9514 1404 393
Answer:
right
Step-by-step explanation:
If you're going to be in the business of classifying triangles based on side lengths, it can be useful to know there is a "form factor" that can help. For sides a, b, c, with long side 'c', it is computed as ...
f = a² + b² - c²
It has the following interpretation with respect to triangle shape:
f > 0 . . . acute
f = 0 . . . right
f < 0 . . . obtuse
__
In this case, we have ...
16² +63² -65² = 256 +3969 -4225 = 0
The triangle is a right triangle.
_____
Additional comment
When the triangle is a right triangle, this is equivalent to a statement of the Pythagorean theorem: c² = a² + b².
For triangles of other shapes, the interpretation is consistent with the Law of Cosines. When the form factor is divided by 2ab, the result is the cosine of the largest angle. That is why >0 means acute and <0 means obtuse.
Fill in the blanks to complete the sentences below. (a) As the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches ______. (b) If a 95% confidence interval results in a sample proportion that does not include the population proportion, then the sample proportion is more than ______ standard errors from the population proportion. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Answer:
a) the proportion of 95% confidence intervals that include the population proportion approaches 0.95
b) Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion
Step-by-step explanation:
a)
Given the the data in the question, confidence level is 95%.
In this case as the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 0.95. hence the expected value of the proportion.
b)
Given the the data in the question, confidence level is 95% and sample proportion
we know that In normal distribution 68% confidence indicate one standard deviation, 95% confidence indicate 2 standard deviation while 99.97% confidence indicate 3 standard deviation.
The sample proportion does not include the population proportion, in 95% confidence from the standard normal table 0.95 value lies within the critical value of 1.96 approximately 2.
hence ( z =2 ) that satisfied the 1.96 standard error from the population proportion
hence, Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion
Using confidence interval concepts, it is found that:
a) As the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 95%.
b) If a 95% confidence interval results in a sample proportion that does not include the population proportion, then the sample proportion is more than 2 standard errors from the population proportion.
Item a:
For a x% confidence interval, approximately x% of confidence intervals will include the population proportion, and this percentage approaches x as the number of intervals increase, hence, the correct sentence is:
As the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 95%.
Item b:
By the Empirical Rule, 95% of the measures are within 2 standard deviations of the mean, hence, the correct sentence is:
If a 95% confidence interval results in a sample proportion that does not include the population proportion, then the sample proportion is more than 2 standard errors from the population proportion.
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f(x) = 5x^2 + 9x – 4
g(x) = – 8x^2 – 3x – 4
Find (f + g)(x).
Answer:
(f + g)(x) = – 3x^2 + 5x - 8
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 5x^2 + 9x – 4 + (– 8x^2 – 3x – 4)
= 5x^2 + 9x – 4 – 8x^2 – 3x – 4
Combine
= – 3x^2 + 5x - 8
The sum of the given functions is defined as the expression (f + g)(x) which is equal to -3x² + 6x – 8.
Use the concept of quadratic function defined as:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
The given functions are:
f(x) = 5x² + 9x – 4
g(x) = – 8x² – 3x – 4
Since (f + g)(x) = f(x) + g(x)
Then put the functions,
(f + g)(x) = (5x² + 9x – 4) + ( – 8x² – 3x – 4)
Rearranging like terms,
(f + g)(x) = 5x²– 8x² + 9x – 3x – 4 – 4
Simplifying it,
(f + g)(x) = -3x² + 6x – 8
Hence,
The expression for (f + g)(x) is -3x² + 6x – 8.
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Which statement best explains the importance of examining multiple perspectives about an event?
It reinforces a specific opinion about the event.
It determines which accounts are biased about the event.
It provides different and sometimes opposing viewpoints about an event.
It requires the use of both primary and secondary sources to learn about the event.
Answer:
It provides different and sometimes opposing viewpoints about an event.
The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges
52.8 30.6 43.2 45.8 33.3
33.3 50.5 44.0 42.0 37.8
Public Colleges
20.3 22.8 28.2 18.5 15.6 25.6
24.1 14.4 28.5 21.8 22.0 25.8
Required:
a. Compute the sample mean and sample standard deviation for private and public colleges.
b. What is the point estimate of the difference between the two population means?
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
Answer:
(a)
[tex]\bar x_1 =41.33[/tex] [tex]\sigma_1 = 7.48[/tex]
[tex]\bar x_2 =22.3[/tex] [tex]\sigma_2 = 4.53[/tex]
(b)
[tex]d = 19.03[/tex]
(c)
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
Step-by-step explanation:
Given
[tex]n_1 = 10\\ n_2 = 12[/tex]
And the accompanying data for private (1) and public (2) colleges
Solving (a): The sample mean and sample standard deviations
Private College
Calculating sample mean
This is calculated as:
[tex]\bar x_i = \frac{\sum x_i}{n_i}[/tex]
[tex]\bar x_1 =\frac{52.8+30.6+43.2 +45.8 +33.3+33.3 +50.5 +44.0 +42.0 +37.8}{10}[/tex]
[tex]\bar x_1 =\frac{413.3}{10}[/tex]
[tex]\bar x_1 =41.33[/tex]
Calculating sample standard deviation
This is calculated as:
[tex]\sigma_i = \sqrt\frac{\sum(x_i - \bar x_i)}{n_i-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{(52.8-41.33)^2+(30.6-41.33)^2+.........+(37.8-41.33)^2}{10-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{503.261}{9}[/tex]
[tex]\sigma_1 = \sqrt{55.9178888889[/tex]
[tex]\sigma_1 = 7.4778264816[/tex]
[tex]\sigma_1 = 7.48[/tex] -- approximated
Public College
Calculating sample mean
[tex]\bar x_2 =\frac{20.3 +22.8 +28.2 +18.5 +15.6 +25.6+ 24.1 +14.4 +28.5 +21.8 +22.0 +25.8}{12}[/tex]
[tex]\bar x_2 =\frac{267.6}{12}[/tex]
[tex]\bar x_2 =22.3[/tex]
Calculating sample standard deviation
[tex]\sigma_2 = \sqrt\frac{(20.3 -22.3)^2+(22.8 -22.3)^2+(28.2 -22.3)^2+(18.5 -22.3)^2+(15.6 -22.3)^2+................+(25.8-22.3)^2}{12-1}[/tex][tex]\sigma_2 = \sqrt\frac{225.96}{11}[/tex]
[tex]\sigma_2 = \sqrt{20.5418181818[/tex]
[tex]\sigma_2 = 4.532308262[/tex]
[tex]\sigma_2 = 4.53[/tex] -- approximated
Solving (b): Point estimate of the difference between the two population means
This is calculated as:
[tex]d = \bar x_1 - \bar x_2[/tex]
[tex]d = 41.33 - 22.3[/tex]
[tex]d = 19.03[/tex]
Solving (c): 95% confidence interval
First, calculate the degrees of freedom:
[tex]df = \frac{(\sigma_1^2/n_1 + \sigma_2^2/n_2)^2}{\frac{(\sigma_1^2/n_1)^2}{n_1 - 1} + \frac{(\sigma_2^2/n_2)^2}{n_2 - 1}}[/tex]
[tex]df = \frac{(7.48^2/10 + 4.53^2/12)^2}{\frac{(7.48^2/10)^2}{10 - 1} + \frac{(4.53^2/12)^2}{12 - 1}}[/tex]
[tex]df = \frac{53.3647}{31.3045/9 + 2.9244/11}[/tex]
[tex]df = \frac{53.3647}{3.7441}[/tex]
[tex]df = 14.2530[/tex]
[tex]df = 14[/tex]
Calculate the critical value (t)
At 95% confidence interval and df = 14;
[tex]df = 14[/tex]
The confidence interval is then calculated as:
[tex]CI = (\bar x_1 - \bar x_2) \± \sqrt{\sigma_1^2/n_1 + \sigma_2^2/n_2}[/tex]
[tex]CI = (41.33 - 22.3) \± \sqrt{7.48^2/10 + 4.53^2/12}[/tex]
[tex]CI = 19.03 \± \sqrt{7.305115[/tex]
[tex]CI = 19.03 \± 2.70[/tex]
Split
[tex]CI = 19.03 - 2.70[/tex] to [tex]19.03 + 2.70[/tex]
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
This implies that:
Private colleges have population mean annual cost of $16.33 to $21.73 more expensive than public colleges
What is the estimated volume of a figure with a length of 3cm, a height of 4cm, and a width that is approximately 2 times the height?
Step-by-step explanation:
Given
length(l)=3cm
height(h)=4cm
breath or width (b)=2×h=2×4=8cm
now it is a cuboid
volume of cuboid=l×b×h=3×8×4=96cm³
Answer:32,cm3
Step-by-step explanation:
Helpppsppspspspspsp plssss
Answer: About 804.25
Step-by-step explanation:
Do the inverse of the circumference formula and then take the radius and put it into the formula for the area of a circle
what is 2.7 kg in g. i need a simple answer
A ladder leans against the side of a house. The angle of elevation of the ladder is 68 , and the top of the ladder is 15 above the ground. Find the distance from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.
Answer:
6.06
Step-by-step explanation:
first draw a diagram, that'll make life easier,
then;
tan68 = opposite/adjacent
tan68 = 15/x
x = 15/tan68
x = 6.06
Pls help !! Pls no links :)
Answer:
A 5 <= A <= 40
Step-by-step explanation:
down point is (5, 50)
up point (40, 350)
so 5 <= A <= 40
HELP PLS DUE NOW BRAINLIEST AND A THANKS
Answer:
D
Step-by-step explanation:
The researcher did no prediction or any (possible)
Hope this helps :)
What is the area of the triangle?
Answer:
45
Step-by-step explanation:
9x10/2=45
since the great drought left the soil completely useless, the people of that country were forced to______ food from other countries
A. export
B. import
C. report on
D. sell
What is the answer?
Answer:
B import food from other countries
Evaluate the math problem
Answer:
b. 25
Step-by-step explanation:
The square root cancels out
and you divide only 100 and 4
Answer:
5 or 25
Step-by-step explanation:
I first got the 25 but when I tried a different formula to make sure it's correct I got 5.
What is m∠G to the nearest tenth? A right angle triangle EFG. The length of EF is 28.2 and GF is 45.8. Angle GFE is given as 90 degrees.
Answer:
31.6°
Step-by-step explanation:
The triangle given us a right angled Triangle
We solve the above question using the trigonometric function of Tangent
The formula is given as:
tan θ = opp/adj
θ = m∠G = ?
Opposite = EF is 28.2
Adjacent = GF is 45.8
tan θ = 28.2/45.8
θ = arc tan (28.2/45.8)
θ = 31.621459805°
Approximately
m∠G = 31.6°
Evaluate (−2)(−3)(−4)(−1)(−2)
Answer:
-48
Step-by-step explanation:
(-2)(-3)(-4)(-1)(-2)
(6)(-4)(-1)(-2)
(-24)(-1)(-2)
(24)(-2)
(-48)
How come the tutors don't work??
Answer:
What do you mean? If you are talking about the Community not always answering Questions well that means your they don't know the right Answer
the Mods are Annoying and very skeptic of the Guidelines of Brainly.
How many degrees and in what direction was the figure rotated?
90 degrees counterclockwise
180 degrees
90 degrees clockwise
Answer: 90 degrees clockwise
Step-by-step explanation:
A recipe calls for 2 1/2cups of flour to make 18 muffins. If someone needs to make 2 1/2 times the recipe, how much flour should the person use?
Enter the mixed number as your answer.
The person should use
(Simplify your answer.)
cups
Answer:
l''kkk 1/2 cups
Step-by-step explanation:
To make 45 muffins the amount of flour required will be 6.25.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a recipe calls for 2 1/2 cups of flour to make 18 muffins. If someone needs to make 2 1/2 times the recipe.
The amount of flour required will be calculated as:-
2 (1/2) flour ⇒ 18 muffins
2.5 flour ⇒ 18 muffins
2.5 x 2.5 flour ⇒ 2.5 x 18 muffins
6.25 flours ⇒ 45 muffins
Therefore, to make 45 muffins the amount of flour required will be 6.25.
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Aaron works at a furniture store. He sells a table that normally costs $670 but is on sale
for 15% off. If he makes 8% commission on
the sale price, how much will he make in
commission?
ASAP PLEASE HELP
WILL MARK BRAINLIEST
Answer:
A, B, and C All have four sides, and they all have opposite sides that are equal. B and C have right angels. A has angels on opposite side that are the same
Step-by-step explanation:
Activists say that the Brazilian government is not doing enough to stop the destruction of the Amazon rain forest. In 2004, the government reported the second-highest rate of destruction ever. Brazil's government estimates that farmers cut down 10,590 square miles (27,430 square kilometers) of rain forest. That is an area larger than Vermont, and it shows an increase from the deforestation of the previous year. In fact, the 2004 figure is nearly that of 1995, in which the Amazon lost a record 11,229 square miles (29,080 square kilometers) of trees. The activists are demanding that officials take the problem more seriously. Do It! The rain forest destruction seems to be _________. Press enter to interact with the item, and press tab button or down arrow until reaching the Submit button once the item is selected favorable relentless tiresome limited
Answer:
tiresome
Step-by-step explanation:
Common sense, if people are constantly complaining about an issue and then start to take a more aggressive approach towards things they would seem to be tiresome from all of the stress.
Find each missing measure
PLS HURRY WILL GIVE BRANLIEST. DON'T RESPOND WITH LINKS
Answer: 1 = 90 2=58 3=90 6=58 7=8
Step-by-step explanation:
I don’t know what 4 and 5 are
620 is invested in an account earning 5.5%interest APR, compounded quarterly. Write a function showing the value of the account after t years
Answer:
Y=620×((1+(0.055÷4))^(4t)
Step-by-step explanation:
Y=X ((1+(r/n))^(nt)
Y future value
X present value 620
R interest rate 0.055
N compound quarterly 4
T time
Height of 10th grade boys is normally distributed with a mean of 63.5 in. and a standard
deviation of 2.9 in.
The area greater than the Z-score is the probability that a randomly selected 14-year
old boy exceeds 70 in.
What is the probability that a randomly selected 10th grade boy exceeds 70 in.?
Answer:
P(Z>2.24) = P(70<X<1e99) = 1.25%
Step-by-step explanation:
Calculate Z-score:
Z=(x-μ)/σ
Z=(70-63.5)/2.9
Z=6.5/2.9
Z=2.24
Find area greater than Z-score:
P(Z>2.24) = P(70<X<1e99) = normalcdf(70,1e99,63.5,2.9) = 0.0125
So the probability that a randomly selected 10th-grade boy exceeds 70 inches is a 1.25% chance.
What is the constant rate of change shown in the table?
2
4
6
8
Answer:
2
Step-by-step explanation:
Since with every 10 seconds, the distance increase by 20 meters
hence, 20/10 = 2
If AABC ~ AEDC, find the value of x.
a. 32
5.8
C. 40
d. 15
Answer:
x = 15
Step-by-step explanation:
If ABC similar to EDC then we can use the similarity ratio to find the value of x
32/(3x-5) = 56/(5x-5) cross multiply the fractions
160x - 160 = 168x - 280 export like terms to the same side of the equation
280 - 160 = 168x - 160x
120 = 8x divide both sides by 8
15 = x
The diameter of a circle on
a coordinate plane has endpoints at (2,3) and (2,8) what is the approximate area of the circle
A. 16 units squared
B. 20 units squared
C. 25 units squared
D. 79 units squared
There are 6 balls in a bucket and 3 of them
are white. If you choose a ball at random,
what is the probability that it will not be
white?
Answer:
[tex] \frac{3}{6} [/tex]
A book has been discounted by 30%. It is on sale for $22.40. Find the original price.
3. A box containing 90 oz. of cereal cost $4.50. What is the price per ounce
Answer: 0.05$ per ounce
Step-by-step explanation:
Answer:0.05 per oz.
Step-by-step explanation: divide 4.50 by the oz