the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
given that
there are 36 independent problems
mean(μ) = 6minutes
standard deviation(σ) = 3 minutes
sample standard deviation = σ/[tex]\sqrt{n}[/tex]
= 3/[tex]\sqrt{36}[/tex]
=3/6
=0.5
the sample mean x of 36 questions answering time approximately follows a normal distribution with mean 6 minutes and sample standard deviation is 0.5 minutes
now we need to find the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
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Helpp Please i will give brainliest to first correct answers
The point of the coordinate plane is ( 0.5 , 1 )
what is coordinate plane ?
The definition of a coordinate plane is as follows: A coordinate plane, often referred to as a rectangular coordinate plane grid, is a two-dimensional plane made up of the Y-axis, a vertical line, and the X-axis, a horizontal line.
solution:
A( -3, -5) and B( 2, 7 ), m:n = 1:1
using section formula
P = [ { (mx2+nx1)/ (m+n) , { (my2+ny1)/ (m+n) }]
= [ 1(2) + 1(-3) / 2 , 1( 7 ) + 1(-5) / 2 ]
= ( 0.5 , 1 )
Hence the coordinate plane point is ( 0.5 , 1 )
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This prism has a right triangle for a base. What is the volume of the prism ?
Step-by-step explanation:
0.5×3×4= 6cm^2
6×8
=48cm^3
Let f(x) be a function defined for all positive real numbers satisfying the conditions f(x)>0 for all x>0 and f(x−y)=√f(xy)+1 for all x>y>0. Determine f(2009).
After evaluation, the resultant value of the function f(2009) is 1.9021.
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Any input for x results in a single output for y.
Considering that x is the input value, we would state that y is a function of x.
So, evaluate f(2009) as follows:
Given that f(x) is a function with all positive real numbers satisfying the requirement that f(x) > 0 and for all x > 0 and also:
[tex]\begin{aligned}&f(x-y)=\sqrt{f(x y)+1} \\&x > 0, y > 0 \\&\text { for, } x=1, \text { and } y=\frac{1}{2} \\&f\left(1-\frac{1}{2}\right)=\sqrt{f\left(1 \times \frac{1}{2}\right)+1} \\&f\left(\frac{1}{2}\right)^2=f\left(\frac{1}{2}\right)+1 \\&f\left(\frac{1}{2}\right)=\frac{1+\sqrt{5}}{2}\end{aligned}[/tex]
Now, consider: x = 2009 and y = 0
[tex]\begin{aligned}&f(2009-0)=\sqrt{f(2009 * 0)+1} \\&f(2009)=\sqrt{f(0)+1} \\&f(2009)=\sqrt{f\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}\right)+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{\sqrt{2}} * \frac{1}{\sqrt{2}}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{f\left(\frac{1}{2}\right)+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{1+\sqrt{5}}{2}+1}+1} \\&f(2009)=\sqrt{\sqrt{\frac{3+\sqrt{5}}{2}}+1} \\&f(2009)=\sqrt{\sqrt{5.2362}+1} \\&=\sqrt{3.6180} \\&=1.9021\end{aligned}[/tex]
Therefore, after evaluation, the resultant value of the function f(2009) is 1.9021.
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Lines KS, ME, and YE are shown.
Complete the table using the word bank to prove
Answer:
there's no picture
Find the values of the variables assuming the figures are parallelograms
Adjacent angles of a parallelogram are supplementary.
[tex]3x+10+8x+5=180 \\ \\ 11x+15=180 \\ \\ 11x=165 \\ \\ \boxed{x=15} \\ \\ \\ \\ 5y+3(15)+10=180 \\ \\ 5y+55=180 \\ \\ 5y=125 \\ \\ \boxed{y=21}[/tex]
What's the first step when solving the equation: -2(x + 5) - 4 = 5x?
Subtract 5x from both sides
Combine like terms on the left side
Distribute 2
Distribute -2
Answer:
i suggest using -2 to multiply the figures in the bracket as a first step
Step-by-step explanation:
then you'll have something like this
-2x - 10 - 4 = 5x
-2x - 14 = 5x
-14 = 5x + 2x
-14 = 7x
x = -14/7
x = -2. hope this helps
The cost of `20` cans of dog food at Store B is `\$18.40`.
Calculate the price for `11` cans of dog food.
Answer:
33.45 is the price of 11 dog food cans
The triangle depicted in the scale drawing has an actual area of 81 square units. What is the scale factor from the scale drawing to the actual triangle? (Note: Each square on the grid has a length of 1 unit.)
The scale factor from the scale drawing to the actual triangle is; 1/3
How to determine the Scale Factor?The area of a triangle is calculated using the formula;
A = ¹/₂bh
Where;
A is area.
b is base.
h is height.
The two sides of the rectangle are 6 units and 3 units. Use the measurements in the formula. "u" is for units.
Thus;
A = ¹/₂(6)(3)
A = 9 square units
The scale factor, represented by the variable "k", tells you how much a shape enlarged or reduced. If "k" is greater than 1, the shape enlarged. If "k" is greater than 0 and less than 1, the shape reduced
In this case, since the drawing is smaller than the actual triangle, the scale factor will be a fraction less than 1 and greater than 0.
The scale factor is used for side length. When it's used to find a side length, we use "k" multiplied by a side. Since the information we know is area, we find k² first, then isolate "k".
Divide the depicted triangle area by the actual area.
k² = 9 ÷ 81
k² = 1/9
√k² = √(1/9)
k = 1/3
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Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 30 mpgwith a standard deviation of 7 mpg. Thirty-one non-hybrid sedans get a mean of 20 mpg with a standard deviation of three mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test at the 5% level to evaluate the manufacturers claim.
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.)
State the null hypothesis
State the alternative hypothesis.
In words, state what your random variable Xhybrid − Xnon−hybrid represents.
State the distribution to use for the test.
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.)
What is the p-value?
what is the Alpha?
Explain how you determined which distribution to use.
99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.
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A coin sold for $271 in 1976 and was sold again in 1988 for $417. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V, = 271.
k=
(Round to the nearest thousandth.)
well, let's noticed, the original amount is $271 and 12 years later it turned to $417, so
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$417\\ P=\textit{initial amount}\dotfill &271\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0\\ t=years\dotfill &12\\ \end{cases}[/tex]
[tex]417=271(1 + \frac{r}{100})^{12}\implies \cfrac{417}{271}=\left( \cfrac{100+r}{100} \right)^{12} \implies \sqrt[12]{\cfrac{417}{271}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[12]{\cfrac{417}{271}}=100+r\implies 100\sqrt[12]{\cfrac{417}{271}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{3.657\approx r} \end{array}}[/tex]
Tell whether x and y are proportional.
Answer:
yes y/x = 5/2
Step-by-step explanation:
y/x = 5/2, 10/4=5/2, 15/6=5/2, 20/8=5/2
the proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y is . (round your answer to at least 2 decimal places.)
The proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y is 0.48
Given:
SSR = 1.9350
SST = 4.012
we are asked to find the proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y.
To find the sample proportion we need to divide.
SSR/SST
= 1.9350/4.012
= 0.48
Hence we get the required answer as 0.48
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can you please help me.
Answer:
I hope this helps for you
Pls answer soon, question is on pic
The inequality and the maximum possible width are 12w ≥ 132 and 11 feet respectively
How to write the inequality that models the situation?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
If the room is 12 feet long and Tom had enough paint to cover an area of 132 square feet. This implies Tom had paint that can cover greater or equal to 132 square feet of area. Thus:
L x w ≥ A
where l = 12 feet, A = 132 square feet
12w ≥ 132 (This is the inequality)
To solve for width:
12w ≥ 132
w ≥ 132 /12
w ≥ 11 feet
Therefore, the inequality is 12w ≥ 132 and the maximum possible width is 11 feet
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Find X : X/2 = 1
X=1/2
X=-2
X=1
X=2
Answer:
x=2
Step-by-step explanation:
x/2 = 1 (multiply by 2 both sides)
x= 2
a right triangle whose hypotenuse is 22 m long is revolved about one of its legs to generate a right circular cone. find the radius, height, and volume of the cone of greatest volume that can be made this way.
The greatest volume of the cone made be 4372.7 m³.
Given, a right triangle whose hypotenuse is 22 m long is revolved about one of its legs to generate a right circular cone.
Let the base of the right triangle be, b
and the height of the right triangle be, h
Using Pythagoras Theorem, we get
22² = b² + h²
484 = b² + h²
Now, the height of the cone be, h and the radius of the cone be, b
Volume of the cone = 1/3πb²h
as, b² = 484 - h²
Volume = 1/3π(484 - h²)h
Volume = 1/3π(484h - h³)
On differentiating, we get
V' = 1/3π(484 - 3h²)
h² = 484/3
h = 22/√3
h = 22√3/3
b = 22√2/√3
Volume = 1/3π(22√2/√3)(22√2/√3)(22√3/3)
Volume = 1/9√3π(22³)(2)
Volume = 4372.7 m³
Hence, the greatest volume of the cone made be 4372.7 m³.
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17. when evaluating an exercise, evaluators record their observations in the exercise evaluation guide (eeg). observations that should be recorded include: a. actual time required for exercise players to complete the critical task(s) b. resources utilized c. inject delivery timing d. a and b e. a and c f. all of the above
When evaluating an exercise, evaluators record their observations in the exercise evaluation guide (eeg). observations that should be recorded include d.) a and b
When analyzing an activity, evaluators record their observations in the Exercise Evaluation Guide (EEG) (EEG). Actual time needed by exercise participants to perform the necessary tasks and resources used are among the observations that should be recorded.
EEGs (Exercise Evaluation Guides) offer a reliable instrument to direct exercise monitoring and data gathering. EEGs list capability aims and crucial tasks that are in line with exercise objectives and core capabilities.
EEGs achieve a number of objectives:
simplifier data gatheringenabling extensive evaluations of the capacity targets of the participating entitiesEncourage the creation of the After-Action Report (AAR)Establish a method that is consistent for evaluating readiness through exercises.Aid organizations in relating exercise outcomes to exercise goals, core competencies, capability targets, and crucial tasks for additional analysis and evaluationTo know more about Exercise evaluation guidelines:
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lilianna has $68. she needs at least $194 for a new cell phone. write an inequality to fit this situation, where y represents the amount of additional money she needs. what's the least amount of additional money she needs to buy the new cell phone? question 18 options: a) 68 y ≤ 194. she needs less than $126 more. b) 68 y > 194. she needs at most $126 more. c) 68 y < 194. she needs more than $126 more. d) 68 y ≥ 194. she needs at least $126 more.
The least amount of extra cash Lilianna requires is $126 and the inequality is [tex]x+$68\geq 194[/tex]
What justifies an inequality?
The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.
Let
The least amount of extra money is x.
The fact that
[tex]x+$68\geq 194[/tex]
The problem is represented by inequality.
Solve for x.
[tex]x+$68\geq 194\\x\geq $126[/tex]
The least amount of money Lilianna requires is $126
and inequality is [tex]x+$68\geq 194[/tex]
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Suppose X1,..., XM iid Binomial(n,p) is a set of M observations drawn independently from a Binomial distribution. (a) Write out the likelihood function. (b) Write out the log-likelihood function. (c) Find the score function by taking the partial derivative of the log-likelihood function. (d) Set the score function equal to zero and solve for the parameter p. (e) Take the second partial derivative of the score function. (f) Check to make sure this value is negative to ensure that the log-likelihood function is concave down.
Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).
What is binomial distribution ?The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.
The fundamental presumptions of the binomial distribution are that each trial has only one possible outcome, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.
The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.
Hence, Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).
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In a random sample of 200 items, 5 items were defective. An estimate of the percentage of defective items in the population is.
If 5 out of 200 things were flawed, the population's estimated defect percent would be 2.5%.
What is percentage?Percent, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By multiplying the total or whole number by 100, one percent (or 1%) is equal to one hundredth of the whole or whole.
Here,
Total number of items=200
number of defective items=5
Percentage of defective items,
=5/200*100
=2.5%
Therefore, if 5 out of 200 things were defective, the population's estimated percentage of defective items is 2.5%.
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a voice teacher selects 8 students from the class to sing for the trustees. the class has 12 men and 13 women. in how many ways can 8 students be selected and arranged in a row with 4 men in the middle and 2 women on each end?
The number of ways that the teacher can arrange the row is 185328000
Given,
Number of male students = 12
Number of female students = 13
Number of students teacher needs to select = 8
The row arrangement is like; 4 men in the middle and 2 women on each end;
Here,
Order of the arrangement is considered.
So, permutation can be used.
Female students selected = ¹³P₂
Male students selected = ¹²P₄
Then,
Number of ways for the arrangement = ¹³P₂ × ¹²P₄
= 15600 × 11880
= 185328000
That is,
The teacher can arrange a row with 4 men in the middle and 2 women on each end in 185328000 ways.
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an active-high input s-r latch has a 1 on the s input and a 0 on the r input. what state is the latch in?
Q=1,Q'=0 as an active-high input s-r latch has a 1 on the s input and a 0 on the r input.
What is s-r latch?An SR latch (Set/Reset) is an asynchronous device that solely depends on the state of the S and R inputs and does not require any input from the control signals. The illustration demonstrates how two NOR gates with a cross-feedback loop may be used to build an SR latch. Set-reset, or S-R, latches are therefore the most basic type of bistable device. We can connect two NOR gates so that the output of one feeds back into the input of the other, and vice versa, to create an S-R latch, as shown below: The Q and not-Q outputs are supposed to be in opposing states.
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Are the expressions 5(m + 1 ) - 1 and 2(2m + 2) + m equivalent
Both the given expression are equivalent expression as 5m + 4.
Given that,
to determine whether the two given expressions are equivalent ot each other,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
5(m + 1 ) - 1 = 2(2m + 2) + m
5m + 5 - 1 = 4m + 4 + m
5m + 4 = 5m + 4
Thus, Both the given expression are equivalent expression as 5m + 4.
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Please help me fast! Which equation has the solution x = 5? Select each correct answer. Responses
32 − 4x = 12 , 11 + 6x = 22 , 18 − 2x = 9 , x/5 + 5 = 6 , 3x + 1 = 9 , 25/x + 4 = 9
Answer:
A ; D ; F
Step-by-step explanation:
32 - 4(5) = 12
32 - 20 = 12 (ok)
11 + 6(5) = 22
11 + 30 = 22
41 = 22 (false)
18-2(5) = 9
18 - 10 = 9
8 = 9 (false)
5/5 + 5 = 6
1 + 5 = 6
6 = 6 (ok)
3(5)+ 1 = 9
15 + 1 = 9
16 = 9 (false)
25/5 + 4 = 9
5 + 4 = 9
9 = 9 (ok)
Consider the expression (2.3x6)+(2.3x4).
Evaluate the expression. Show your work
Answer:
The solution to the given expression would be 23.
Step-by-step explanation:
1. Remove the parentheses:
[tex]2.3*6+2.3*4[/tex]
2. Multiply the numbers 2.3 by 6: 13.8
[tex]13.8+4*2.3[/tex]
3. Multiply the numbers 2.3 by 4: 9.2
4. Add the numbers 13.8 by 9.2: 23
= [tex]23[/tex] ←Our Final Solution
____________________________________________
Hope this helps!
a large population of mice in a laboratory has an average weight 32 grams with a standard deviation of 4 grams. a scientist weighs a random sample of 25 mice for an experiment. if the sample mean of the 25 mice is 30.4 grams, would this be significant evidence, at the 5 percent level of significance, against the hypothesis that the average weight of all mice is indeed 32 grams?
We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).
In the given question,
The population mean is 32g with a st. dev. of 4g.
We collect a sample of n=25 mice with a sample average of 30.4g.
We wish to test the hypothesis that these were drawn randomly from the population.
So our null hypothesis is
H0: mean = 32
Our alternative hypothesis is
HA: mean ≠ 32.
This is a two-sided test.
A sample mean should have the same mean as the population mean, and the sample st. dev. should be (pop st. dev./√n).
In this case, under the null hypothesis, the sample mean should be distributed with an average of 32 and a st. dev. of 4/√25 = 4/5 = 0.8.
To test this hypothesis, we need to calculate a test statistic and compare it to a critical value of the standard normal distribution.
Our test statistic is:
z = (Observed value - hypothesized value) / (st. dev. in sample mean)
z = (30.4-32)/0.8
z = -1.6/0.8
z = -2.
The critical value of the z-distribution with α/2 = 0.05/2 = 0.025 is 1.96.
We REJECT the null hypothesis that these rats came from a population with a mean of 32 in favour of the alternative that they were selected in a way that the mean was different from 32 because our test statistic is bigger than this (in absolute value).
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The right answer is:
A colony of laboratory mice consists of several thousand mice. The average weight of all the mice is 32 grams with a standard deviation of 4 grams. A laboratory assistant was asked by a scientist to select 25 mice for an experiment. However, before performing the experiment the scientist decided to weigh the mice as an indicator of whether the assistant’s selection constituted a random sample or whether it was made with some unconscious bias (perhaps themice selected were the ones that were slowest in avoiding the assistant, which might indicate some inferiority about this group). If the sample mean of the 25 mice was 30.4, would this be significant evidence, at the 5 percent level of significance, against the hypothesis that the selection constituted a random sample?
ou need to buy some chicken for dinner tonight. you found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.29 a pound. is it worth the extra drive? first, determine what information you need to answer this question, then click here to display that info (along with other info). how much chicken will you be buying? 3 pounds how much far are the two stores? my neighborhood store is 2.3 miles away, and takes about 7 minutes. the store across town is 8.4 miles away, and takes about 22 minutes. how kind of mileage does your car get? it averages about 23 miles per gallon in the city. how many gallons does your car hold? about 14 gallons how much is gas? about $3.87/gallon right now. going to the close store is cheaper going to the further store is cheaper the cheaper option saves you $ give your answer to the nearest cent.
1) $9.27 (far store), $9.87 (near store)
2) $0.169 per mile
3) 4.6 miles , 16.8 miles
4) $0.78, $2.84
5) $10.05 to the far store, $12.71 to the near store
What is Cost?
A mathematical formula known as the cost function is used to graph how production costs will change depending on the output level. To put it another way, it calculates the overall cost of production based on the quantity that is produced.
1) Let's compare chicken costs:
$3.09 * 3 = $9.27 (far store)
$3.29 * 3 = $9.87 (near store)
2) Now let's look at how much it costs to travel in your car:
[tex]\frac{3.87}{23} = 0.169\ per \ mile[/tex]
= $0.169 per mile.
3) Next, let's look how much it costs to travel to each store from the gas used. Multiply by 2 because you not only have to drive there, but also back home for the round trip:
2.3 miles * 2 = 4.6 miles
8.4 miles * 2 = 16.8 miles
4) Now to find the cost of gas for the respective trips:
$0.169 * 4.6 = $0.78
$0.169 * 16.8 = $2.84
5) We can just eyeball it from here that it's not worth it to travel, but for completion's sake, let's add the gas and chicken costs together:
$9.27 + $0.78 = $10.05 to the far store
$9.87 + $2.84 = $12.71 to the near store
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Write a number in which the value of the digit in the thousands place has one-tenths the value of the digit in the ten-thousands place.
The answer is 10,000
What is the bottom row and the 2 bottom ones thx Ill give brainly to the one who is right
Which shows the solution for the
following system of equations?
y = 2x
2x+y=-4