Answer:
[tex]1 \frac{1}{6}[/tex] or 6/5
Step-by-step explanation:
72/60
= 6/5
= 1 1/5
= 1.2 (in decimal)
Answer:
6/5
Step-by-step explanation:
Martha has a ribbon that is 1 3/4 meters long. She cuts the ribbon into 3 equal-sized pieces. She uses 1 of the pieces to make gift bows. Each bow uses 7/48 of a meter of ribbon. How many gift bows does Martha make?
Answer:
4 gifts
Step-by-step explanation:
We have in total have a ribbon that measures 1.75 meters, and divide that into three equal pieces, therefore:
1.75 / 3 = 0.5834
Now, we are told that we must calculate how many bows he can make, knowing that each bow is 7/48, therefore:
0.5834 / (7/48) = 4
Which means that you can make 4 gifts since you can make 4 bows in total
An angle of 800 terminates in which quadrant?
I
II
III
IV
Answer:
This angle lies in the I quadrant.
Step-by-step explanation:
The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth.
When the angle is more than 360º we can divide the angle by 360º and cut off the whole number part.
If we divide 800º by 360º, the integer part would be 2 and the remaining is 80º. Now we should find the quadrant for this angle.
[tex]\frac{800}{360}=2\frac{80}{360}[/tex]
When the angle is between 0º and 90º, the angle is a first quadrant angle. Since 80º is between 0º and 90º, it is a first quadrant angle.
Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable.
a. The number of light bulbs that burn out in the next year in a room with 19 bulbs
b. The usual mode of transportation of people in City Upper A
c. The number of statistics students now doing their homework
d. The number of home runs in a baseball game
e. The exact time it takes to evaluate 67 plus 29
f. The height of a randomly selected person
Answer:
a. The number of light bulbs that burn out in the next year in a room with 19 bulbs: is a discrete random variable.
b. The usual mode of transportation of people in City Upper A: is not a random variable because its outcome isn't numerical.
c. The number of statistics students now doing their homework: is a discrete random variable.
d. The number of home runs in a baseball game: is a discrete random variable.
e. The exact time it takes to evaluate 67 plus 29: is a continuous random variable.
f. The height of a randomly selected person: is a continuous random variable.
Step-by-step explanation:
A random variable often used in statistics and probability, is a variable that has its possible values as numerical outcomes of a random experiment or phenomenon. It is usually denoted by a capital letter, such as X.
In statistics and probability, random variables are either continuous or discrete.
1. A continuous random variable is a variable that has its possible values as an infinite value, meaning it cannot be counted.
Example are the height of a randomly selected person, time it take to move from Texas to New York city, etc.
2. A discrete random variable is a variable that has its possible values as a finite value, meaning it can be counted.
Examples are the number of light bulbs that burn out in the next year in a room with 19 bulbs, the number of chicken in a district etc.
Answer:
A random variable in statistics can be loosely defined as a variable whose values depend on the outcome of a random phenomenon. These variables are variables that can be the results of an experiment not yet performed, or the results of an already performed experiment whose already existing result is uncertain.
A discrete random variable is finite and has a countable range of values.
A continuous random variable takes on numerical values in an interval of values and has no countable range of value.
a. The number of light bulbs that burn out in the next year in a room with 19 bulbs--- discrete random variable
b. The usual mode of transportation of people in City Upper A---
not a random variable
c. The number of statistics students now doing their homework --- discrete random variable
d. The number of home runs in a baseball game --- discrete random variable
e. The exact time it takes to evaluate 67 plus 29 --- continuous random variable
f. The height of a randomly selected person--- continuous random variable
What is the absolute value of 7 and -7?
Absolute value represents distance from zero on a number line.
-7 and 7 are the same distance away from zero, 7 units.
To visualize this, take a look at the image I have made below.
Answer:
both are 7
Step-by-step explanation:
absolute value is always a positive number.
2. What is the sum of 4 tens and 6 tens?
Answer:
100
Step-by-step explanation:
4 tens + 6 tens = 10 tens = 10*10 = 100
(1 point) A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 25 times, and the man is asked to predict the outcome in advance. He gets 18 out of 25 correct. What is the probability that he would have done at least this well if he had no ESP
Answer:
2.16% probability that he would have done at least this well if he had no ESP
Step-by-step explanation:
For each coin toss, there are only two possible outcomes. Either he predicts the correct outcome, or he does not. The tosses are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Fair coin:
Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]
Coin is flipped 25 times
So [tex]n = 25[/tex]
What is the probability that he would have done at least this well if he had no ESP?
[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 18) = C_{25,18}.(0.5)^{18}.(0.5)^{7} = 0.0143[/tex]
[tex]P(X = 19) = C_{25,19}.(0.5)^{19}.(0.5)^{6} = 0.0053[/tex]
[tex]P(X = 20) = C_{25,20}.(0.5)^{20}.(0.5)^{5} = 0.0016[/tex]
[tex]P(X = 21) = C_{25,21}.(0.5)^{21}.(0.5)^{4} = 0.0004[/tex]
[tex]P(X = 22) = C_{25,22}.(0.5)^{22}.(0.5)^{3} = 0.0001[/tex]
The others(23, 24 and 25) are close to 0.
[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) = 0.0143 + 0.0053 + 0.0016 + 0.0004 = 0.0216[/tex]
2.16% probability that he would have done at least this well if he had no ESP
What is the scale factor of a triangle with a vertex of A (-6,4) that has been dilated with the center of dilation at the origin so the vertex of its image is a' (-24,16)?
Answer:
4
Step-by-step explanation:
When the dilation is about the origin, the scale factor is the ratio of the coordinates of the image to the original.
A'/A = (-24/-6, 16/4) = (4, 4) . . . . scale factors are both 4 for x any y
The dilation scale factor is 4.
The vector wequalsaiplusbj is perpendicular to the line axplusbyequalsc and parallel to the line bxminusayequalsc. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below.
a. x + √3y = 1
b. (1 - √3)x + (1 + √3)y = 8
Answer:
[tex]\theta=45^{\circ}[/tex]
Step-by-step explanation:
We are given that the equation of lines
[tex]x+\sqrt 3y=1[/tex]
[tex](1-\sqrt 3)x+(1+\sqrt 3)y=8[/tex]
According to question
The vector perpendicular to the lines is given by
[tex]i+\sqrt 3j[/tex] and [tex](1-\sqrt 3)i+(1+\sqrt 3)j[/tex]
Therefore, the angle between two vectors is given by
[tex]cos\theta=\frac{a_1a_2+b_1b_2}{\sqrt{a^2_1+b^2_1}\sqrt{a^2_2+b^2_2}}[/tex]
Using the formula
[tex]cos\theta=\frac{1(1-\sqrt 3)+\sqrt 3(1+\sqrt 3)}{2\times 2\sqrt 2}[/tex]
[tex]cos\theta=\frac{1-\sqrt 3+\sqrt 3+3}{4\sqrt 2}=\frac{1}{\sqrt 2}[/tex]
[tex]cos\theta=cos 45^{\circ}[/tex]
[tex]\theta=45^{\circ}[/tex]
Hence, the acute angle between the lines is given by
[tex]\theta=45^{\circ}[/tex]
simplify : 7w - 8( -9 - 3w)
Answer:
Step-by-step explanation:
7w + 72 + 24w
31w + 72
Help help , please help!! Giving brainliest if correct . The x-values in the table for f(x) were multiplied by -1 to create the table for g(x) What is the relationship between the graphs of the two functions? A. They are reflections of each other across the y-axis B. They are reflections of each other across the x-axis C. The graphs are not related D. They are reflections of each other over the line x = y
Answer:
A
Step-by-step explanation:
The two graphs are each other reflected over the y axis since the x coordinate is reflected
a student in greece discovers a pottery bowl that contains 29% of its original amount of C-14
Answer:
The age of the pottery bowl is 12,378.7 years
Step-by-step explanation:
The amount of C-14 after t yeas is given by the following equation:
[tex]N(t) = N(0)e^{-kt}[/tex]
In which N(0) is the initial amount and k is the decay rate.
In this question, we have that:
[tex]k = 0.0001[/tex]
So
[tex]N(t) = N(0)e^{-0.0001t}[/tex]
Age of the pottery bowl:
29% of its original amount of C-14. So we have to find t for which N(t) = 0.29N(0). So
[tex]N(t) = N(0)e^{-0.0001t}[/tex]
[tex]0.29N(0) = N(0)e^{-0.0001t}[/tex]
[tex]e^{-0.0001t} = 0.29[/tex]
[tex]\ln{e^{-0.0001t}} = \ln{0.29}[/tex]
[tex]-0.0001t = \ln{0.29}[/tex]
[tex]t = -\frac{\ln{0.29}}{0.0001}[/tex]
[tex]t = 12378.7[/tex]
The age of the pottery bowl is 12,378.7 years
A cognitive psychologist would like to evaluate the claim that the omega-3 fatty acids can help improve memory in normal adult humans. One group of participants is given a large dose of fish extract containing the Omega-3 (500 mg), and a second group is given a placebo containing no Omega-3 (0 mg). The researcher asks each participant to read the front page of a local newspaper thoroughly every morning and to take their prescribed dosage (of either Omega-3 or placebo) immediately afterwards. The researcher gives each participant a memory test at the end of two weeks and records how many news items each participant remembers from the past three weeks of news. Answer the following:
A) What names would you give the independent and dependent variables;
B) Is the dependent variable discrete or continuous?
C) What scale of measurement (nominal, ordinal, interval or ratio; and continuous or discrete) is used to measure the independent variable?
D) What research method is being used (experimental or observational)? Explain why you conclude that the research method is one or the other.
Answer:
(a)
Independent Variable- Dosage of Omega-3 Fatty AcidsDependent Variable - Number of news item remembered(b)Discrete
(c)Ratio Scale and Discrete Variable
(d) Experimental Method
Step-by-step explanation:
The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.
(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).
The memory test involves measuring the number of items each participant remembers from the past three weeks of news.
Therefore:
Independent Variable- Dosage of Omega-3Dependent Variable - Number of news item remembered(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.
(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.
Since the dosage is given in multiples of 50mg, it is a discrete variable.
(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.
What is the measure of angle D?
Enter your answer as a decimal, round only your final answer to the nearest hundredth.
Answer: Angle D= 0.51 radians or 29.05°
Step-by-step explanation:
For this problem, we can use our trigonometry to find the measure of angle D.
Since this is a right triangle, we know we can use sine, cosine, and tangent. We are focusing on angle D, so we would see which trigonometric function best fits angle D. Looking at where 25 ft and 45 ft are labeled, we can use tangent. Tangent of opposite/adjacent. Now that we know this, we can set up an equation. Let's use θ in place for angle D.
tan(θ)=25/45
tan(θ)=5/9
Since we want to find θ, we would do inverse tangent.
θ= [tex]tan^-^1(\frac{5}{9} )[/tex]
θ=0.507
θ=0.51
This answer is in radians. In degrees, it is 29.05°.
Select the number line model that matches the expression |8 - 1|
Answer:
Option B is correct
Step-by-step explanation:
Original expression is |8 - 1| = 7 = distance between number 1 and number 8
=> Option B is correct
Hope this helps!
The number line model that matches the expression |8 - 1| which is correct option(B)
What is the graph?The graph can be defined as a pictorial representation or a diagram that represents data or values.
What is the expression?The expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given the expression as |8 - 1|,
The value of the expression would give us 7. Meaning that the distance between coordinate 8 and 1 is 7 units.
The graphs given models the expression, |8 - 1|.
Option A, would match |-8 -1| = 5 units
Option B, would match |8 - 1| = 7 units.
Therefore, the answer is option (B).
Learn more about graph here :
https://brainly.com/question/16608196
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Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer? A: x^2 + 8x – 308 = 0 B: x^2 – 8x + 308 = 0 C: x^2 + 8x + 308 = 0 D: x^2 − 8x − 308 = 0
Answer:
A
Step-by-step explanation:
The smaller negative integer is x.
The larger one is x+8, since they are 8 units apart.
The equation would be:
x*(x+8)=308
Let's simplify it by distributing.
x^2+8x=308
Subtract 308 from both sides.
x^2+8x-308=0
Therefore, the answer would be A.
Please answer this question !! 20 points and brainliest !!
Answer:
yes, they are parallel; the general form equation differs only in the constant.
Step-by-step explanation:
Subtract y from the first equation and multiply by 2.
y -y = 1/2x -y +3
0 = x -2y +6
x -2y +6 = 0 . . . . . put in general form
Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.
This means the lines are parallel.
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat A at time t hours is given by a function A(t) and the amount in Vat B is given by B(t). The two vats contain the same amount of water at t=0. You have a formula for the rate of flow for Vat A and the amount in Vat B: Vat A rate of flow: A(t)-3t2+24t-21 Vat B amount: B(t)-2t2+16t+40
(a) Find all times at which the graph of A(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum of A(t) smaller t= 1 gives a local minimum larger t= 7 l maximum
(b) Let D(t)-B(t)-A(t). Determine all times at which D(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum. (Round your times to two digits after the decimal.) xgives a Select x gives a Select smaller t- larger t=
(c) Use the fact trruntain the same amount of water at ta0 to find the formula for A(), the amount in Vat A at time t Enter a number
(d) At what time is the water level in Vat A rising most rapidly? t- hours
(e) what is the highest water level in Vat A during the interval from t=0 to t=10 hours? gallons
(f) What is the highest rate at which water flows into Vat B during the interval from t-0 to t-10 hours? gallons per hour
(g) How much water flows into VatA during the interval from t=1 to t-8 hours? gallons
Note: The first file attached contains the clear and complete question
Answer:
a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7
A(t) has a local maximum at t=7
A(t) has a local minimum at t=1
b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74
D(t) has a local maximum at t=1.59
D(t) has a local minimum at t=7.74
c) A(t) = (-t^3) + 8(t^2) -21t + 40
d) The water level in vat A is rising most rapidly at t = 4 hrs
e) 138 gallons
f) 18 gallons per hour
g) 98 gallons
Step-by-step explanation:
For clarity and easiness of expression, the calculations are handwritten and attached as files below.
Each step is neatly expressed and solutions to each part of the question are clearly written
6z+10=-2
pls answer'
i willmarke brainlest
Answer:
Step-by-step explanation: 6z=-2-10
6z= -12
z=-12/6
then z= -2
One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife's score 2 2 3 3 4 2 1 1 2 4 Husband's score 2 1 2 3 2 1 1 1 2 4 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)(1) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)(2) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)(3) What is the p-value? (Round your answer to four decimal places.)(4) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =
Answer;
1) The t-distribution is most suitable for this problem.
2) Test statistic = 2.356
3) p-value = 0.0214
4) Alpha = 5% = 0.05
5) The p-value is greater than the significance level at which the test was performed, meaning that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.
Step-by-step Explanation:
Wife's score 2 2 3 3 4 2 1 1 2 4
Husband's score 2 1 2 3 2 1 1 1 2 4
To conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife, we first take the difference in the respomses of wives and husbands
x = (wife's score) - (husband's score)
Wife's score 2 2 3 3 4 2 1 1 2 4
Husband's score 2 1 2 3 2 1 1 1 2 4
Difference | 0 | 1 | 1 | 0 | 2 | 1 | 0 | 0 | 0 | 0
To use the hypothesis test method, we have to make sure that the distribution is a random sample of the population and it is normally distributed.
The question already cleared these two for us that this sample size is randomly selected from the population and each variable is independent from the other.
The question also already explained that the distribution is assumed to be normally distributed.
1) The distribution to use for this test is the t-distribution. This is because the sample size isn't very large and we have no information about the population mean and standard deviation.
For any hypothesis testing, we must first define the null and alternative hypothesis
Since we want to investigate whether the husbands are happier, that the mean difference is negative, that is less than 0,
The null hypothesis, which normally counters the claim to be investigated, would be that there isnt evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness isn't less than 0, that it is equal to or greater than 0.
And the alternative hypothesis, which usually confirms the claim to be tested, is that there is significant evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness is less than 0.
Mathematically, if μ is the mean difference in happiness of wives and husbands,
The null hypothesis is represented as
H₀: μ ≥ 0
The alternative hypothesis is represented as
Hₐ: μ < 0
2) To obtain the test statistic, we need the mean and standard deviation first.
Mean = (sum of variables)/(number of variables) = (5/10) = 0.5
Standard deviation = σ = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = 6(0 - 0.5)² + 3(1 - 0.5)² + (2 - 0.5)² = 1.5 + 0.75 + 2.25 = 4.5
σ = √(4.5/10) = 0.671
we compute the t-test statistic
t = (x - μ)/σₓ
x = sample mean difference = 0.50
μ = 0
σₓ = standard error of the sample mean = (σ/√n)
where n = Sample size = 10,
σ = Sample standard deviation = 0.671
σₓ = (0.671/√10) = 0.2122
t = (0.50 - 0) ÷ 0.2122
t = 2.356
3) checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 10 - 1 = 9
Significance level = 5% = 0.05
The hypothesis test uses a one-tailed condition because we're testing only in one direction.
p-value (for t = 2.356, at 0.05 significance level, df = 9, with a one tailed condition) = 0.021441 = 0.0214
4) Alpha = significance level = 5% = 0.05
5) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.0214
0.0214 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.
Hope this Helps!!
Suppose that it costs $200 per day to search for chanterelle mushrooms at Pt. Reyes National Seashore. On an average day, the total weight of mushrooms M found at Pt. Reyes is M = 100x-x^2 pounds ,where x is the number of people mushroom hunting on that day. Chanterelles can be sold for $60 per pound. How many more people will go mushroom hunting than is socially optimal?
Answer:
For an overall profit, we need at least 97 people to go mushroom hunting.
Any number of people that is more than the socially optimal number should go mushroom hunting on any given day.
Step-by-step explanation:
The socially optimal number of people that will go mushroom hunting is the number where amount spent to go mushroom hunting equally balances the amount obtained by selling the mushrooms obtained.
If x people go mushroom hunting in a day, the total cost of hunting for that day = 200x
The amount of mushroom obtained is given as
M = (100x - x²) in pounds
The selling price of 1 pound = $60
The cost of M pounds = 60M = 60(100x - x²)
= (6000x - 60x²)
At socially optimal number,
200x = 6000x - 60x²
60x² - 6000x + 200x = 0
60x² - 5800x = 0
x(60x - 5800)
x = 0 or (60x - 5800) = 0
x = 0 or x = (5800/60) = 96.67
Socially optimal number of people = 0 or 96.67
For realistic purposes, we take the socially optimal number of people that went mushroom hunting as 96.67
Any number above this number will result in an overall profit, and any number below it results in an overall loss.
So, for an overall profit, we need at least 97 people to go mushroom hunting.
Hope this Helps!!
Answer:
48 people
Step-by-step explanation:
When allocating resources to a particular task it is important to assign optimal units of resources.
In this scenario if the people hunting mushrooms are too many they will not make profit. But an optimal number will guarantee everyone makes positive profit.
Optimal = (M÷x)Px - 200= 0
Optimal= {(100x -x^2) ÷ x} * 60 = 200
Optimal = 6000 - 60x = 200
x= 96.666~ 97 people
However to maximise profit MTB = MTC
Socially Optimal quantity = 60(100x - x^2) -200
∂(Socially Optimal amount) ÷ ∂ x= 6000 - 120x - 200
x = 48.33~ 48 people
So 48 more people go mushroom hunting than is socially optimal
Write an equation that represents the line. Use exact numbers.
Answer:
y=3x/4 +2Step-by-step explanation:
(0;2) and (4;5)
(x1;y1) ; (x2;y2)
y=mx+b
m=(y2-y1)/(x2-x1)
m=(5-2)/4-0)
m=3/4
y=mx+b=> 2=3/4 *0+b; => b=2
So, y=3x/4 +2
Please answer this math question ! WILL GIVE BRAINLIEST !!
Answer:
(2, -2)
Step-by-step explanation:
y = -2x + 2
y = 2x - 6
Solve by elimination (make sure they're in the same form)
2y = -4
y = -2
plug -2 into either equation for y and solve for x
-2 + 6 = 2x
4 = 2x
x = 2
the population of a country increased by 3%, 2.6%, and 1.8% in three successive years. what was the total percentage increase in the country's population over the three year period?
please tell me how u did it
Answer:
The total percentage increase in the country's population over the three year period is 7.6%.
Step-by-step explanation:
Let x be the original population of a country.
It is provided that the population increased by 3%, 2.6%, and 1.8% in three successive years.
Compute the population of the country after three years as follows:
[tex]\text{New Population}=\text{Origibal Population}\times I_{1}\%\times I_{2}\%\times I_{3}\%[/tex]
[tex]=x\times [1+\frac{3}{100}]\times [1+\frac{2.6}{100}]\times [1+\frac{1.8}{100}]\\\\=x\times 1.03\times 1.026\times 1.018\\\\=1.07580204\cdot x\\\\\approx 1.076\cdot x[/tex]
The new population after three years is 1.076 x.
Compute the total percentage increase in the country's population over the three year period as follows:
[tex]\text{Total Increase}\%=\frac{\text{New Population}\ -\ \text{Original Population}}{\text{Original Population}}\times 100[/tex]
[tex]=\frac{1.076x-x}{x}\times 100\\\\=0.076\times 100\\\\=7.6\%[/tex]
Thus, the total percentage increase in the country's population over the three year period is 7.6%.
r. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes. To determine the unit price for each item, his daughter sets up and solves the system of equations shown. 6p + 3n = 18 and 2n = p 6(2n) + 3n = 18 12n + 3n = 18 15n = 18; n = $1.20 Onions cost $1.20 per pound. Analyze the daughter’s solution. Which statements are true? Check all that apply. The equation 2n = p should be 2p = n. The equation 6p + 3n = 18 should be 6n + 3p = 18. The actual cost of the onions is $3.00 per pound. Potatoes cost $0.60 per pound. Potatoes cost $1.50 per pound. Potatoes cost $2.40 per pound.
Answer:
The equation 2n = p should be 2p = n. The actual cost of the onions is $3.00 per pound. Potatoes cost $1.50 per pound.Step-by-step explanation:
The wording "onions cost twice as much as potatoes" is understood to mean the cost per pound of onions (n) is equal to two times the cost per pound of potatoes (2p). Then the appropriate equation would be ...
2p = n
Then the solution is ...
6p +3(2p) = 18
12p = 18
p = 18/12 = 1.50
n = 2p = 2(1.50) = 3.00
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The equation should be 2p = n; onions cost $3.00 per pound; potatoes cost $1.50 per pound.
find the value of x (4x-5)
Step-by-step explanation:
use distributive property to multiply x by 4x-5
[tex]4x ^{2} - 5[/tex]
Answer:
BRAINLEST
Step-by-step explanation:
[tex]4 { \times }^{2} - 5x[/tex]
this is the answer
how to simplify 4e + 6f + 7e - f
Answer:
11e+5f
Step-by-step explanation:
Combine like terms:
4e+7e+6f-f
11e+5f
Answer:
11e +5f
Step-by-step explanation:
4e + 6f + 7e - f
Combine like terms
4e+7e +6f-f
11e +5f
Enter the number that belongs in the green box
Answer:
B =107
Step-by-step explanation:
<B = <D
We can find <D from the sum of the angles of a triangle
32+ D +41 = 180
73+ D = 180
D = 180-73
D =107
Therefore B =107
Which is the graph of F(x) =(2)^x
Answer:
Down below
Step-by-step explanation:
The equation [tex]F(x) =(2)^x[/tex] can also be written as [tex]y=2^x[/tex] , because F of x of f(x) is actually y
Suppose that the cost of a paving stone is $2.50, plus $0.15 for every 4 cubic inches of concrete.
How much would each paving stone cost?
Answer:
6 different sized paving stones,$16
Complete question:
What if the 360 cubic-inch paving stones are 4 inches thick and any whole number length and width are possible? How many different paving stones could be made? Suppose that the cost of having stone is $2.50, plus $0.15 for every 4 cubic inches of concrete how much would each paving stone cost?
Step-by-step explanation:
V= B x h
B= V / h=> 360 / 4
B= 90 sq inch
Considering the factors of 90: 1,2,3,5,6,9,10,15,18,30,45,90
Now, make table with base height and volume for each pair of factors. (see figure in the attachment)
We'll have 6 different sized paving stones.
As each stone has a vol of 360 inches³. Diving by 4 in order to find how many 4 inch³ per stone
Concrete=$0.15 x (360/4) => $0.15 x 90
Concrete= $13.5
The cost of the stone plus the concrete will be:
cost= $2.50 + concrete
cost= $2.50 + $13.5
cost=$16
There are 8 women and 10 men with a chance to be on a game show. The producer of the show is going to choose 10 of these people at random to be contestants. What is the probability that the producer chooses 3 women and 7 men? Round your answer to three decimal places.
10 TO 13 IS THE PROBLEM