Answer:
2
Step-by-step explanation:
Answer:
Use the distance formula to determine the distance between two points.
Exact Form:
2 √ 24041
Decimal Form:
310.10320862
Which of the following statements are correct when deciding whether to use the z or the t distribution?A. Use z when we have a normal population and we know the standard deviation B. Use t when the population is normal and the population standard deviation is not known
Using normal distribution concepts, we can conclude that the correct statement is:
B. Use t when the population is normal and the population standard deviation is not known
-------------------------
Both the z and the t distributions are for normal variables.If the population standard deviation is known, the z-distribution is used.If the population standard deviation is now known, only the sample standard deviation, the t-distribution is used.Option A is wrong as the standard deviation is know in both cases, only in one case it is the sample(t-distribution) and the other is the population(z-distribution).Thus, option B is correct.A similar problem is given at https://brainly.com/question/21774082
Getaway Travel Agency surveyed a random sample of 454545 of their clients about their vacation plans. Of the clients surveyed, 212121 expected that they would go on 333 vacations in the next year. There are 516516516 Getaway Travel Agency clients. Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 333 vacations in the next year? Choose 1 answer: Choose 1 answer:
Answer:
241 clients
Step-by-step explanation:
His problem can be solved using the principle of proportionality or rule three.
We can take advantage of the proportion between respondents who tell us the number of respondents and how many expect to go on vacation and the total number of workers, therefore:
Respondents /// Whole company
Vacations 21 x
Total 45 516
then x equals:
x = (516 * 21) / (45)
x = 240.8
x = 241 clients
This means that approximately 241 clients expect to go on vacation throughout the company.
Answer:
241
Step-by-step explanation:
its the answer for khan academy
hope this helps
AB and DE are chords that intersect at point F inside circle C as shown. If the measure of arc EA = 40° and the measure of arc DB = 70°.
What is the measure of ∠AFE?
Select one or more:
a. 700
b. 400
c. 1250
d. 550
Answer:
[tex]d) \ 55\textdegree[/tex]
Step-by-step explanation:
-we apply the relationship of chords intersecting within a circle:
-when two chords intersect to form a vertex of an angle within a circle, the measure of the angle is equal to one-half the sum of the measures of the two arcs intercepted by the angle and its vertical angle:
[tex]\angle AFE=0.5(arc\ EA +arc \ BD)\\\\=0.5(40+70)\\\\=55\textdegree[/tex]
Hence, the measure of ∠AFE is 55°
A good rule of thumb is to design the horizontal stabilizer so that its area is about 1/6 to 1/8 of the area of the wing. If the area of the wing is 101.25 cm2, which of the following would be a good horizontal stabilizer design?
answer choices:
Stabilizer with area = 32 cm2.
Stabilizer with area = 20 cm2.
Stabilizer with area = 14 cm2.
Stabilizer with area = 11 cm2.
650grams= how many kg
Answer:
0.65 kilograms
Step-by-step explanation:
Answer:
0.65 kg
Step-by-step explanation:
[tex] \because \: 1 \: gram = \frac{1}{1000} kg \\ \\ \therefore \: 650 \: grams = \frac{650}{1000} \\ \\ \red{ \boxed{\bold {\therefore \: 650 \: grams =0.65 \: kg} }}[/tex]
The Students at Winwood elementary school collected 574 cans of food in 20 days for a food drive. What was average number of cans of food collected each day
Answer:
About 29
Step-by-step explanation:
575 cans of food / 20 days = About 28.75 cans a day, rounded to 29.
Answer:
28.7 cans
Step-by-step explanation:
We want to find the unit rate for cans per day
To find this, divide the number of cans by the number of days
cans/days
574/20
28.7
About 28.7 cans per day
The first artificial satellite to orbit Earth was Sputnik I, launched by the Soviet Union in 1957. The orbit was an ellipse with Earth's center as one focus. The orbit's highest point above Earth's surface was 583 miles, and its lowest point was 132 miles.a) find an equation of the orbit.b) how far from Earth is the other focus?c) What is the length of the major axis?
Answer:
A) (x²/127806.25) + (y²/76956) = 1
B) 451 miles
C) 715 miles
Step-by-step explanation:
Center is at (0,0) and focus is at (c,0) while vertex is at (a,0)
Thus, a - c = 132 miles
and a + c=583 miles
Adding both equations together, we have;
2a= 715 miles
Thus, a = 715/2
a = 357.5 miles
Since a+c=583
Thus, c = 583-357.5 = 225.5 miles
Now, for an ellipse it is defined by; a² = b² + c²
a² = 357.5² = 127806.25
c² = 225.5² = 50850.25
So, b² = 127806.25 - 50850.25
b² = 76956
b = √76956
b = 277.409
A) Equation of tangent to ellipse which is equation of orbit would be;
(x²/a²) + (y²/b²) = 1
Thus,
(x²/127806.25) + (y²/76956) = 1
B) distance between the earth and the other focus is = 2c = 2 x 225.5 = 451 miles
C) Length of other major axis = 2a = 2 x 357.5 = 715 miles
a) The equation of the orbit is \(\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\). b) The distance from the center to the other focus is calculated using the formula \(c = \sqrt{(583+3963)^2 - 132^2}\). c) The length of the major axis is \(2(583+3963)\).
Explanation:a) To find an equation of the orbit, we can use the standard form equation for an ellipse:
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\] where \((h,k)\) represents the center of the ellipse, \(a\) represents the distance from the center to the vertices along the major axis, and \(b\) represents the distance from the center to the co-vertices along the minor axis. In this case, the center of the ellipse is the Earth's center, which is at the origin \((0,0)\). The highest point of the orbit is 583 miles above the Earth's surface, so the distance from the center to the vertices along the major axis is 583 miles + the radius of the Earth. The radius of the Earth is approximately 3963 miles. The lowest point of the orbit is 132 miles above the Earth's surface, so the distance from the center to the co-vertices along the minor axis is 132 miles. Substituting the values into the equation:
\[\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\]
b) The distance from the center to the other focus can be found using the relationship \(c = \sqrt{a^2 - b^2}\), where \(c\) represents the distance from the center to the foci. Substituting the values into the equation:
\[c = \sqrt{(583+3963)^2 - 132^2}\]
c) The length of the major axis can be found using the formula \(2a\), where \(a\) represents the distance from the center to the vertices along the major axis. Substituting the values into the equation:
\[2a = 2(583+3963)\]
A six-pack of soda is on sale for 2.46. Find the cost of one can of soda and drop the appropriate value into the answer blank.
$0.41
$0.50
$0.45
$0.38
Answer:
$0.41
Step-by-step explanation:
Take the total cost and divide by the number of cans
2.46/ 6
.41
The price is 41 cents per can or$.41
A convenience sample of forty people is taken from a population. Which of the following is a reason why you can not make a statistical inference on the population?
The sample size is not large enough.
The population isn’t given to be approximately normal.
The sample is not given to be normally distributed.
The wrong sampling method was used.
Answer:
The wrong sampling method was used.
Step-by-step explanation:
In convenience sampling, first few responses are considered and not all parameters are considered. This is the easiest method of sampling but least effective
(D) The wrong sample method was used.
Sample:The term 'sample' can mean -
A sample is a statistical term for a portion of a population.A digital discrete sample of a continuous analog signal is called a sample (signal).A sample, a specimen, or a little amount of anything.An illustration showing the meeting point of a color channel and a pixel.Sample history is an abbreviation for the questions that emergency medical personnel should ask.A product sample is a small amount of a consumer good that is provided to a customer so that they can test it out before making a purchase.Statistics:The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. Populations can refer to a variety of groupings of individuals or things, such as "every individual living in a nation" or "each atom making up a crystal." Every facet of data, including the planning of data collecting in terms of the layout of surveys and experiments, is covered by statistics.Therefore, the correct answer if the problem is (D) the wrong sample method was used.
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Ten less than a number is three more than six times the number.
Write it as an equation:
X - 10 = 6x + 3
Now solve for x:
Subtract 3 from both sides:
x-13 = 6x
Subtract 1 x from both sides:
-13 = 5x
Divide both sides by 5:
x = -13/5
Answer:
x = -2.6.
Step-by-step explanation:
Let the number be x, then:
x - 10 = 6x + 3
x - 6x = 3 + 10
-5x = 13
x = -13/5
= -2.6.
n^2-5n-24
show all work
Answer:
-3,8
Step-by-step explanation:
1) we can factor this since this quadratic function is in the form of
ax^2+bx+c
where we need to find out what*what=c
and what+what=b
since c is -24 and b is -5 we need to figure out the factors of -24 which equal -5:
-8+3=-5
and
-8*3=-24
hence -8 and 3 is our factors, next we will substitute them in place of "b"
so
n^2-8n+3n-24
split this equation in two groups:
group 1) n^2-8n
group 2) 3n-24
gcf of group 1= n
so
n(n-8)
gcf of group 2: 3
so
3(n-8)
next take numbers outside of parentheses and group them together:
so (n+3) (n-8)=0
since anything times 0 is equal to 0, either (n+3) is 0 or (n-8) is 0
so
n+3=0
n=-3
n-8=0
n=8
hence n=-3,8
Hope this helps!
What is the following product?
Answer:
b
Step-by-step explanation:
The square root of b times the square root of b is simply b.
b^(1/2)*b^(1/2) = b^1 = b
Somebody please help me with this
A box contains three plain pencils and 5 pens. A second box contains three colored pencils and three crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon form the second box are selected?
Answer:
Therefore the probability that a pen from the first box and a crayon from the second box are selected is [tex]\frac5{16}[/tex]
Step-by-step explanation:
Probability:
The ratio of the number of favorable outcomes to the number all possible outcomes of the event.
[tex]Probability=\frac{\textrm{The number favorable outcomes}}{\textrm{The number all possible}}[/tex]
Given that,
Three plain pencils and 5 pens are contained by the first box.
Total number of pens and pencils is =(3+5)=8
The probability that a pen is selected from the first box is
=P(A)
[tex]=\frac{\textrm{The number pens}}{\textrm{Total number of pens and pencils}}[/tex]
[tex]=\frac{5}{8}[/tex]
A second box contains three colored pencils and three crayons.
Total number of pencils and crayons is =(3+3)=6
The probability that a crayon is selected from the second box is
=P(B)
[tex]=\frac{\textrm{The number of crayon}}{\textrm{Total number of crayons and pencils}}[/tex]
[tex]=\frac{3}{6}[/tex]
Since both events are mutually independent.
The required probability is multiple of the events
Therefore the required probability is
[tex]=\frac58\times \frac36[/tex]
[tex]=\frac5{16}[/tex]
An employee joined a company in 2009 with a starting salary of $50,000. Every year this employee receives a raise of $1000 plus 5% of the salary of the previous year.
a) Set up a recurrence relation for the salary of this employee n years after 2009.
b) What will the salary of this employee be in 2017?
c) Find an explicit formula for the salary of this employee n years after 2009.
Answer:
(a) The required recurrence relation for the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].
(b)The salary of the employee will be $83421.88 in 2017.
(c) [tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]
Step-by-step explanation:
Summation of a G.P series
[tex]\sum_{i=0}^n r^i= \frac{r^{n+1}-1}{r-1}[/tex]
(a)
Every year the salary is increasing 5% of the salary of the previous year plus $1000.
Let [tex]a_n[/tex] represents the salary of the employee of n years after 2009.
Then [tex]a_{n-1}[/tex] represents the salary of the employee of (n-1) years after 2009.
Then [tex]a_n= a_{n-1}+5\%.a_{n-1}+1000[/tex]
[tex]=a_{n-1}+0.05a_{n-1}+1000[/tex]
[tex]=(1+0.05)a_{n-1}+1000[/tex]
[tex]=1.05a_{n-1}+1000[/tex]
The required recurrence relation for the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].
(b)
Given, [tex]a_0=\$50,000[/tex]
[tex]a_n=1.05a_{n-1}+1000[/tex]
Since 2017 is 8 years after 2009.
So, n=8.
∴ [tex]a_8[/tex]
[tex]=1.05 a_7+1000[/tex]
[tex]=1.05(1.05a_6+1000)+1000[/tex]
[tex]=1.05^2a_6+1.05\times 1000+1000[/tex]
[tex]=1.05^2(1.05a_5+1000)+1.05\times 1000+1000[/tex]
[tex]=1.05^3a_5+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^3(1.05a_4+1000)+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^4a_4+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^4(1.05a_3+1000)+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^5a_3+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^5(1.05a_2+1000)+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^6a_2+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^6(1.05a_1+1000)+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^7a_1+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^7(1.05a_0+1000)+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^8a_0+1.05^7\times1000+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^8a_0+(1.05^7+1.05^6+1.05^5+1.05^4+1.05^3+1.05^2+1.05+1)1000[/tex]
[tex]=1.05^8 \times 50,000+\frac{1.05^8-1}{1.05-1}\times 1000[/tex]
[tex]=1.05^8\times 50,000+20,000(1.58^8-1)[/tex]
[tex]=70,000\times 1.05^8-20,000[/tex]
≈$83421.88
The salary of the employee will be $83421.88 in 2017.
(c)
Given, [tex]a_0=\$50,000[/tex]
[tex]a_n=1.05a_{n-1}+1000[/tex]
We successively apply the recurrence relation
[tex]a_n=1.05a_{n-1}+1000[/tex]
[tex]=1.05^1a_{n-1}+1.05^0.1000[/tex]
[tex]=1.05^1(1.05a_{n-2}+1000)+1.05^0.1000[/tex]
[tex]=1.05^2a_{n-2}+1.05^1.1000+1.05^0.1000[/tex]
[tex]=1.05^2(1.05a_{n-3}+1000)+(1.05^1.1000+1.05^0.1000)[/tex]
[tex]=1.05^3a_{n-3}+(1.05^2.1000+1.05^1.1000+1.05^0.1000)[/tex]
...............................
.................................
[tex]=1.05^na_{n-n}+\sum_{i=0}^{n-1}1.05^i.1000[/tex]
[tex]=1.05^na_0+1000\sum_{i=0}^{n-1}1.05^i[/tex]
[tex]=1.05^n.50,000+1000.\frac{1.05^n-1}{1.05-1}[/tex]
[tex]=1.05^n.50,000+20,000.(1.05^n-1)[/tex]
[tex]=(50,000+20,000)1.05^n-20,000[/tex]
[tex]=70,000 . \ 1.05^n-20,000[/tex]
[tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]
The employee’s salary is dictated by the recurrence relation where S_n = S_(n-1) + 1000 + 0.05*S_(n-1). This formula is used to iteratively calculate the salary increase each year, providing an accurate salary for any given year after 2009. However, an explicit formula for this scenario may not be straightforward due to the increment's dependency on the previous year's salary.
Explanation:The subject of this problem is recurrence relation, a mathematical concept that uses a formula to establish the relationship between successive terms in a numerical sequence. The employee's salary problem can be expressed by the following recurrence:
Part a)
S_n = S_(n-1) + 1000 + 0.05*S_(n-1), where S_n represents the salary in year n and S_(n-1) refers to the prior year's salary.
Part b)
To calculate the salary in 2017, you start with the initial salary in 2009 and apply the formula for each subsequent year. After doing this for 8 years (2017 being 8 years past 2009), the salary is found to be $60,796.32.
Part c)
Unfortunately, a simple explicit formula may not exist for this scenario because of percentage increment based on the previous year's salary. However, the salary can be accurately calculated for any given year using the recurrence relation established in Part (a).
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A rectangle has a lenght that is 9 inches less than twice its width. The area of the rectangle is 180 square inches. What is the width of the rectangle?
Answer:
12 inches
Step-by-step explanation:
In this question, we are asked to calculate the width of a rectangle having a length 9 inches less than twice it’s width and given the area of the rectangle.
First, we identify that the length is 9 inches less than twice the width
meaning if length is l and width is w; then l = (2w-9) inches
Mathematically the area of the rectangle is l * w ; meaning w * (2w-9)
This has a value equal to 180
w * (2w-9) = 180
opening the bracket;
2w^2 -9w = 180
2w^2 -9w - 180 = 0
solving this quadratic equation;
w = 12 or -7.5
since width cannot be negative, w = 12 inches
Answer:
The width of the triangle is 18.65 inches
Step-by-step explanation:
From the question, we have;
Length, L = Width, W - 9
Also the area is given by
L × W = 180
Therefore, we have
(W - 9) × W= 180
W² - 9·W = 180
W² - 9·W - 180 = 0
Factorizing or solving with quadratic formula
[tex]\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
a = 1
b = -9 and
c = -180
we get
(W + 9.65)(W-18.65) =0
Therefore W = - 9.65 or 18.65
Therefore, the Width, W = 18.65 and the length = W - 9 = 18.65 - 9 =9.65
The width of the triangle = 18.65 inches.
Josie is training for a race. The ratio of the number minutes she runs to the number of miles she runs is 24 to 3 She plans to run 10 miles. How many minutes will it take her?
Answer:
80 minutes
Step-by-step explanation
24/3=8
8mins/1 mile
8 minsx10 miles= 80 mins for 10 miles
Hello, please look at the attachment and do the following :
A) Complete the ven diagram. ( what number goes in the middle and what number goes to the bottom left of the diagram out of the circle?).
B) How many students study only french
C) How many students learn spanish
Answer:
F25 A B S14 BOTH S AND F IS 32IN THE MIDDLE
Step-by-step explanation:
14 study Spanish, 25 study French.
71 total students - 14 - 25 = 32
A 32 would be put in the middle where the circles overlap, which means 32 students are studying both languages.
B) only French would be the 25 shown in the circle marked F
C) 14 + 32 = 46 total students study Spanish
What is f(−2) for f(x) = 3x−5
Step-by-step explanation:
Given
f(x) = 3x - 5
f(-2) = 3 * (-2) - 5
= -6 -5
= - 11
Answer:
f(×)=
Step-by-step explanation:
[tex] f(- 2 )= 3( - 2) - 5 [/tex]
[tex] - 2 = - 6 - 5[/tex]
[tex] - 2 = - 11[/tex]
Select the correct answer.
Sam's height is 15 centimeters less than 2 times Martha's height. If Sam Is 185 centimeters tall, and Martha's height is x, the relationship
between the heights can be represented by the equation 2x - 15 = 185. What Is Martha's height?
A 90
B. 95
°C 100
D. 105
Reset
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Answer:
C. 100 cm
Step-by-step explanation:
2x-15=185
+15 +15
2x=200
/2 /2
x=100
This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane.
xxx yyy
-79−79minus, 79 -68−68minus, 68
-68−68minus, 68 -51−51minus, 51
-57−57minus, 57 -34−34minus, 34
What is the xxx-intercept of the line?
Answer:
(-35, 0)
step-by-step explanation:
The x-intercept of the line does not exist.
Explanation:The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept, we need to look for a point on the graph where y is equal to zero. Based on the given table, there is no pair of coordinates where the y value is equal to zero. Therefore, the line does not intersect the x-axis and the x-intercept does not exist.
Shelly buys desk to sell in her furniture store. She marks up the price by 35% and sells the desk for $290.25. What price did Shelly pay for the desk.
Answer:
Shelly paid $215 for the desk
Step-by-step explanation:
In this question, we are asked to calculate the price a particular desk was bought given the price at which it was sold and the percentage of profit associated with the sales of the desk. In other words, we are calculating the cost price
Mathematically,
% profit = (selling price - cost price)/cost price * 100%
Our percentage profit here is 35% and our selling price is $290.25, we are left with calculating the selling price. let’s input these values into the equation;
Before that, let’s say the cost price is $x
35 = (290.25-x)/x * 100
100(290.25-x) = 35x
29025 -100x = 35x
135x = 29025
x = 29025/135
x = $215
In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of _______.
2a is used in the equation because the _______ is a point on the hyperbola and it is the difference in the distances from this point to the foci.
This can be shown algebraically if we let a be the distance from the ______ to the vertex. Then, the difference of the distances is (c + a) – _______.
Answer:
1. 2a
2. Vertex
3. Center
4. (c-a)
Step-by-step explanation:
The missing black in the paragraph will be 2a, vertex, center, and (c – a).
What is a hyperbola?The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of 2a.
2a is used in the equation because the Vertex is a point on the hyperbola, and it is the difference in the distances from this point to the foci.
This can be shown algebraically if we let a be the distance from the Center to the vertex. Then, the difference of the distances is (c + a) – (c – a).
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A football selling for 35% off the original price the original price was 60 what is a sales price of the football
Answer:
Sales Price = $21.00
New Price = $39.00
Step-by-step explanation:
Convert 35% into a decimal and multiply that with the $60.00. After you get the product, which is $21.00, you then need to subtract $21.00 from $60.00 and that gets you $39.00.
A store offers 20% off all items. If x is the original purchase price, which expression represents the final price
with the discount? Select all that apply.
O
A 1.2x
B. 0.8x
X-0.2x
EX+0.2x
Answer:
0.2x
Step-by-step explanation:
Answer:
0.2x---------------------------------------------------------------------------------------
Which of the following is the inverse of y = 3 Superscript x?
The one that is an the inverse of y = 3 Superscript x is y = 3x is f-1(x) = 1/3x.
What is the inverse about?The use of the idea of inverse function to look for the solution is given below:
Note that, y = 3x
Then let f(x) = y = 3x
One will need to Switch x and y and as such, x = 3y
Then one should express y in terms of x and as such, y = 1/3 x
Since f(x) = y ⇒ x = f-1(y)
Then f-1(y) = 1/3x
Therefore, the inverse of y = 3x is f-1(x) = 1/3x.
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Find the measure of an angle whose supplement is sixteen times its complement. Hint: Supplement and complement of an angle are (180-0) and (90-0) respectively.
Answer:
The angle is 84 degrees
Step-by-step explanation:
Let's call the angle by 'x'.
the supplement of x is equal to 180-x, and the complement of x is equal to 90-x.
If the supplement is sixteen times the complement, we can write the following equation:
(180 - x) = 16 * (90 - x)
180 - x = 1440 - 16x
16x - x = 1440 - 180
15x = 1260
x = 84
The angle is 84 degrees.
Answer:
84⁰
Step-by-step explanation:
Complement = 90 - x
Supplement = 180 - x
Given:
180 - x = 16(90 - x)
180 - x = 1440 - 16x
15x = 1260
x = 84
A ball is thrown into the air with an initial upward velocity of 46 ft/s. Its height (h) in feet after t seconds is given by the function h equals negative 16 t squared plus 46 t plus 6. After how many seconds will the ball hit the ground? A. 3 B. 4 C. 5 D. 6
Answer:
t = 3 seconds
Step-by-step explanation:
This is a quadratic equation. First set it up and set it equal to 0 (the ground).
-16t² + 46t + 6 = 0
The quadratic formula is (-b ± √(b² - 4ac))/2a
a= -16
b = 46
c = 6
Plug those numbers into the equation and solve which will result in -.125 or 3.
The time of course can not be negative in this case. Therefore, t=3 seconds.
The ball will hit the ground after 3 seconds.
Explanation:The problem deals with the quadratic equation representing the motion of the ball. When the ball hits the ground, the height (h) is 0. So, we need to solve the equation -16t^2 + 46t + 6 = 0 for (t). The roots of this quadratic equation can be found using the quadratic formula, t = [-b ± sqrt(b^2 - 4ac)]/2a. Substituting a=-16, b=46, and c=6 into the formula, you will find the solutions are t = 3 seconds and t = -0.375 seconds. Therefore, the ball will hit the ground after 3 seconds. The correct choice is A. 3.
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Solve for r 4r + 8 = 7.2 + 5r
Answer: r=0.8
Step-by-step explanation:
4r + 8 = 7.2 + 5r
-4r -4r
8=7.2+r
8-7.2=r
0.8=r
Answer: [tex]r=0.8[/tex]
Step-by-step explanation:
-Solve:
[tex]4r+8=7.2+5r[/tex]
-Subtract [tex]5r[/tex] from both sides:
[tex]4r+8-5r=7.2[/tex]
Combine [tex]4r[/tex] and [tex]5r[/tex] to get [tex]-r[/tex]:
[tex]-r+8=7.2[/tex]
-Subtract [tex]8[/tex] from [tex]7.2[/tex] to get [tex]-0.8[/tex]:
[tex]-r=7.2-8[/tex]
[tex]-r=-0.8[/tex]
-Multiply both sides by [tex]-1[/tex]:
[tex]r=0.8[/tex]
-Result:
[tex]r=0.8[/tex]
Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis. Region R is rotated about the line y=-2. Find the volume of Region R after being rotated.
The volume of rotation of region R is [tex]192\pi[/tex] cubic units.
Given information:
Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis.
Region R is rotated about the line y=-2.
So, the region R is a rectangle with length 6 units (x=0 to x=6), and the height of the rectangle is 4 units (y=0 to y=4).
After rotating this rectangle about y=-2, we will get a hollow cylinder.
The outer radius of the cylinder will be,
[tex]R=4-(-2)=6[/tex]
The inner radius of the cylinder will be,
[tex]r=0-(-2)=2[/tex]
And the length of the cylinder is 6 units.
So, the volume of the solid formed after the rotation will be,
[tex]V=\pi R^2L-\pi r^2L\\V=\pi L(R^2-r^2)\\V=\pi \times 6(6^2-2^2)\\V=\pi\times 6 \times 32\\V=192\pi[/tex]
Therefore, the volume of rotation of region R is [tex]192\pi[/tex] cubic units.
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To find the volume of the solid formed by rotating region R about the line y=-2, we use the washer method which results in a volume of 216π cubic units.
Explanation:The problem involves calculating the volume of a solid of revolution, which is formed when a two-dimensional region is rotated around a line that does not intersect the region.
Region R is defined as the area bounded by y=4, x=6, the y-axis, and the x-axis. The volume of the solid formed by rotating this region around the line y=-2 can be calculated using the washer method, which involves integrating over the area of concentric washers.
The general formula for the volume V of a washer is given by V = π∫[R2(x) - r2(x)]dx , where R(x) and r(x) are the outer and inner radii of the washers, respectively. In this case, the outer radius is R(x) = 4 - (-2) = 6 and the inner radius is r(x) = -2 - (-2) = 0.
Therefore, the volume V is:
V = π∫06[62 - 02 ]dx = π∫0636dx = 36π∫06dx = 36π[6] = 216π cubic units.