 year = 365.25 days.
Naudia rode her bike two miles south. Then, she went east for three miles to reach her destination. How far is she
from her starting point?
The distance of Naudia from starting point based on distance travelled is 13 miles.
The distance travelled by Naudia and distance from starting point will form right triangle. Distance between Naudia and her final destination is the straight line or hypotenuse.
So, the expression will be -
Distance of South² + distance of East² = Distance from starting point
Distance form starting point = 2² + 3²
Distance form starting point = 4 + 9
Distance form starting point = 13 miles
Thus, the required distance is 13 miles.
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Which is a correct solution for the following system of Inequalities
The solutions of the system of inequalities are the points on the purple region, one example of a solution is (-2, -2)
Which is a correct solution for the system of inequalities?When we have a system of inequalties (so we have 2 or more inequalities) the solutions are the points (x, y) that are solutions of both inequalities at the same time.
Here we can see the graph of a system, such that the solution set of one of the inequalities is represented by the red shaded area, and the solution set of the other inequality is represented by the blue shaded area.
The solution set of the system is represented by the intersection between the areas, which is the purple area.
So any point on that region is a solution to the system, for example, the point (-2, -2) is a solution.
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help me please i need immediate help
The mean height of the members of the football club is 163.4 to rounded to 1 decimal place.
How to calculate the mean heightThe mean height It is calculated by summing up all the data values and dividing by the total number of data points. The mean can also be represented by the point at which the frequency polygon would balance if it were a physical object.
The values with their corresponding frequencies are:
height: 120 × frequency: 8 = 960
height: 140 frequency: 11 = 1549
height: 160 frequency: 17 = 2720
height: 180 frequency: 18 = 3240
height: 200 frequency: 10 = 2000
sum frequency = 64
sum of all data values = 10460
mean height = 10460/64
mean height = 163.4375
Therefore, the mean height of the members of the football club is 163.4 to rounded to 1 decimal place.
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How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?
We assume that we have a plot given like the graph attached.
We have n points and we need to find How many of the 9 people listed in the scatterplot have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?
So for this case we need to have the predicted value y^ and the real value y. We are going to put these two values and the difference
yi yi^ |yi - yi^|
157 161.5 4.5
163 163.1 0.1
175 167 8.0
171 170.5 0.5
173 172.5 0.5
173 174.3 1.3
172 176 4.0
183 178 5.0
178 180 2.0
So as we can see we have 4 points out of the 9 who satisfy the condition
|yi - yi^| >= 3.
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Can someone help me please? I know the answer but the equation. Thanks.
Answer:
Equation is x-5 = 37
Reason:
x = starting temperature
We start with x degrees, and decrease by 5 degrees.
We go from x to x-5
The x-5 is now 37 degrees
Therefore, we arrive at the equation x-5 = 37
To solve this equation, add 5 to both sides and you'll get x = 42
Nice work on getting the correct value of 42.
Enter your answer as a fraction.
Show your work please!
The probability that the first bar Iesha selects will be lemon and the second will be raisin= 2/45.
What is probability ?
Probability can be defined as the ratio number of favourable outcomes and total number of outcomes.
Note this selection is done without replacement hence after each selection sample size will reduce
Given data,
Samples 3 chocolate chip bars,
2 peanut butter bars,
1 lemon bar, and
4 raisin bars
Sample size S= [3+2+1+4]= 10
Probability that first selection is lemon = 1/10
Probability that second selection is raisin = 4/9
Hence the probability that the first bar Iesha selects will be lemon and the second will be raisin= 1/10*4/9 = 4/90= 2/45
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A right rectangular prism measures 12 cm tall, 8 cm long, and 5 cm wide.
A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled?
Enter your answer, to the nearest tenth, in the box
Answer: Volume of a right prism = BH where B is the area of the base and H is its height.
So Volume = 16 × 12 = 192 cm^3
Step-by-step explanation:
The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
The graph of a line passing through the points (2, -4) and (0, 0). The correct answer would be an option (A).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The table represents a linear relationship.
x: −1 0 1 2
y: 2 0 −2 −4
As per the points, the graph has been attached below
Here we can see that the shown graph of a line passing through the points (2, -4) and (0, 0)
So the attached graph shows this relationship.
Hence, the correct answer would be option (A).
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