Answer:
Step-by-step explanation:
Given that:
Mean μ= 100
standard deviation σ = 2.6
sample size n = 9
sample mean X = 100.6
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]H_o : \mu \leq 100[/tex]
[tex]H_1 :\mu > 100[/tex]
The numerical value for the test statistics is :
[tex]z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{100.6- 100}{\dfrac{2.6}{\sqrt{9}}}[/tex]
[tex]z = \dfrac{0.6}{0.8667}[/tex]
z = 0.6923
At ∝ = 0.05
[tex]t_{\alpha/2 } = 0.025[/tex]
The critical value for the z score = 0.2443
From the z table, area under the curve, the corresponding value which is less than the significant level of 0.05 is 1.64
P- value = 0.244
c> If the true population mean is 101.3 ;
Then:
[tex]z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{101.3- 100.6}{\dfrac{2.6}{\sqrt{9}}}[/tex]
[tex]z = \dfrac{0.7}{0.8667}[/tex]
z = 0.808
From the normal z tables
P value = 0.2096
helpppp with this will give bralienst but need hurry
Answer:
20.25is how much each friend gets.Step-by-step explanation:
40.50/2 = 20.25
You have to divide by 2. This way both of the people will get the same amount of money.
Answer:
each friend will get
Step-by-step explanation:
20 .25
as 40 .50 ÷ 2 = 20 .25
hope this helps
pls can u heart and like and give my answer brainliest pls i beg u thx !!! : )
A shoes store sells three categories of shoes, Athletics, Boots and Dress shoes. The categories are stocked in the ratio of 5 to 2 to 3. If the store has 70 pairs of boots, how many shoes do they have in total?
Answer:
350 pairs
Step-by-step explanation:
If the ratio of Athletics, Boots, and Dress shoes is 5 to 2 to 3, it means that for every 2 pairs of Boots they have 5 pairs of Athletics shoes and 3 pairs of dress shoes.
So, if they have 70 pairs of boots, we can calculate the number of Athletics as:
[tex]\frac{5*70}{2} =175[/tex]
And if they have 70 pairs of boots, the number of dress shoes are:
[tex]\frac{3*70}{2}=105[/tex]
Finally, they have 70 pairs of boots, 175 pairs of athletics, and 105 pairs of dress shoes. It means that they have 350 pairs in total.
70 + 175 + 105 = 350
According to Pew Research, 64% of American believe that fake news causes a great deal of confusion.Twenty Americans are selected at random.
James runs on the school track team he runs 4 2/3 miles and 3/4 of an hour. What is James' speed in miles per hour?
Answer:
6 2/9 miles per hour
Step-by-step explanation:
Take the miles and divide by the hours
4 2/3 ÷ 3/4
Change to an improper fraction
( 3*4+2)/3 ÷3/4
14/3 ÷3/4
Copy dot flip
14/3 * 4/3
56/9
Change back to a mixed number
9 goes into 56 6 times with 2 left over
6 2/9 miles per hour
Answer:
6 2/9 miles per hour
Step-by-step explanation:
Divide the miles by the hour.
4 2/3 ÷ 3/4
Reciprocal
4 2/3 × 4/3
Convert to improper fraction.
14/3 × 4/3
56/9
Convert to mixed fraction.
9 × 6 + 2
6 2/9
ANSWER FAST PLEASE HELP
Answer:
see below
Step-by-step explanation:
Because two sides are congruent, the triangle in the diagram is isosceles which means that angle c = angle e because of the Base Angles Theorem. We know that angle c = 63 degrees because we see that it's vertical to a 63 degree angle, and vertical angles. Since angle c = angle e, angle e = 63 degrees. Since angles e and b form a linear pair, they are supplementary, meaning that they add up to 180 degrees which means that angle b = 180 - 63 = 117 degrees. To find angle d, we notice that d and c are alternate interior angles, and since these angles are congruent in parallel lines, angle d = 63 degrees as well. To find angle a, we know that the sum of angles in a triangle is 180 degrees so angle a = 180 - 63 - 63 = 54 degrees.
See in the attachment.
The bar graph below shows trends in several economic indicators over the period . Over the six-year period, about what was the highest consumer price index, and when did it occur? Need help with both questions!
Each week, Rosario drives to an ice-skating rink that is 60 miles away. The round-trip takes 2.75 hours. If he averages 55 miles per hour on his way to the rink, which equation can be used to find x, the number of miles per hour he averages on his way home?
Answer:
The answer to your question is x = 4d/t - S1
Step-by-step explanation:
Data
total time = t = 2.75 hours
Initial speed = S1 = 55 mi/h
Final speed = x
distance = d = 60 mi
Formula
speed = distance / time
Average speed = (Initial speed + final speed)/2 or
= (S1 + x)/2
Substitution
(S1 + x)/2 = 2(d) / t
Solve for x
x = (2d/t)2 - S1
Simplification and result
x = 4d/t - S1
write the statement for 6x-3=9
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
The statement for [tex]6x - 3 = 9[/tex] is :
[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
A rectangle is 2 inches longer than it is wide. Numerically, its area exceeds its perimeter by 20. Find the perimeter. ____________________ in
Answer:28
Step-by-step explanation: 6 x 8 = 48 6+6+8+8=28
The perimeter of rectangle is 28 inches
What is Perimeter of rectangle?The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle = 2(l + w), where 'l' is the length and 'w' is the width of the rectangle.
For example
The length of a bedsheet is 120 inches and the width is 85 inches. How much lace will be needed to put around its border?
Given, length = 120 inches; width = 85 inches.
Perimeter of a rectangle = 2(l + w).
On substituting the values of length and width in this formula, we get,
Perimeter = 2(l + w) = 2(120 + 85)= 2 × 205 = 410 inches.
Let he breadth be x
length= x+ 2
Area= Perimeter + 20
x² + 2x = 4x+ 4 + 20
x² - 2x -24 = 0
x² - 2x -24 = 0
(x- 6) (x+ 4)=0
x= 6, -4
So, length= 8 inches and breadth = 6 inches.
Hence, the Perimeter of rectangle= 2( 8 +6)= 2*14= 28 inches
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One positive integer is 6 less than twice another. The sum of their squares is 801. Find the integers
Answer:
[tex]\large \boxed{\sf 15 \ \ and \ \ 24 \ \ }[/tex]
Step-by-step explanation:
Hello,
We can write the following, x being the second number.
[tex](2x-6)^2+x^2=801\\\\6^2-2\cdot 6 \cdot 2x + (2x)^2+x^2=801\\\\36-24x+4x^2+x^2=801\\\\5x^2-24x+36-801=0\\\\5x^2-24x-765=0\\\\[/tex]
Let's use the discriminant.
[tex]\Delta=b^4-4ac=24^2+4*5*765=15876=126^2[/tex]
There are two solutions and the positive one is
[tex]\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{24+126}{10}=\dfrac{150}{10}=15[/tex]
So the solutions are 15 and 15*2-6 = 30-6 = 24
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations. Let I(t) denote the number of infected individuals. Suppose that the total population is 2000, the proportionality constant is 0.0001, and that 1% of the population is infected at time t-0, write down the intial value problem and the solution I(t).
dI/dt =
1(0) =
I(t) =
symbolic formatting help
Answer:
dI/dt = 0.0001(2000 - I)I
I(0) = 20
[tex]I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
Step-by-step explanation:
It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.
Also given I(t) is the number of the infected individual at a time t.
[tex]\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}[/tex]
Given total population is 2000. So the non infected population = 2000 - I.
[tex]\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I[/tex]
Now, I(0) is the number of infected persons at time t = 0.
So, I(0) = 1% of 2000
= 20
Now, we have dI/dt = 0.0001(2000 - I)I and I(0) = 20
[tex]\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k[/tex]
[tex]\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}[/tex]
The required expressions are presented below:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
Analysis of an ordinary differential equation for the spread of a disease in an isolated population
After reading the statement, we obtain the following differential equation:
[tex]\frac{dI}{dt} = k\cdot I\cdot (n-I)[/tex] (1)
Where:
[tex]k[/tex] - Proportionality constant[tex]I[/tex] - Number of infected individuals[tex]n[/tex] - Total population[tex]\frac{dI}{dt}[/tex] - Rate of change of the infected population.Then, we solve the expression by variable separation and partial fraction integration:
[tex]\frac{1}{k} \int {\frac{dI}{I\cdot (n-I)} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \int {\frac{dl}{l} } + \frac{1}{kn}\int {\frac{dI}{n-I} } = \int {dt}[/tex]
[tex]\frac{1}{k\cdot n} \cdot \ln |I| -\frac{1}{k\cdot n}\cdot \ln|n-I| = t + C[/tex]
[tex]\frac{1}{k\cdot n}\cdot \ln \left|\frac{I}{n-I} \right| = C\cdot e^{k\cdot n \cdot t}[/tex]
[tex]I(t) = \frac{n\cdot C\cdot e^{k\cdot n\cdot t}}{1+C\cdot e^{k\cdot n \cdot t}}[/tex], where [tex]C = \frac{I_{o}}{n}[/tex] (2, 3)
Note - Please notice that [tex]I_{o}[/tex] is the initial infected population.
If we know that [tex]n = 2000[/tex], [tex]k = 0.0001[/tex] and [tex]I_{o} = 20[/tex], then we have the following set of expressions:
Differential equation[tex]\frac{dI}{dt} = 0.0001\cdot I\cdot (2000-I)[/tex] [tex]\blacksquare[/tex]
Initial value[tex]I(0) = \frac{1}{100}[/tex] [tex]\blacksquare[/tex]
Solution of the differential equation[tex]I(t) = \frac{20\cdot e^{\frac{t}{5} }}{1+20\cdot e^{\frac{t}{5} }}[/tex] [tex]\blacksquare[/tex]
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Frank’s been traveling a lot lately as part of his job. During the past 30 days,he’s been out of town 18 days. What fraction represents the number of the 30 days that frank has been out of town? Explain how you got your answer
Answer:
[tex]n = \frac{3}{5}[/tex]. Which means that Frank has been travelling out of the town 3 days for each five days.
Step-by-step explanation:
The fraction ([tex]n[/tex]) is obtained by dividing the number of days that Frank has been out of town (18 days) in the given period (30 days). That is to say:
[tex]n = \frac{t}{T}[/tex]
[tex]t[/tex] - Out-of-the-town period, measured in days.
[tex]T[/tex] - Given period, measured in days.
If [tex]t = 18\,days[/tex] and [tex]T = 30\,days[/tex], then:
[tex]n = \frac{18\,days}{30\,days}[/tex]
[tex]n = \frac{3}{5}[/tex]
Which means that Frank has been travelling out of the town 3 days for each five days.
1. There are a total of 230 mint and chocolate sweets in a jar. 60% of the total number of sweets were mint sweets. After more chocolate sweets were added into the jar, the percentage of the mint sweets in the jar decreased to 40% How many chocolate sweets were added into the jar?
2. In August, 36% of the people who visited the zoo were locals and the rest were foreigners. In September, the percentage of local visitors decreased by 25% while the percentage of foreign participants increased by 50%. In the end, there were 161 fewer visitors in August than in September. How many visitors were there in September?
Answer:
1. 115 chocolates were added
2. 861 visitors in September
Step-by-step explanation:
1.
Initially:
m=number of mints
60% of 230 sweets were mints =>
m = 230*0.6 = 138 mints
initial number of chocolates, c1 = 230 - 138 = 92
Now chocolates were added
138 mints represented 40% of the total number of sweets, so
total number of sweets = 138 / 0.4 = 345
Number of chocolates added = 345 - 230 = 115
2.
In August 36% were locals, 64% were from elsewhere.
In suptember,
locals decreassed by 25% to 36*0.75=27% (of August total)
foreigner increased by 50% to 64*1.5=96% (of August total)
Total Inrease = 96+27-100 = 23% of August total = 161 visitors
August total = 161/0.23 = 700 visitors
September total = 700 + 161 = 861 visitors
The current particulate standard for diesel car emission is .6g/mi. It is hoped that a new engine design has reduced the emissions to a level below this standard. Set up the appropriate null and alternative hypotheses for confirming that the new engine has a mean emission level below the current standard. Discuss the practical consequences of making a Type I and a Type II error. (continue #5) A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4. Find the p-value of the test. Do you think that H0 should be rejected? Explain. To what type of error are you now subject?
Answer:
Step-by-step explanation:
From the summary of the given statistics;
The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:
Null hypothesis:
[tex]H_0: \mu = 0.60[/tex]
Alternative hypothesis:
[tex]H_a: \mu < 0.60[/tex]
Type I error: Here, the null hypothesis which is the new engine has a mean level equal to .6g/ml is rejected when it is true.
Type II error: Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.
Similarly;
From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.
Sample size n = 64
sample mean [tex]\overline x[/tex] = .5 g/ml
standard deviation σ = .4
From above, the normal standard test statistics can be determined by using the formula:
[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]
[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]
z = -2.00
The p-value = P(Z ≤ -2.00)
From the normal z distribution table
P -value = 0.0228
Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.
Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.
4
Consider the following equation.
-)* + 12 = 25 – 3
Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.
12
X
12
A I=
33
Edmentum. All rights reserved.
The solution to the equation above using three iterations of successive approximation is x = 25/16
What is an equation solution?The solution of an equation is the true values of the equation
The equation is given as:
[tex]5^{-x} + 7 =2x + 4[/tex]
Equate to 0
[tex]5^{-x} + 7 -2x - 4 = 0[/tex]
Write the equation as a function
[tex]f(x) = 5^{-x} + 7 -2x - 4[/tex]
The equation has a solution only when the function f(x) equals 0.
From the graph, we have:
x = 1.5
So, we have:
[tex]f(1.5) = 5^{-1.5} + 7 -2*1.5 - 4[/tex]
Evaluate
f(1.5) = 0.089
Set x to 1.52 to determine a closer value of f(x) to 0.
[tex]f(1.52) = 5^{-1.52} + 7 -2*1.52 - 4[/tex]
Evaluate
f(1.52) = 0.047
Set x to 1.54 to determine a closer value of f(x) to 0.
[tex]f(1.54) = 5^{-1.54} + 7 -2*1.54 - 4[/tex]
Evaluate
f(1.54) = 0.004
Notice that 0.004 is closer to 0 than 0.047 and 0.089
The closest value to 1.54 is 25/16 in the given options
Hence, the solution to the equation above using three iterations of successive approximation is x = 25/16
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What is the length of in the right triangle below?
A.
120
B.
C.
D.
218
Answer:
b. sqrt(120)
Step-by-step explanation:
a^2+b^2=c^2
a^2+7^2=13^2
13^2-7^2=a^2
120=a^2
sqrt(120)=a
This is using Pythagorean theorem
Laura wants to place one flower every 3/4 meters along the path from the gate to the main entrance of her home. The path is 12 meters long. How many flowerpots will she need?
Answer:
16 flowerpots
Step-by-step explanation:
12 divided by 3/4=16
Please answer this correctly without making mistakes
Answer:
d = 115.4 mi
Step-by-step explanation:
Since it gives us the distance in between the locations, we simply label the distances:
From the Garbage to the Hotel is 58.3 miles.
From the Hotel to the Hardware Store is 57.1 miles.
We are trying to find the distance from the Garbage to the Hardware Store, we simply add the distances between:
58.3 mi + 57.1 mi = 115.4 mi
Question 6 of 10
Which equation matches the graph of the greatest integer function given
below?
what is 328.1 × 0.63 what answer
Answer:206.703
Step-by-step explanation: you have to multiply 328.1 times 0.63 then you get your answer.
Answer:
206.703
Step-by-step explanation:
328.1 × 0.63=206.703
as a sales person at Trending Card Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $400 worth of merchandise in one month, he is paid $500. If he sells $700 worth of merchandise in one month, he is paid $575. Find justin's salary if he sells $2500 worth of merchandise
Answer:
$1025
Step-by-step explanation:
We can use the 2-point form of the equation of a line to write a function that gives Justin's salary as a function of his sales.
We start with (sales, salary) = (400, 500) and (700, 575)
__
The 2-point form of the equation of a line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
salary = (575 -500)/(700 -400)(sales -400) +500
salary = 75/300(sales -400) +500
For sales of 2500, this will be ...
salary = (1/4)(2500 -400) +500 = (2100/4) +500 = 1025
Justin's salary after selling $2500 in merchandise is $1025.
Help me!!! please!!!
Answer:
a) The five ordered pairs are:-
(1,60) , (2,120) , (3,180) , (4,240) , (5,300)
b)When You divide the y value by x value for each ordered pair u find the slope.
c)The graph shows a proportional relationship.Because as x-value increases so does y-value.
d)Y=mx+b--> Y=60x (No y-intercept because it starts from 0)
e)If a person hiked for 9 hours then the distance would be 540. Because If u plug in the number of hours in the x value of the equatione then u will get 540. Here's the work:-
Y=60(9)
Y=540
Step-by-step explanation:
Hope it helps u. And if u get it right pls give me brainliest.
A political action committee is interested in the proportion of all registered voters who will vote "Yes" on a measure to expand the use of solar energy. Match the vocabulary word with its corresponding example.
__________The proportion of registered voters who will vote Yes on the measure.
__________The 1000 registered voters who participated in the study.
__________The proportion of the 1000 registered voters that were surveyed who will vote Yes on the measure.
_________Yes or No for each registered voter All registered voters in the US
_________The list of Yes and No answers that were given by the 1000 participants in the study
a. Sample
b. Statistic
c. Parameter
d. Data
e. Variable
f. Population
Answer: parameter: The proportion of registered voters who will vote Yes on the measure.
Sample: The 1000 registered voters who participated in the study.
Statistic: The proportion of the 1000 registered voters that were surveyed who will vote Yes on the measure.
Variable: Yes or No for each registered voter
Population: All registered voters in the US
Data: The list of Yes and No answers that were given by the 1000 participants in the study.
Step-by-step explanation:
Definitions of the given terms:
Population: Large groups of individuals having similar characteristics as per the researcher's point of view.Sample: It is a subset of the population used to represent it.Parameter: Measure of particular characteristics in the population. Statistic: Measure of particular characteristics in the sample.Variable: Characteristics that vary.Data: A collected information facts and statistics.Hence, by using the above definitions, we have
Parameter: The proportion of registered voters who will vote Yes on the measure.Sample: The 1000 registered voters who participated in the study. Statistic: The proportion of the 1000 registered voters that were surveyed who will vote Yes on the measure.Variable: Yes or No for each registered voter.Population: All registered voters in the US. Data: The list of Yes and No answers that were given by the 1000 participants in the study.Use multiplication or division of power series to find the first three nonzero terms in the maclaurin series for the given function. (Enter your answers as a comma-separated list.)
y=(e^-x^2)cosx
Answer:
1 , - ( 3x^2/2), + (25x^4/24).
Step-by-step explanation:
We are given the following information:
y = (e^-x^2)cosx.
STEP ONE: Write out the power series out(either by deriving it or otherwise).
If you check the power series table, you will get the power series for the two functions that is cos x and e^-x^2.
e^-x^2 = 1 - (x^2) + ( x^4/2! ) - (x^6/3!) +...
Cos x = 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...
STEP TWO: Multiply both the power series of e^-x^2 and Cos x together because we are to determine or find the first three nonzero terms in the maclaurin series for the given function.
1 - (x^2) + ( x^4/2! ) - (x^6/3!) +... - 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...
= 1 - ( 3x^2/2) + (25x^4/24).
= 1, - ( 3x^2/2) , + (25x^4/24) => comma- separated list.
The diagram shows a right triangle and three squares. The area of the largest square is 363636 units^2 2 squared. Which could be the areas of the smaller squares?
Answer:
The answers are A. and B.
Step-by-step explanation:
Since the area of the largest square is 36. We need two numbers that equal 36. and A. had 6 and 30 so i picked it and it was right and B. is 28 and 8 which also equals 36. But, C. is 4 and 16 which is not 36. So A. and B. are the answers. Hope this helps! :)
We can use the Pythagorean theorem (a^2+b^2=c^2)(a
2
+b
2
=c
2
)left parenthesis, a, squared, plus, b, squared, equals, c, squared, right parenthesis to determine possible areas of the two smaller squares.
\text{Area of a square} =\text{side}^2Area of a square=side
2
start text, A, r, e, a, space, o, f, space, a, space, s, q, u, a, r, e, end text, equals, start text, s, i, d, e, end text, squared
So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2a
2
,b
2
a, squared, comma, b, squared and c^2c
2
c, squared in the Pythagorean theorem.
Hint #22 / 6
For example, in the diagram above, the area of the square that shares a side with the hypotenuse is 363636 square units. So, c^2=36c
2
=36c, squared, equals, 36.
Hint #33 / 6
Let's fill in the possible values to see if they make the equation true.
\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 6 + 30 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}
a
2
+b
2
a
2
+b
2
6+30
36
=c
2
=36
=
?
36
=
✓
36
The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.
So, 666 and 303030 could be the areas of the smaller squares.
Hint #44 / 6
\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 8 + 28 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}
a
2
+b
2
a
2
+b
2
8+28
36
=c
2
=36
=
?
36
=
✓
36
The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.
So, 888 and 282828 could be the areas of the smaller squares.
Hint #55 / 6
\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 4 + 16 &\stackrel{\large?}{=}36 \\\\ 20 &\neq 36\\\\ \end{aligned}
a
2
+b
2
a
2
+b
2
4+16
20
=c
2
=36
=
?
36
=36
The sum of the areas of the squares connected to the two shorter triangle sides is not equal to the area of the square connected to the longest side.
So, 444 and 161616 could not be the areas of the smaller squares.
Hint #66 / 6
The area of the smaller squares could be:
666 and 303030
888 and 2828
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09 *Note: An increase in film speed would lower the value of the observation in microjoules per square inch. We may also assume the speeds of the film follow a normal distribution. Use this information to construct a 98% interval estimate for the difference in mean speed of the films. Does decreasing the thickness of the film increase the speed of the film?
Answer:
A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Step-by-step explanation:
We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.
For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.
Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;
P.Q. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15
[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06
[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11
[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09
[tex]n_1[/tex] = sample of 25-mil film = 8
[tex]n_2[/tex] = sample of 20-mil film = 8
[tex]\mu_1[/tex] = population mean speed for the 25-mil film
[tex]\mu_2[/tex] = population mean speed for the 20-mil film
Also, [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005
Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.
So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;
P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98 {As the critical value of t at 14 degrees of
freedom are -2.624 & 2.624 with P = 1%}
P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98
P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ) = 0.98
P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98
98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]
= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]
= [-0.042, 0.222]
Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.
i know the answer i just need the working! please help...
=====================================================
Work Shown:
A = mass, in kg, of 1 apple
B = mass, in kg, of 1 empty basket
10A = mass of 10 apples
10A+B = mass of 10 apples and basket = 0.5
35A = mass of 35 apples
35A + B = mass of 35 apples and basket = 1.05
The system of equations we have is
[tex]\begin{cases}10A+B = 0.5\\35A+B = 1.05\end{cases}[/tex]
There are a number of ways to solve. As the top left corner of your paper indicates, we can use a matrix to solve. Either using row reduction or matrix inverse math.
We could also use elimination which I find easiest in this case. I'll use that method. Subtract the equations straight down. Note how the B terms become B-B = 0B = 0 which go away. The A terms become 10A-35A = -25A, and the terms on the right hand side become 0.5-1.05 = -0.55
--------
We're left with the equation
-25A = -0.55
Divide both sides by -25 to isolate A
A = -0.55/(-25)
A = 0.022
The mass of one apple is 0.022 kg
--------
Use this value of A to find B
10A + B = 0.5
10*0.022 + B = 0.5
0.22 + B = 0.5
B = 0.5 - 0.22
B = 0.28
Or we could use the other equation to solve for B
35A + B = 1.05
35(0.022) + B = 1.05
0.77 + B = 1.05
B = 1.05 - 0.77
B = 0.28
Either way, the empty basket's mass is 0.28 kg
Amber says that the data set is left-skewed because the box is farther to the left on the number line. (A) Is Amber correct? (B) Explain your reasoning.
the domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values excpet 2. what are the restrictions on the domain of (u•v)(x)?
Answer:
[tex](-\infty, 0) \cup (0,2) \cup (2,\infty)[/tex]
Step-by-step explanation:
Remember that the domain of the product of functions is the intersection of domains, therefore when you intercept them you get the following interval.
[tex](-\infty, 0) \cup (0,2) \cup (2,\infty)[/tex]
Albert's Cafe uses 5 bags of coffee every day. How many days will 5/8 of a bag of coffee last?
Answer:
1 day.
Step-by-step explanation:
Given:
Albert's cafe uses 5 bags of coffee every day.
Required:
How many days will 5/8 bag of coffee last?
'How many days will 5/8 bag of coffee last?'
In this sentence we can see that there are 8 bags of coffee. The question in other words is Albert's Cafe is using 5 bags of coffee out of the 8 bags of coffee, and how many days will these last.
In the given we can see that the Cafe uses 5 bags of coffee per day, so the answer is 1 day.
Hope this helps ;) ❤❤❤