The population of a town is given by the equation p = 200,000 3/4t where t is the number of years since the population was first recorded in the year 2010 Fill in the table below.
Answers
The population increase according to the given years will be 27500, 23750 and 20833.
What is multiplication?Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the number.
In this question,
p = 200,000 3/4t
When t=0
p=0
When t=1
p= 20000 3/4= 27500
when t=2
p= 20000 3/8 = 23750
When t=3
p= 20000 3/12 = 20833
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Related Questions
x = -3y - 17 2x + 3y = -7
Answers
Answer:
x = 10
y = -9
Step-by-step explanation:
x = -3y - 17
2x + 3y = -7
Plug in x
2 (-3y - 17) + 3y = -7
-6y - 34 + 3y = -7
-3y = 27
y = -9
Plug in the value you got for y back into the equation to find the x value
x = -3(-9) - 17
x = 10
What is the next number in the sequence 3, 4, 7, 12, 19
Answers
Answer:28
Step-by-step explanation:
Answer: 28
Explanation: Look for a pattern or reason for the following number in the sequence. In this case 3+1=4, 4+3=7, 7+5=12, 12+7=19, so the probable answer is to add the following odd number to the last one in the line to get the next. (19+9=28)
Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching
jim
rate, in
of the cupric chloride.
min
After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so
he used the data to calculate the following least squares regression equation for predicting the etching rate from
the room temperature:
= 2 + 5
1
-2
What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5
min
Answers
The residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min is equals to the -2 μm/min.
The residual for each observation in statistics is the difference between predicted values of y (dependent variable) and observed values of y. That is Residual= observed y value − predicted y.
Here, cupric chloride is used to etch circuit boards. The linear regression equation is, y = 2 + (1/5)x
where, x = temperature in °C
y = etching rate in μm/min
Observed value of etching rate of cupric chloride = 5 μm/min for 25°C
To determine the estimated or predicted value of etching rate of cupric chloride, we substite x = 25, in the above linear equation, y = 2 + (1/5)x
=> y = 2 + (1/5)× 25
=> y = 7
So, Predicted Value = 7 μm/min
Observed Value = 5 μm/min.
Residual = Observed Value - Predicted
= 5 - 7 = -2
Hence, required value is -2 μm/min.
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Complete question:
Calculating and interpreting residuals You might need: Calculator Alexander uses cupric chloride to etch circuit boards. He recorded the room temperature, in °C, and the etching rate, in μm/min of the cupric chloride. After plotting his results, Alexander noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the etching rate from the room temperature: y = 2 + 5/x, What is the residual if the room temperature was 25°C and the cupric chloride had an etching rate of 5 μm/min. ? Show Calculator
If Jacob spent 45$ on dinner and wanted to top the waitress 15%, which of the following would be a good estimate for the tip?
Answers
Answer: 6.75
Step-by-step explanation:
45 x 0.15= 6.75
115% divide by 100 = 1.5
1.5 x 45$ is $67.50
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = sin(√n)/√n
Answers
The given sequence an = sin(√n)/√n converges to limit 0 as n approaches infinity
The mentioned nth term of the sequence is an = sin(√n)/√n. To determine the convergence or divergence of the sequence and find its limit, we can use the limit comparison test, which is based on comparing the given sequence with a known sequence whose convergence or divergence is already known.Suppose bn is a known sequence whose convergence or divergence is already known. Then, by the limit comparison test, the given sequence converges or diverges according as the sequence bn converges or diverges.
To apply the limit comparison test, we need to find a suitable sequence bn whose convergence or divergence is known. For this, we observe that sin x ≤ x for all x > 0. Hence, we have 0 ≤ sin(√n)/√n ≤ 1/√n, where the inequality follows by dividing both sides of sin x ≤ x by √n and substituting x = √n. Also, we know that the sequence bn = 1/√n converges to 0 as n approaches infinity. Therefore, by the limit comparison test, the given sequence an = sin(√n)/√n also converges to 0 as n approaches infinity.
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The _________ method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.- Non probability sampling- Systematic sampling- Simple random sampling - Stratified sampling
Answers
The Simple random sampling method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.
What is Simple random sampling?
The Simple random sampling is a sampling technique in which every member of the population has an equal chance of being chosen as a sample. The samples are chosen randomly, without any specific criterion. In this method, the selection of individuals for the sample is done without any specific pattern. This means that each member of the population is equally likely to be selected as a sample.In Simple random sampling, each member of the population is assigned a number, and the samples are selected using a random number generator or drawing names out of a hat. The selected samples are then analyzed to make predictions about the entire population.For example, if a researcher wanted to know the average age of students in a school, they might use Simple random sampling to choose a sample of 50 students. The researcher would assign each student a number and then use a random number generator to select the samples.There are some advantages and disadvantages of Simple random sampling, which are listed below:Advantages of Simple random sampling It is easy to understand and conduct the process.Each member of the population has an equal chance of being selected as a sample.It ensures that the sample is representative of the entire population.Disadvantages of Simple random sampling It can be time-consuming to select the samples.There may be a chance of human error when selecting samples.The sample size may not be large enough to draw meaningful conclusions.
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7,600 dollars is placed in a savings account with an annual interest rate of 6%. If no money is added or removed from the account, which equation represents how much will be in the account after 7 years?
Answers:
M=7,600(1+0.06)(1+0.06)
M=7,600(1-0.06)^7
M=7,600(1+0.06)^7
M=7,600(0.06)^7
Answers
Step-by-step explanation:
The equation that represents how much will be in the account after 7 years is:
M = 7,600(1+0.06)^7
Here's the explanation:
The formula for calculating the future value (M) of a present value (P) invested at an annual interest rate (r) for a certain number of years (t) is M = P(1+r)^t.
In this case, the present value (P) is 7,600 dollars, the annual interest rate (r) is 6% or 0.06, and the number of years (t) is 7.
Substituting these values into the formula, we get M = 7,600(1+0.06)^7. This represents how much will be in the account after 7 years if no money is added or removed from the account.
evaluate the diagram below, and find the measures of the missing angles
Answers
Answer:
A=100
B= 80
C=80
D=100
E=80
F=80
G=100
Step-by-step explanation:
Find the volume and surface area of soda if the radius is 6cm and the height is 11cm
Answers
The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.
To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:
Volume of cylinder = πr²h
Surface area of cylinder = 2πrh + 2πr²
Substituting the given values, we get:
Volume = π × 6² × 11
Volume = 1,026.72 cubic centimeters (rounded to two decimal places)
Surface area = 2π × 6 × 11 + 2π × 6²
Surface area = 452.39 square centimeters (rounded to two decimal places)
Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.
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calculator may be used to determine the final numeric value, but show all steps in solving without a calculator up to the final calculation. the surface area a and volume v of a spherical balloon are related by the equationA³ - 36πV² where A is in square inches and Vis in cubic inches. If a balloon is being inflated with gas at the rate of 18 cubic inches per second, find the rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches.
Answers
The rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches is 4.96 square inches per second.
The surface area of a spherical balloon and the volume of the balloon are related by the equation [tex]A³ - 36πV²[/tex], where A is in square inches and V is in cubic inches. To find the rate at which the surface area of the balloon is increasing, we can use derivatives. We start by taking the derivative of the equation [tex]A³ - 36πV²[/tex] with respect to time (t).
[tex]d/dt[A³ - 36πV²] = 3A²dA/dt - 72πVdV/dt[/tex]
Given the rate at which the balloon is being inflated with gas (dV/dt) and the area and volume of the balloon (A, V) at the given instant, we can solve for the rate at which the area is increasing (dA/dt).
[tex]dA/dt = (3A² - 72πV)dV/dt / 36πV[/tex]
Plugging in the given values for A, V, and [tex]dV/dt,[/tex]we can calculate dA/dt:
[tex]dA/dt = (3(153.24)² - 72π(178.37))(18)/(36π(178.37)) ≈ 4.96[/tex]
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Tyra will flip a red and yellow counter and spin a spinner labeled A-E. If Tyra flips the counter and spins the spinner, then list only the outcomes in which a red counter and a vowel are spun. (Select all that apply)
red, A
red, E
yellow, A
yellow, E
red, B
Answers
There are two possible outcomes where a red counter and a vowel are spun: a)red, A and b) red, E.
To see why, we can make a table listing all the possible outcomes of flipping a red or yellow counter and spinning a spinner labeled A-E:
A B C D E
Red A B C D E
Yellow A B C D E
We can then circle the outcomes that satisfy the condition of spinning a red counter and a vowel: red, A and red, E.
Therefore, the selected outcomes are:
red, A
red, E
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Which expression is equivalent to (4−2x)(4+2x)
Answers
The expression that is equivalent to (4 - 2x)(4 + 2x) is equal to 16 - 4x^2 approximately.
To simplify the expression (4 - 2x)(4 + 2x), we can use the FOIL method, which stands for First, Outer, Inner, Last. This method involves multiplying each term in the first factor by each term in the second factor and then combining like terms.
Using the FOIL method, we get:
(4 - 2x)(4 + 2x) = 4 × 4 + 4 × 2x - 2x × 4 - 2x × 2x
Simplifying the expression, we get:
16 + 8x - 8x - 4x^2
The two middle terms cancel each other out, leaving us with:
16 - 4x^2
We can also check our answer by factoring the simplified expression back to the original expression. If we factor 16 - 4x^2, we get:
16 - 4x^2 = 4(4 - x^2)
We can then use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b), to factor further:
4(4 - x^2) = 4(2 + x)(2 - x)
This gives us back the original expression, (4 - 2x)(4 + 2x), confirming that 16 - 4x^2 is equivalent to (4 - 2x)(4 + 2x).
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I need help solving this question:
Answers
Answer:
The answer is letter D.
Step-by-step explanation:
Ye
Answer:
The answer is C
x -10 < -20
x < -20 + 10
x< -10
The sign won't change to the other side because the variable we were asked to find is in the positive form.
The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answers
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
source: trust me bro
Nine percent of men are color blind. Researchers need at least 60 men with this trait, so they randomly select 700 men. Estimate the probability that at least 60 color-blind men are in the sample. Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability. Round your answer to four decimal places. Provide your answer below:
Answers
The estimated probability is 0.9537 (rounded to four decimal places).Hence, the answer is 0.9537.
Question: Nine percent of men are color blind. Researchers need at least 60 men with this trait, so they randomly select 700 men. Estimate the probability that at least 60 color-blind men are in the sample. Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability. Round your answer to four decimal places. Provide your answer below:
Solution:
Let the probability of the man having the trait of color blindness be p. Then, p = 0.09, and the sample size is n = 700.Mean and Variance of Binomial Distribution are:μ = np and σ² = np(1 − p)Here, p = 0.09, n = 700μ = np = 700(0.09) = 63Andσ² = np(1-p) = 700(0.09)(0.91) = 5.679Now we need to find the probability that at least 60 color-blind men are in the sample.i.e., P(X≥60)By using the Central Limit Theorem, we can approximate this binomial distribution as a normal distribution with mean μ = 63 and variance σ² = 5.679.P(X≥60) can be calculated using the following formula:P(Z≥((60-63)/√(5.679))) = P(Z≥(-1.684))Now we need to look at the z-table or use the calculator to find the value of P(Z≥(-1.684))P(Z≥(-1.684)) = 0.9537 (rounded to four decimal places)Therefore, the estimated probability is 0.9537 (rounded to four decimal places).Hence, the answer is 0.9537.
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Help me solve it I need to show my work please help
Answers
Step-by-step explanation:
5x - 30 = 3x
2x = 30
x = 15
that's the answer
An equation is given.
x² + 9 = 6x
What is one solution to the equation?
x=
Answers
Step-by-step explanation:
x²-6x+9=0
using the almighty formula where a=1 , b=-6 , c=9
In Exercise 5.12 , we were given the following joint probability density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide: f(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhere
Are Y1 and Y2 independent?
Answers
The conclude that the Y1 and Y2 are not independent.
The joint probability density function for the random variables Y1 and Y2 for a mixture of insecticide isf(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhereTo verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Therefore, we need to find the marginal density functions of Y1 and Y2.Probability Density Function:We know that for a given joint probability density function, the probability density function of Y1 is given by integrating over all possible values of Y2, and vice versa.Mathematically,P(Y1)=∫0∫1f(y1,y2)dy2... (1)P(Y2)=∫0∫1f(y1,y2)dy1... (2)Using equation (1) to calculate P(Y1), we get, P(Y1)=∫0∫1f(y1,y2)dy2=∫0∫1(2)dy2=2... (3)Similarly, we can use equation (2) to calculate P(Y2) as follows:P(Y2)=∫0∫1f(y1,y2)dy1=∫0∫1(2)dy1=2... (4)Product of marginal density functions:Now we can find the product of marginal density functions as follows:P(Y1)P(Y2)=2×2=4... (5)Thus, to verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Since 2 ≠ 4, Y1 and Y2 are not independent. Hence, we can conclude that the Y1 and Y2 are not independent.
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Select the two correct answers.
Which statements correctly describe the equation shown?
y = 4 × 18
a. the value of y is more than 18.
b. The value of y is 4 times as many as 18.
c.The value of y is 4 fewer than 18.
d.The value of y is 4 times as much as 18.
e.The value of y is 18 more than 4.
f. The value of y is 18 fewer than 4.
Answers
Statement d is also correct because it means the same thing as statement b, just using different phrasing.
What is an equation?It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equal sign (=). The equation represents a relationship between the expressions on both sides, indicating that they have the same value.
According to question:The two correct statements that describe the equation y = 4 × 18 are:
b. The value of y is 4 times as many as 18.
d. The value of y is 4 times as much as 18.
Statement b is correct because the equation y = 4 × 18 means that y is equal to 4 times the value of 18, or y = 4 × 18 = 72.
Statement d is also correct because it means the same thing as statement b, just using different phrasing. "As much as" and "many as" are interchangeable in this context, and both mean "multiplied by."
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state the null hypothesis and alternative hypothesis, in notation, for the individual t-test for testing the slope coefficient associated with?
Answers
The null hypothesis and alternative hypothesis in the notation for the individual t-test for testing the slope coefficient associated with a simple linear regression are given below:
Null hypothesis: H₀: β₁ = 0
Alternative hypothesis: Hₐ : β₁ ≠ 0
The hypothesis test is used to determine whether or not there is sufficient evidence to support the alternative hypothesis that the slope of the regression line is not equal to zero. The null hypothesis is that the slope of the regression line is equal to zero.
Therefore, we will use the individual t-test for the slope coefficient to test the hypothesis regarding the slope of the regression line. The formula for the t-test for the slope coefficient is given below:
t = (b₁– β₁) / SEb₁
Where b₁ is the sample slope coefficient β₁ is the hypothesized value of the slope coefficient (i.e., 0) SEb₁ is the standard error of the slope coefficient.
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Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.06 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.
(a) For first-time college students, what is the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places)?
(b) For transfer students, what is the ratio in favor of having graduated in the top 25 percent of their high school class?
Odds and Probability:
Odds in favor of an event is expressed as a ratio:
O
(
f
)
=
favorable cases
:
unfavourable cases
Similarly odds against are expressed as:
O
(
a
)
=
unfavorable cases
:
favourable cases
.
Odds and probability are closely related, as the probability in favor of an even is computed as:
P
=
favorable cases
favorable cases+unfavorable cases
Answers
The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.
(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
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Laura invierte en un pagaré $12,000. 00 a 7 días cuál es la ganancia en pesos?
Answers
As per the promissory note record, the profit in pesos is 0.098%
To do this, we'll need to use a number line to help us understand the relationship between time and the interest rate.
Let's say, that the interest rate on Laura's promissory note is 5% per year. We can represent this on a number line by dividing the line into 365 equal segments, one for each day of the year.
Each segment would represent 1/365th of the total interest rate, or approximately 0.014% (5%/365).
Now, we can mark off the first 7 segments on the number line to represent the 7 days that Laura is holding the investment. The total interest she'd earn over those 7 days would be equal to the sum of the values of those 7 segments.
In this case, that would be 7 x 0.014%, or approximately 0.098%.
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Complete Question:
Laura invests $12,000 in a promissory note. 00 to 7 days what is the profit in pesos?
The coordinates of the endpoints of PQ are P( – 12,7) and Q( – 4, – 9). Point R is on PQ and divides it such that PR:QR is 3:5
Answers
The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.
Using the distance formula, we have:
d(P,Q) = √((x2-x1)² + (y2-y1)²)
= √((-4-(-12))² + (-9-7)²)
= √(8² + (-16)²)
= √(320)
= 8 √(5)
Since PR:QR is 3:5, we can set up the following equation:
d(P,R)/d(R,Q) = 3/5
Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.
Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)
Using the distance formula again, we can find the distance between P and R:
d(P,R) = (3/8) d(P,Q)
= (3/8) (8 √(5))
= 3 √(5)
Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:
d(R,Q) = (5/3) d(P,R)
= (5/3) (3 √(5))
= 5 √(5)
Finally, we can use the midpoint formula to find the coordinates of R:
x = (-12 + (3/8) (8))/2 = -8
y = (7 + (-1))/2 = 3
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Complete Question:
The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?
4. (5pts each) Given f(x) = 6x² +1and g(x) = 11x +7 determine the following:
a (fog)(x)\
b. (fog)(-3)
=6XTI
Answers
Answer:
(fog)(x) = 726x^2 + 924x + 295, and (fog)(-3) = 6,817.
in which of the following numbers is the value of the 5 digit 10 times it value in the number 4,597
Answers
According to the question the value of the 5 digit in 4,597 is 9.
What is digit?Digit is a numerical symbol used to represent numbers in the decimal system. It is a single symbol used to represent a number ranging from 0 to 9. Digits are used to represent numbers in all forms of mathematical calculations and equations. The most common digits used in calculations are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit has an associated numerical value, which can be used to create larger numbers or to perform complex mathematical operations.
The answer is D) 9. The value of the 5 digit in 4,597 is 5. To find the 10 times its value, you must multiply 5 by 10, which equals 50. Therefore, the value of the 5 digit in 4,597 is 9.
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I NEED HELP BADLY PLEASE HELP
Answers
Answer: 0.11
Step-by-step explanation:
5/45=0.11
square root both sides
x=4 (plus or minus)
the area of a square is base x height, for a square it’s just side squared
if the area is 225, the side would be the square root of 225 and the units would be in instead of in^2
there aren’t any options so i’m not sure what it’s looking for but this is my best guess:
11.9860 is greater than the square root of 121.
square root of 121 is 11
irrational numbers would be the ones with the root. the rational numbers would be 0 and -1/16.
5/45 is 0.1111111… so it would be 0.1 with the line over the 1 to indicate that it’s a recurring decimal
Katie's car averages 32 miles per hour. She has marked her distance traveled after 12, 13, and 14 hours. List the elements in the range of the function that would be used to determine how far Katie has traveled at each mark. Separate each elements from least to element with a comma and write the
greatest.
Pls hurry
Answers
So, the distance traveled after 12 hours is 32 × 12 = 384 miles.
The distance traveled after 13 hours is 32 × 13 = 416 miles.
The distance traveled after 14 hours is 32 × 14 = 448 miles.
Therefore, the range of the function that would be used to determine how far Katie has traveled at each mark is:
384, 416, 448 (from least to greatest).
To determine the distance traveled by Katie at different marks, we can use the formula Distance = Rate × Time.
Explanation:To determine how far Katie has traveled at each mark, we can use the formula:
Distance = Rate × Time
So, the elements in the range of the function that would be used to determine how far Katie has traveled at each mark are 384 miles, 416 miles, and 448 miles.
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At the end of the reaction, Marco finds that the mass of the contents of the
beaker is 247 g. He repeats the experiment and gets the same result.
a Has he made a mistake?
Suggest why Marco got this result. how the
b
Answers
Answer: To determine if Marco has made a mistake, we would need to know the expected mass of the contents of the beaker before the reaction took place. If the expected mass was 247 g or close to it, then Marco may not have made a mistake.
However, if the expected mass was significantly different from 247 g, then it is possible that Marco made a mistake in his experiment. It could be a measurement error, a calculation error, or a procedural error.
There are several reasons why Marco may have obtained a mass of 247 g at the end of the reaction. One possibility is that the reaction produced a product that was relatively volatile, and some of it was lost during the experiment. Another possibility is that Marco did not completely dry the product before weighing it, which could result in a higher measured mass due to the presence of residual moisture.
To determine the exact reason why Marco obtained a mass of 247 g, further investigation and experimentation would be needed.
Step-by-step explanation:
Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs:
173 191 182 190 172 147 146 139 175 136 179 153 107 195 135 140 138 Fill in the blanks as the data for the five-number summary:
Min = [min] Q1 = [Q1] M = [Median] Q3 = [Q3] Max = [Max]
Answers
The five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.
How to find the minimum, maximum?In statistics, the five-number summary is a set of descriptive statistics that provide a summary of the distribution of a dataset. The five-number summary consists of the minimum value, the first quartile (Q1), the median (M), the third quartile (Q3), and the maximum value.
To find the five-number summary for the given data on the number of calories in a hot dog for each of 17 brands of meat hot dogs, we need to order the data from smallest to largest.
107 135 136 138 139 146 147 153 172 173 175 179 182 190 191 195
The minimum value is the smallest value in the dataset, which is 107.
The first quartile (Q1) is the value that is greater than or equal to 25% of the data and less than or equal to 75% of the data. To find Q1, we take the median of the lower half of the data:
Q1 = median(107, 135, 136, 138, 139, 146, 147, 153) = 138
The median (M) is the value that is in the middle of the dataset when the data is ordered from smallest to largest. For the given data, there are 17 values, so the median is the 9th value:
M = median(107, 135, 136, 138, 139, 146, 147, 153, 172, 173, 175, 179, 182, 190, 191, 195) = 175
The third quartile (Q3) is the value that is greater than or equal to 75% of the data and less than or equal to 25% of the data. To find Q3, we take the median of the upper half of the data:
Q3 = median(172, 173, 175, 179, 182, 190, 191, 195) = 190
The maximum value is the largest value in the dataset, which is 195.
Therefore, the five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.
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1 0 6
0 1 1
0 0 0
Find the solution(s) to the system, if it exists. State the solution as a point (be sure to use parentheses), use parameter(s) s and t if needed. If the system is inconsistent, then state no solution.
Answers
The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
To solve the system of equations:
1x + 0y + 60z = 1
1x + 10y + 0z = 0
0x + 0y + 0z = 0
The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:
From the first equation, we get x = 1 - 60z
From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z
Therefore, the solution to the system can be written as a point in terms of z as:
(x, y, z) = (1 - 60z, -10 + 600z, z)
Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:
(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.
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