Answer:
3.06×10^-6
Step-by-step explanation:
0.00000306 = 3.06×0.000001 = 3.06×10^-6
__
Your calculator or spreadsheet can display numbers in scientific notation.
A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are asked to code a standard function in both languages, and the time (in minutes) is recorded. The data follow:
Programmer Design Language 1 Design Language 2
1 17 18
2 15 14
3 21 20
4 13 11
5 18 22
6 24 21
7 15 10
8 14 13
9 21 19
10 23 24
11 13 15
12 18 20
(a) Is the assumption that the difference in coding time is normally distributed reasonable?
(b) Find a 95% confidence interval on the difference in mean coding times. Is there any indication that one design language is preferable?
(a) The assumption that the difference in coding time is normally distributed
isis not
reasonable.
(b) The 95% confidence interval is (
,
) Round your answers to 3 decimal places (e.g. 98.765).
There is no / is significant indication that one design language is preferable at a 5% significance level.
Answer:
Step-by-step explanation:
The histogram shown in the attached file show that the distribution of differences is approximately normal.
So, we can assume that the distribution is normal.
.
b)
The 95% confidence level for [tex]\mu _D=\mu_1-\mu_2[/tex] is found
[tex]\bar d \pm t_{0.025,11}\frac{S_D}{\sqrt{n} }[/tex]
[tex]=0.666667 \pm 2.201\frac{(2.964436)}{\sqrt{12} } \\\\0.666667 \pm 2.201(0.85576)\\\\=0.666667+ 1.883525474=2.5502\\\\=0.666667- 1.883525474=-1.2169\\\\=(-1.2169,2.5502)[/tex]
since 0 is in the confidence interval. we do not reject the null hypothesis.
No, there is no indication of one design language is available.
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
The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.
a. Set up a vector equation for this problem. Include a statement of what the variables in your equation represent.
b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared.
$$\begin{matrix}
\text{Nutrient} & \text{General Mills Cherrios} & \text{Quaker 100% Natura Cereal}\
\text{Calories} & \text{110} & \text{130}\
\text{Protein (g)} & \text{4} & \text{3}\
\text{Carbhydrate (g)} & \text{20} & \text{18}\
\text{Fat (g)} & \text{2} & \text{5}\
\end{matrix}$$
Answer:
(a)
[tex]\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]
(b)
[tex]\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right][/tex]
1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal will give the desired mixture.
Step-by-step explanation:
Given the mixture of cereals below:
[tex]\left|\begin{array}{c|c|c}&$General Mills &$Quaker \\$Nutrient&$Cherrios &100\% $Natural Cereal\\----&---&---\\$Calories&110&130\\$Protein (g)&4&3\\$Carbhydrate (g)&20&18\\$Fat (g)&2&5\end{array}\right|[/tex]
Suppose a mixture of these two portions of cereals is to be prepared that contain exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.
(a)Let x be the number of servings of Cheerios
Let y be the number of servings of Natural Cereal
From the table above, we have
[tex]110x+130y=295\\4x+3y=9\\20x+18y=48\\2x+5y=8[/tex]
Then a vector equation for this problem is:
[tex]\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]
(b) Next, we obtain an equivalent matrix equation of the data
[tex]\left[\begin{array}{ccc}110&130\\4&3\\20&18\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]
This is of the form AX=B. To solve for X we, therefore have an equivalence matrix:
[tex]\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right][/tex]
Next, we row reduce the matrix using a calculator to obtain the matrix:
[tex]\left[\begin{array}{ccc}1&0&1.5\\0&1&1\\0&0&0\\0&0&0\end{array}\right][/tex]
Therefore:
1x+0=1.5
0x+y=1
x=1.5 and y=1
To get the required mixture, we use 1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal.
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
 any help would be great
Answer:
k = P - m - n
Step-by-step explanation:
The question is asking you to rearrange the equation so that k is alone on one side.
P = k + m + n
P - k = (k + m + n) - k
P - k = m + n
(P - k) - P = m + n - P
-k = m + n - P
-1(-k) = -1 (m + n - P)
k = -m - n + P
The equation is completely simplified so this is your answer.
Students are given a spinner with 5 equal sectors numbered 1-5. They are instructed to spin 50 times and record the number the arrow lands on. If there are 5 groups of students spinning, which of the following is most likely the total number of times the spinner lands in the 3 sector?
Answer: Around 50 times.
Step-by-step explanation:
If the spinner is fair, then each number should have the same probability, that is P = 1/5 = 0.20 for each of the numbers.
Now, we know that we have 5 groups, and each group spins 50 times (so we have a total of 5*50 = 250 spins)
Then we can expect to see the number 3 around:
0.20*150 = 50
4(x-2+y)=
?????????????
[tex]\text{Solve:}\\\\4(x-2+y)\\\\\text{Use the distributive property:}\\\\4x-8+4y\\\\\text{Since you can't simplify it any further, that'll be your answer}\\\\\boxed{4x-8+4y}[/tex]
Answer:
4x-8+4y
Explanation:
///
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 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
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
Diya spent 2/5 of her money on a dress and 1/2 of the reminder on a doll. She spent $8 more o the dress than the doll. How much money did she have left?
year 6 Mathematics
Answer:
$24
Step-by-step explanation:
2/5 — dress
3/5 — remainder
1/2 of remainder = 1/2 × 3/5 = 3/10 — doll
rewrite fraction spent on dress: 4/10
dress - doll = $8
4/10 - 3/10 = 1/10
1/10 = $8
fraction of money left = 10/10 - 4/10 - 3/10
= 3/10
amount of money left = $8 × 3
$24
A sample of size =n48 has sample mean x=54.6 and sample standard deviation =s9.2. Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Construct a 99.9% confidence interval for the population mean μ. Round the answers to one decimal place. A 99.9% confidence interval for the population mean is:____________ .
Answer:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
Step-by-step explanation:
Info given
[tex]\bar X=54.6[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=9.2 represent the sample standard deviation
n=48 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
The Confidence is 0.999 or 99.9%, and the significance is [tex]\alpha=0.001[/tex] and [tex]\alpha/2 =0.0005[/tex], and the critical value would be [tex]t_{\alpha/2}=3.51[/tex]
And replacing we got:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
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.
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
The weight of an organ in adult males has a bell-shaped distribution with a mean of 300grams and a standard deviation of 20 grams. Use the empirical rule to determine the following.
(a) About 95% of organs will be between what weights?
(b) What percentage of organs weighs between 280 grams and 320grams?
(c) What percentage of organs weighs less than 280 grams or more than 320 grams?
(d) What percentage of organs weighs between 240 grams and 340 grams?
Answer:
a) Within 260 grams and 340 grams.
b) 68%
c) 32%
d) 97.35%
Step-by-step explanation:
The empirical rule 68-95-99.7 for bell-shaped distributions tells us that:
Approximately 68% of the data is within 1 standard deviation from the mean.Approximately 95% of the data is within 2 standard deviation from the mean.Approximately 99.7% of the data is within 3 standard deviation from the mean.a) The data that covers 95% of the organs is within 2 standard deviations (z=±2).
Then we can calculate the bounds as:
[tex]X_1=\mu+z_1\cdot\sigma=300+-2\cdot 20=300+-40=260 \\\\X_2=\mu+z_2\cdot\sigma=300+2\cdot 20=300+40=340[/tex]
b) We have to calculate the number of deviations from the mean (z-score) we have for the values X=280 and X=320.
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{280-300}{20}=\dfrac{-20}{20}=-1\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{320-300}{20}=\dfrac{20}{20}=1\\\\\\[/tex]
As there are the bounds for one standard devaition, it is expected tht 68% of the data will be within 280 grams and 320 grams.
c) This interval is complementary from the interval in point b, so it is expected that (100-68)%=32% of the organs weighs less than 280 grams or more than 320 grams.
d) We apply the same as point b but with X=240 and X=340 as bounds.
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{240-300}{20}=\dfrac{-60}{20}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{340-300}{20}=\dfrac{40}{20}=2\\\\\\[/tex]
The lower bound is 3 deviations under the mean, so it is expected that (99.7/2)=49.85% of the data will be within this value and the mean.
The upper bound is 2 deviations above the mean, so it is expected that (95/2)=47.5% of the data will be within the mean and this value.
Then, within 240 grams and 340 grams will be (49.85+47.5)=97.35% of the organs.
What is the numerator for the simplified sum?
Answer:
The numerator would be [tex]4x+6[/tex]
Step-by-step explanation:
[tex]\frac{x}{x^{2}+3x+2 } +\frac{3}{x+1}[/tex]
= [tex]\frac{4x^{2}+10x+6 }{x^3+4x+5x+2}[/tex]
= [tex]\frac{2(2x+3)(x+1)}{(x+1)(x+1)(x+2)}[/tex]
= [tex]\frac{4x+6}{x^2+3x+2}[/tex]
the numerator is always the top number/value of a fraction thus it being [tex]4x+6[/tex]
brainliest pls
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
A cylindrical tank has a radius of 2 m and a height of 9 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)
Answer:
3,325,140 Joules
Step-by-step explanation:
Work done by the pump = Force applied to pump * distance covered by the water.
Since Force = mass * acceleration due to gravity
Force = (density of water * volume of the tank) * acceleration due to gravity
F =ρVg
Workdone = (ρVg )* d
Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m
[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]
Workdone by the pump = 1000 * 113.10 * 9.8 * 3
Workdone by the pump = 3,325,140Joules
Please help. I’ll mark you as brainliest if correct . I don’t understand this math problem. Thank you .
Answer:
That can be factored as
(x -1 (1/3) ) * ( x +3) * (x -4/5)
and the zeroes are located at:
x = 1.33333333... x = -3 and x = .8
Step-by-step explanation:
Answer:
[tex]\boxed{\sf \ \ \ f(x)=(x+3)(5x-4)(3x-4) \ \ \ }[/tex]
Step-by-step explanation:
We need to factorise the following function
[tex]f(x)=15 x^3+13 x^2-80 x+48[/tex]
-3 is a trivial solution, we can notice that f(-3)=0
so we can factorise by (x+3)
let s note a, b and c real and let s write
[tex]f(x)=15 x^3+13 x^2-80 x+48=(x+3)(ax^2+bx+c)[/tex]
[tex](x+3)(ax^2+bx+c) = ax^3+bx^2+cx+3ax^2+3bx+3c=ax^3+(b+3a)x^2+(3b+c)x+3c[/tex]
let s identify...
the terms in [tex]x^3[/tex]
15 = a
the terms in [tex]x^2[/tex]
13 = b + 3a
the terms in x
-80 = 3b+c
the constant terms
48 = 3c
so it comes, c=48/3=16, a = 15, b = 13-3*15=13-45=-32
so [tex]f(x)=(x+3)(15x^2-32x+16)[/tex]
[tex]\Delta=32^2-4*15*16=64[/tex]
so the roots of [tex](15x^2-32x+16)[/tex] are
[tex]\dfrac{32-8}{15*2}=\dfrac{24}{30}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]
and
[tex]\dfrac{32+8}{15*2}=\dfrac{40}{30}=\dfrac{20}{15}=\dfrac{4}{3}[/tex]
so [tex]f(x)=(x+3)(5x-4)(3x-4)[/tex]
the zeros are -3, 4/5, 4/3
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.
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
A box is filled with 6 red cards, 8 green cards and 4 blue cards what is the probability that the card is not green that is chosen
Answer:
10/18
=5/9
pls mark as brainliest
Answer:
5/9
Step-by-step explanation:
6 red cards, 8 green cards and 4 blue cards = 18 total cards
not green cards = 6 red+ 4 blue = 10 cards
P( not green) = number not green / total
= 10/18
=5/9
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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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.
Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?
1)Yes as the probability of six having the correct shape is not unusual
2)NO. as the probability of six having the correct shape is unusual
3)Yes as the probability of six having the correct shape is unusual
4) No. as the probability of six having the correct shape is not unusual
Solution:
If exactly 6 of the 10 have the right shape, it means that the probability of success for the sample is
6/10 = 0.6
Expressing the probability in terms if percentage, it becomes
0.6 × 100 = 60%
Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success for the population is 89.4%
Comparing both probabilities, the probability of only 6 having the right shape is unusual. Therefore, the correct option is
3)Yes as the probability of six having the correct shape is unusual
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%.
6z+10=-2
pls answer'
i willmarke brainlest
Answer:
Step-by-step explanation: 6z=-2-10
6z= -12
z=-12/6
then z= -2
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
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!!
(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