Answer:
D. Logical Fallacies
Step-by-step explanation:
Let's break this down:
fallacy: A false or mistaken idea.
By this definition, we can see that "false" would go with the word "faulty". A logical Fallacy is is a false or mistaken idea that's intended to sound logical. I hope this helps you!!
In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.5 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then.
We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year.
The men in our sample married at an average age of 25.3 years, with a standard deviation of 5.4 years. That results in a t-statistic of 0.937 What is the P-value for this?
Answer:
[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=25.3[/tex] represent the sample mean
[tex]s=5.4[/tex] represent the sample standard deviation
[tex]n=40[/tex] sample size
[tex]\mu_o =24.5[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is higher than 24.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 24.5[/tex]
Alternative hypothesis:[tex]\mu > 24.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{25.3-24.5}{\frac{5.4}{\sqrt{40}}}=0.937[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(39)}>0.937)=0.177[/tex]
A random sample of 10 college students was drawn from a large university. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. We want to determine if we can infer at the 5% significance level that the population mean is not equal to 20.
Answer:
[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value would be:
[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.
Step-by-step explanation:
Information given
22, 17, 27, 20, 23, 19, 24, 18, 19, and 24
The sample mean and deviation for these data are:
[tex]\bar X=21.3[/tex] represent the ample mean
[tex]s=3.199[/tex] represent the sample standard deviation for the sample
[tex]n=10[/tex] sample size
[tex]\mu_o =20[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean is equal to 20 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 20[/tex]
Alternative hypothesis:[tex]\mu \neq 20[/tex]
The statistic would be:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing the info given we got:
[tex]t=\frac{21.3-20}{\frac{3.199}{\sqrt{10}}}=1.29[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value would be:
[tex]p_v =2*P(t_{(9)}>1.29)=0.229[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is different from 20.
A family is taking a trip. During the first 2 hours, they travel at a rate of 25 miles per hour. They then take a break for 2 hours and do not travel during that time. They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day. What is the average speed for their first day of travel? How much time elapsed from the start of their trip until they stopped for the day? Δt=
Answer:
Average speed v = 24.29 mph
Total time taken ∆t = 7 hours
Step-by-step explanation:
Given;
the first 2 hours, they travel at a rate of 25 miles per hour
t1 = 2 hours
v1 = 25 mph
then take a break for 2 hours and do not travel during that time
t2 = 2 hours
v2 = 0
They finally travel again for another 3 hours at a rate of 40 miles per hour before stopping for the day.
t3 = 3 hours
v3 = 40 mph
Total time taken ∆t = sum of time taken for the day travel
∆t = t1 + t2 + t3
Substituting the values;
∆t = 2 + 2 + 3 = 7 hours
The average speed v = total distance travelled/total time taken
v = d/∆t .......1
Total distance travelled d = Σ(velocity × time)
d = v1t1 + v2t2 + v3t3
d = 25 × 2 + 0×2 + 40 × 3
d = 50 + 0 + 120
d = 170 miles
Substituting into equation 1.
v = 170 miles ÷ 7 hours
Average speed v = 24.29 mph
What is the meassure of XYZ in the diagram below HELP ASSAP :)
Could someone please give me the answer to this?
Answer:
36.87
Step-by-step explanation:
The cosine of an angle in a right triangle is the length of the adjacent side divided by the length of the hypotenuse, which in this case is 4/5. Therefore, the measure of this angle is the arc cosine of 4/5, or about 36.87 degrees. Hope this helps!
) How many kilowatt hours would the model predict on a day that has 14 hours of possible daylight?
Question:
A solar power company is trying to correlate the total possible hours of daylight (simply the time from sunrise to sunset) on a given day to the production from solar panels on a residential unit. They created a scatter plot for one such unit over the span of five months. The scatter plot is shown below. The equation line of best fit for this bivariate data set was: y = 2.26x + 20.01
How many kilowatt hours would the model predict on a day that has 14 hours of possible daylight?
Answer:
51.65 kilowatt hours
Step-by-step explanation:
We are given the equation line of best fit for this data as:
y = 2.26x + 20.01
On a day that has 14 hours of possible daylight, the model prediction will be calculated as follow:
Let x = 14 in the equation.
Therefore,
y = 2.26x + 20.01
y = 2.26(14) + 20.01
y = 31.64 + 20.01
y = 51.65
On a day that has 14 hours of daylight, the model would predict 51.65 kilowatt hours
What is the y-intercept of the graph that is shown below? On a coordinate plane, a line goes through points (negative 2, 0) and (4, 0).
Answer:
b = 0
Step-by-step explanation:
Because the line passes through x values when y = 0, it means that the line is y = 0. The slope would be 0, and because we are given 2 coordinates we can determine that the y intercept would be at 0.
Answer:
c
Step-by-step explanation:
hope this helps i just had this question on edge 2020
dentify the reference angle for each given angle, . degrees. degrees. degrees. degrees.
Answer:
S, Z, F
Step-by-step explanation:
i know its not the question but its for anyone who found this and needs it for edge lol
Solve the equation, keeping the value for x as an improper fraction. 2/3 x = − 1/2 x + 5
Answer:
[tex]x= 30/7[/tex]
Step-by-step explanation:
[tex]2/3 x = -1/2 x + 5[/tex]
[tex]2/3x+1/2x = + 5[/tex]
[tex]7/6x=5[/tex]
[tex]x=5 \times 6/7[/tex]
[tex]x= 30/7[/tex]
What is 2-2x greater than negative 20?
Answer:
no.
Step-by-step explanation:
Answer: -2x-18
Step-by-step explanation:
4. (16 points) A company with a fleet of cars found that in a random sample of 65 chosen and tested cars that 30 had emissions systems which failed to meet pollution control guidelines. A statistician is interested in testing if there is enough evidence to conclude that more than 30% of the fleet might be out of compliance regarding pollution control guidelines. Perform a five step hypothesis test using a 0.05 significance level. Write out the hypotheses: Determine critical value(s): Compute the test statistic: Determine the decision: Write the concluding statement:
Answer:
Null hypothesis:[tex]p\leq 0.3[/tex]
Alternative hypothesis:[tex]p > 0.3[/tex]
Critical value: [tex] z_{\alpha/2}= 1.64[/tex]
Test statistic: [tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]
For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%
Step-by-step explanation:
Information given
n=65 represent the random sample taken
X=30 represent the number of cars with emissions systems which failed to meet pollution control guidelines
[tex]\hat p=\frac{30}{65}=0.462[/tex] estimated proportion of cars with emissions systems which failed to meet pollution control guidelines
[tex]p_o=0.30[/tex] is the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion for this case is higher than 0.3 or no, the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.3[/tex]
Alternative hypothesis:[tex]p > 0.3[/tex]
The statistic for this case would be:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.462 -0.3}{\sqrt{\frac{0.3(1-0.3)}{65}}}=2.85[/tex]
The critical value for this case would be taking in count the significance level in the right tail:
[tex] z_{\alpha/2}= 1.64[/tex]
For this case the calculated value is higher than the critical value so then we can reject the null hypothesis. And we can conclude that the true proportion of cars with emissions systems which failed to meet pollution control guidelines for this case is significantly higher than 0.30 or 30%
A factory ship the 100 boxes with 15 skateboards in each box and 10 boxes with 15 helmets in each box
Answer:
150(10s + h)
Step-by-step explanation:
We need to write an expression for the total items they shipped.
Let each skateboard be s.
Let each helmets be h.
The factory ships 100 boxes with 15 skateboards in each box. That is:
100 * (15 * s) = 1500s
The factory ships 10 boxes with 15 helmets in each box. That is:
10 * (15 * h) = 150h
The total number of items shipped is therefore:
1500s + 150h = 150(10s + h)
This expression represents the total number of items shipped.
Hello, what is all the scale factors of two.?
Answer:
all even numbers
Step-by-step explanation:
Answer:
Any and all of the Even numbers are scale factors of two!
At hockey practice., Lars has the puck in front of the net, as shown. He is exactly 8 m away from the middle of the net, which is 2 m wide. Within what angle must Lars fire his shot in order to get it in the net, to nearest degree?
Answer:
14.25°
Step-by-step explanation:
distance from middle of the net = 8 m
width of the net = 2 m
this is a case of a triangle with height 8 m, and base 2 m. We are required to find the angle facing the base.
We can get this angle by splitting the triangle into two right angle triangles with base of 1 m, and then solve for the angle facing the base.
We use the trigonometric function; tan∅ = opp/adj
opp is the side facing the angle = 1 m
adj is the height of the triangle (usually, it is the side besides the opposite side and the longest side; the hypothenus)
adj = 8 m
tan∅ = [tex]\frac{1}{8}[/tex] = 0.125
∅ = [tex]tan^{-1}[/tex] 0.125 = 7.125°
Angle within which Lars must fire his shot = 2 x ∅
= 2 x 7.125° = 14.25°
Please help I’ll mark you as brainliest if correct!
Answer:
(x+7)^2+(y-8)^2=1
(x-x value of center)^2+(y-y value of center)^2=radius
Answer:
(x + 7)² + (y - 8)² = 1
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = - 7, k = 8, r = 1
(x -(-7))² + (y - 8)² = 1²
(x + 7)² + (y - 8)² = 1
Find three times five-twelfths, expressed as a decimal.
Answer:
The answer will be 1.25
Step-by-step explanation:
In order to make 512 into a decimal, you take the top number or numerator, which is 5 , and take your bottom number or your denominator, which is 12 , and divide 5 by 12 which will give you0.416666667
Hey there! :)
Answer:
1.25
Step-by-step explanation:
Begin by multiplying the fractions:
[tex]\frac{3}{1}* \frac{5}{12}= \frac{3*5}{1*12} = \frac{15}{12}= \frac{5}{4}[/tex]
Convert [tex]\frac{5}{4}[/tex] into a decimal:
5/4 = 1.25.
100 points for brainiest
Please try!!
Use this link in my comment!
Answer:
I couldn't find the link you wanted me to click.
Anyway the Pyramid Volume Formula is
Volume= (Area of the Base * Height) ÷ 3
It's hard to determine the volume because I can't tell the dimensions from the graphic.
I'd guess the answer to question 4 is "A" means area of the base
Step-by-step explanation:
Traffic speed: The mean speed for a sample of cars at a certain intersection was kilometers per hour with a standard deviation of kilometers per hour, and the mean speed for a sample of motorcycles was kilometers per hour with a standard deviation of kilometers per hour. Construct a confidence interval for the difference between the mean speeds of motorcycles and cars at this intersection. Let denote the mean speed of motorcycles and round the answers to at least two decimal places. A confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
Construct the 98% confidence interval for the difference μ 1-y 2 when x 1 475.12, x 2-32134, s 1-43.48, s 2-21.60, n 1-12, and n 2-15. Use tables to find the critical value and round the answers to two decimal places. A 98% confidence interval for the difference in the population means is ________.
Answer:
Step-by-step explanation:
Hello!
X₁: speed of a motorcycle at a certain intersection.
n₁= 135
X[bar]₁= 33.99 km/h
S₁= 4.02 km/h
X₂: speed of a car at a certain intersection.
n₂= 42 cars
X[bar]₂= 26.56 km/h
S₂= 2.45 km/h
Assuming
X₁~N(μ₁; σ₁²)
X₂~N(μ₂; σ₂²)
and σ₁² = σ₂²
A 90% confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
The parameter of interest is μ₁-μ₂
(X[bar]₁-X[bar]₂)±[tex]t_{n_1+n_2-2}[/tex] * [tex]Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }[/tex]
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{175; 0.95}= 1.654[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{134*16.1604+41*6.0025}{135+42-2} } = 3.71[/tex]
[(33.99-26.56) ± 1.654 *([tex]3.71*\sqrt{\frac{1}{135} +\frac{1}{42} }[/tex])]
[6.345; 8.514]= [6.35; 8.51]km/h
Construct the 98% confidence interval for the difference μ₁-μ₂ when X[bar]₁= 475.12, S₁= 43.48, X[bar]₂= 321.34, S₂= 21.60, n₁= 12, n₂= 15
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{25; 0.99}= 2.485[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{11*(43.48)^2+14*(21.60)^2}{12+15-2} } = 33.06[/tex]
[(475.12-321.34) ± 2.485 *([tex]33.06*\sqrt{\frac{1}{12} +\frac{1}{15} }[/tex])]
[121.96; 185.60]
I hope this helps!
Kennedy and Olivia go to the movie theater and purchase refreshments for their friends.
Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks.
Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a drink, to the nearest cent.
Answer:
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
Step-by-step explanation:
Let the price of popcorn be x
Let the price of drink be y.
price of 12 bags of popcorn will be 12x
price of 2 drinks will be 2y
it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."
thus
12x + 2y = 77.50
dividing LHS and RHS by 2 we have
12x/2 + 2y/2 = 77.50/2
=> 6x + y = 38.75 _________(1)
__________________________________________________
price of 3 bags of popcorn will be 3x
price of 6 drinks will be 6y
it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."
thus
3x + 6y = 51.00
dividing LHS and RHS by 3 we have
3x/3 + 6y/3 = 51/3
=> x + 2y = 17 _____________(2)
__________________________________________________
Thus we have two equation
6x + y = 38.75 _________(1)
x + 2y = 17
=> x = 17 - 2y
putting this value of x in equation 1 we have
6( 17 - 2y) + y = 38.75
=> 102 - 12y + y = 38.75
=> 102 - 11y = 38.75
=> -11y = 38.75 -102
=> -11y = -63.25
=> y = -63.25/-11 = 5.75
as we have x = 17 - 2y
using 5.75 in place of y
x = 17 - 2(5.75 )
=> x = 17 - 11.5
=> x = 5.5
Thus, system of equations are
6x + y = 38.75
x + 2y = 17
price of drink is $5.75
Make r the subject of the formula
Answer:
[tex]r=\frac{-a+p}{a+p}[/tex]
Step-by-step explanation:
[tex]-pr+p=ar+a[/tex]
[tex]-ar-pr+p=a[/tex]
[tex]-ar-pr=a-p[/tex]
[tex]r(-a-p)=a-p[/tex]
[tex]r=\frac{-a+p}{a+p}[/tex]
Answer:
[tex]r = \frac{p - a}{(p + a)} [/tex]
Step-by-step explanation:
[tex]p = \frac{a(1 + r)}{(1 - r)} \\ p(1 - r) = a(1 + r) \\ p - pr = a + ar \\ p - a = pr + ar \\ p - a = r(p + a) \\ \frac{p - a}{(p + a)} = \frac{r(p + a)}{(p + a)} \\ \frac{p - a}{(p + a)} = r[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The circle graph shows the different vitamins present in a health drink. Identify the measure of arc AB. Please help!
Answer:
79.2° (First Option)
Step-by-step explanation:
To find mAB, recognize that the percents given for the pie chart can represent the percent area of the sector of the circle, the percent measure of the central angle that forms the sector, or the percent measure of the length of the arc.
The measure of an arc is equal to the measure of the central angle between the radii that form its endpoints. So, mAB=m∠AOB.
The measure of the central angle AOB that forms AB is 22 percent of the whole circle, or (0.22)360∘. So, mAB=0.22(360∘)=79.2∘
Therefore, the measure of arc AB
is 79.2∘.
The measure of the arc AB of a circle showing the different vitamins present in a health drink is 79.2 degrees.
Calculate the measure of arcThe measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.
How to find the measure of arc AB.As the measure of an arc is always equivalent to the measure of the central angle between the radii that form its endpoints.
Thus [tex]m\angle{AOB}=\widehat{AB}[/tex].
First, find the measure of angle AOB.
Since the measure of angle AOB shows 22% of vitamins of the whole circle.
This means that the measure of angle AOB is 22% of 360 degrees.
Then we will get
[tex]m\angle{AOB}=\dfrac{22}{100}\times 360^{\circ}\\m\angle{AOB}=79.2^{\circ}[/tex]
Here the measure of angle AOB is 79.2 degrees.
And since [tex]m\angle{AOB}=\widehat{AB}[/tex].
Therefore the measure of arc AB is 79.2 degrees.
That means option A [tex]79.2^{\circ}[/tex] is correct option.
Learn more about the measure of arc here- https://brainly.com/question/12555201
#SPJ2
Eric's average income for the four months of the year 1450 point to $5 what must be his average income for the remaining eight months so that his average for the year is $1780.75
Answer:
$2668.63
Step-by-step explanation:
If the average of 4 months is $5
Meaning the total sum for 4 months
4×5 =$20
If the average for the year was $1780.75
It means the total sum for a year is;
$1780.75×12 =$21369
This means the money received for the remaining 8 months is;
$21369-$20=$21349
Hence the average income for the remaining 8months is ;
The total amount for 8 months / 8;
$21349/8= $2668.625
$2668.63
What’s the value of x?
Answer:
x =20
Step-by-step explanation:
7x- 99 = 2x+1 ( vertically opposite angles)
7x - 2x = 1 +99
5x = 100
x =100/5
x =20
hope it helps
A prominent medical school conducted a study that concluded adults with high blood pressure who consistently ate small amounts of low sugar dark chocolate experienced a significant reduction in blood pressure. As the study was being reviewed prior to publication in a medical journal, it was discovered that the Jershey Chocolate Company provided substantial funding for this research.
a) Identify any bias in this study.
b) Is it reasonable to conclude that adults with high blood pressure who consistently eat small amounts of low sugar dark chocolate experience a significant reduction in blood pressure?
Step-by-step explanation:
In the given question, the study was performed to analyse the effect of eating dark chocolate on the person with hypertension or increased blood pressure.
a) The biasness in the experiment could be that the funding for the study has been provided with a Private Company which mainly aims at selling their product.
b) The research is reasonable as it has been proved that eating a small amount of Dark chocolate can help cardiovascular disease like hypertension or increased blood pressure.
If f(x + 2) = 6x2 + 5x − 8. Find f(6).
Answer:
108
Step-by-step explanation:
We can rewrite f(x+2) to make it easier to evaluate:
f(x+2) = (6x +5)x -8
Since we want f(6), we want x+2 = 6, or x=4.
f(6) = (6·4 +5)·4 -8 = 29·4 -8
f(6) = 108
what is the nominal annual interest rate
Answer:
the nominal interest rate is the periodic interest rate.
it is the periodic interest rate times the number of periods per year.
00:00
Joseph and Molly each have coin collections.
Joseph starts with 15 coins in his collection and adds 25 coins each month.
Molly starts with 25 coins in her collection and adds 25 coins each month.
Drag numbers from the box to complete the table showing the number of coins in their collections after 4 months.
115
75
65
40
100
90
50
125
Coin Collections
Month
Joseph
Molly
-
Start
15
25
1
1
2
3
4
Answer:
Step-by-step explanation:
Joseph : y = 25x + 15
Molly: y = 25x + 25
Joseph: y = 25(4)+ 15= 100+ 15= 115
Molly: y = 25(4)+ 25= 100+25= 125
Answer:
I hope this helps! <:
Step-by-step explanation:
The start is 15 and 25 so you keep on adding 25 to each of them, let's start with 15, 15+25=40 and 40 plus 25 is 65 and 65+25 is 90 the last one is 90+25= 115, now let's move on to 25. 25+25= 50 and the next one is 50+25=75 and then 75+25=100 and 100+25= 125.
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 55 ounces and a standard deviation of 6 ounces.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
a) 95% of the widget weights lie between _______ and ________.
b) What percentage of the widget weights lie between 37 and 67 ounces?c) What percentage of the widget weights lie above 49 ?
Answer:
a) For this case and using the empirical rule we can find the limits in order to have 9% of the values:
[tex] \mu -2\sigma = 55 -2*6 =43[/tex]
[tex] \mu +2\sigma = 55 +2*6 =67[/tex]
95% of the widget weights lie between 43 and 67
b) For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:
[tex] 100 -0.15-2.5 = 97.85[/tex]
c) We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%
Step-by-step explanation:
For this case our random variable of interest for the weights is bell shaped and we know the following parameters.
[tex]\mu = 55, \sigma =6[/tex]
We can see the illustration of the curve in the figure attached. We need to remember that from the empirical rule we have 68% of the values within one deviation from the mean, 95% of the data within 2 deviations and 99.7% of the values within 3 deviations from the mean.
Part a
For this case and using the empirical rule we can find the limits in order to have 9% of the values:
[tex] \mu -2\sigma = 55 -2*6 =43[/tex]
[tex] \mu +2\sigma = 55 +2*6 =67[/tex]
95% of the widget weights lie between 43 and 67
Part b
For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:
[tex] 100 -0.15-2.5 = 97.85[/tex]
Part c
We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%
if 36-k=4+k what is the value of K?
36 - k = 4 + k
36 - 4 = k + k
32 = 2k
32/2 = k
16 = k
Steps:
Step 1: Simplify both sides of the equation
36−k=4+k
36+−k=4+k
−k+36=k+4
Step 2: Subtract k from both sides
−k+36−k=k+4−k
−2k+36=4
Step 3: Subtract 36 from both sides
−2k+36−36=4−36
−2k=−32
Step 4: Divide both sides by -2
−2k/−2 = −32/−2
Description:
Since we are trying to find the value of K, we need to simplify both sides of the equation. After that your answer will come as −k+36=k+4. Now the second step is to subtract k from both sides, your equation will come as −2k+36=4. Thirdly we need to subtract 36 from both sides, your equation will come as −2k=−32. Now you need to divide both sides by -2. After you do that, you will get your answer which is k=16.
Answer: k=16
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2]a^4+(root under 2b)^4
3]x^4+5x^2+9
4]p^2-10xp+16x^2-q^2+6xq
solve it
Answer:
1) a^4 + 16b^4
2) x^4 + 5x^2 + 9
3) p^2 − 10px − q^2 + 6qx + 16x^2
Step-by-step explanation:
1) a^4 + (2b)^4
= a^4 + 16b^4
2) x^4 + 5x^2 + 9
There are no like terms.
Answer:
= x^4 + 5x^2 + 9
3) p2 − 10xp + 16x2 − q2 + 6xq
= p^2 − 10px − q^2 + 6qx + 16x^2