Smaller angle = 50
Larger angle = 130
Let smaller angle be x degree
=> larger angle= [tex]3x - 20[/tex]
Since these angles are supplementary , So
[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]
So smaller angle would be 50 deg & larger angle would be 130 deg.
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MAT 171
1. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-4
Find a possible formula for P(x)
2. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5, 36).
Find a formula for P(x).
3. The polynomial of degree 3. P(x), has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=-2. The y-intercept is y=-1.8.
Find a formula for P(x).
Using the Factor Theorem, the polynomials are given as follows:
1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Item a:
The parameters are:
[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
Item b:
The roots are:
[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
Item 3:
The roots are:
[tex]x_1 = x_2 = 3, x_3 = -2[/tex]
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
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How can the next term in the infinite sequence 1, 5, 12, 22, 35, be generated? O Square the term number, subtract the term number from the result, multiply by 3, and divide the result by 2. O Square the term number, multiply the result by 3, divide by 2, and subtract the term number from the result. O Square the term number, divide the result by 2, subtract the term number, and multiply the result by 3. O Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
Check the forward differences of the sequence.
• first-order differences
5 - 1 = 4
12 - 5 = 7
22 - 12 = 10
35 - 22 = 13
• second-order differences (i.e. differences of the first differences)
7 - 4 = 3
10 - 7 = 3
13 - 10 = 3
The second differences are all 3 (as far as we know), so the sequence of first differences is arithmetic/linear, which means the original sequence is quadratic. Let the [tex]n[/tex]-th term be
[tex]x_n = an^2 + bn + c[/tex]
Given that [tex]x_1=1[/tex], [tex]x_2=5[/tex], and [tex]x_3=12[/tex], we have
[tex]\begin{cases} a + b + c = 1 \\ 4a + 2b + c = 5 \\ 9a + 3b + c = 12 \end{cases} \implies a=\dfrac32, b=-\dfrac12, c=0[/tex]
and so the [tex]n[/tex]-th term of the sequence is generated by the rule
[tex]x_n = \dfrac{3n^2 - n}2[/tex]
which most closely resembles the last option,
Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
Find the nature of the graph of the function y = 9x4 + 8x - 2 using end
behavior.
the end behavior is:
as x ⇒ ∞, f(x) ⇒∞as x ⇒- ∞, f(x) ⇒∞What is the end behavior of the function?
If we have a polynomial of even degree, then the end behavior in both ends is the same one.
Particularly, in these cases (even degree) we only need to look at the leading coefficient. If it is positive, then as x tends to infinity and negative infinity, the function tends to infinity.
In this case, the polynomial is:
y = 9x⁴ + 8x - 2
Notice that the degree is 4, even, and the leading coefficient is 9 (positive).
Then the end behavior is:
as x ⇒ ∞, f(x) ⇒∞as x ⇒- ∞, f(x) ⇒∞If you want to learn more about end behaviors:
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....................
..................................
quest
The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On
which day would you expect that number to be reached?
D)
10
Days People
1
26
2
30
3
34
4
38
5
42
6 46
og php?totalQuestions-10&testid-5
strand-5716&element-18789&condition-random #
Answer:
Day 5 ................
The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries. 1 2 3 3 4 9 9 11 11 11 14 14 19 22 23 24 25 29
The range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
What is a Range?A range is given to a parameter to allow maximum leverage to the parameter. for example, if a vendor wants a rod of diameter 20 cm, then he may give a range of ±1 cm., which means he will accept the rod of 19(20-1) cm to 21(20+1) cm.
The range of the numbers of medals won by these countries is,
Range = Max - Min = 29 - 1 = 28
To find the standard deviation we need to know the following details,
Sum of the number of medals = ∑x = 234Sum of the square of the number of medals = ∑x² = 4372Number of observations = n = 18Now, the standard deviation of medals won by these countries is,
[tex]\sigma = \sqrt{\dfrac{\sum x^2 - \frac1n (\sum x)^2}{n-1}}\\\\\sigma = \sqrt{\dfrac{\4372 - \frac{234^2}{18}}{18-1}}\\\\\sigma = 8.845[/tex]
The variance of the numbers of medals won by these countries is,
v = σ²
v = 78.2353
Hence, the range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
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simplify completely 12x^2 -4x^2+8x over -2x
Answer:
-4*(x+1)
Step-by-step explanation:
Simplify
⇒ 8x2 + 8x/-2x
2: Pulling out like terms
4.1 Pull out like factors :
8x2 + 8x = 8x • (x + 1)
Canceling Out :
4.2 Canceling out x as it appears on both sides of the fraction line
Final result :
-4 • (x + 1)
Answer:
-4(x+1)
Step-by-step explanation:
factor out -2x
-2x(-6x + 2x - 4) / -2x
the -2x in numerator and denominator cancel out
-6x + 2x - 4
-4x - 1
-4(x+1)
Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region bounded by the line y =3x -6 and line y=-2x+8 is 12/5 units
How to find the area?y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6
Multiply and simplify.
y = 42/5 - 6
Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5
Subtract and simplify.
y = 12/5
These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
2x = 8
x = 4
The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
A = 1/2bh
Substitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)
A = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
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is y=6x-3 a function
Yes it is
Step-by-step explanation:
it is a linear function as it is written in the standard form Y=MX+C
Which of the following is the graph of y = -2√x-3+2?
I presume you meant [tex]y=-2\sqrt{x-3}+2[/tex].
The graph is shown in the attached image.
A cone has a volume of 350 cubic meters. The area of the base is 70 square meters. What is the height of the cone? Show work
Answer: The height is 15
Step-by-step explanation:
Vcone = pi * r^2 * h / 3
Area of the base = pi*r^2 = 70 so...
350 = 70 * h / 3
350 = (70/3) * h multiply both sides by 3/70
350 (3/70) = h = 15 m
What is the best estimate of the perimeter of the figure on the grid if each square has side lengths of 1 mm?
Answer:
4mm
Step-by-step explanation:
you have to add both sides after substituting each of the 4 sides by 1mm
which gives you the total of 4
y - wy = m (solve for w)
I need an answer ASAP.
answer:
w = (-m+y)/y
Step-by-step explanation:
y-wy = m
-wy = m-y
y = -(m-y)/w
wy= -m + y
w = (-m+y)/y
.
What is the approximate area of the shaded sector in the circle shown below
A.29.04 in^2
B.13.51 in^2
C.7.26 in^2
D.6.75^2
Answer:
please provide the diagram
Step-by-step explanation:
for the solution figure is necessary so provides us to solve this problem
rewrite the equation y-8=2 into slope form
Answer:
y=2x+16 is the slope intercept form
Step-by-step explanation:
sorry if its wrong tried!!!
Find domain and range of
f(x) = -x2 - 4x + 2
Answer:
domain is all reals
Step-by-step explanation:
sorry I couldn't find the range
Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.
Which is the equation for y?
Answer:
y = -t
Step-by-step explanation:
Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.
⇒ parametric equation of line passing through a point (a₁, b₁, c₁)
and parallel to a vector <a, b, c> is given by :
x =a₁ + at , y = b₁ + bt , z = c₁ + ct
now according to question:
given -
point, P(1, 0, -3)
line, x = −1 + 2t , y = 2−t, and z = 3+3t.
so from the line the vector is= <2, -1, 3>
now using above formula,
equation of line is = x = 1 + 2t , y = −t, and z = -3+3t.
we have to solve for 'y' only,
⇒ y = -t (answer)
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A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour. At 2 p.m., the amount of oil left in
the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 ounces.
Based on the average rate of oil burning per hour, how much oil, in ounces, was in the
lantern at 12 noon?
SHOW WORK!
Answer:
09
Step-by-step explanation:
09
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The rate at which the oil burns.
1 hour = 2/3 ounce
At 12 noon = 193/3 = 64.33 ounces
At 2 pm = 63 ounces
At 5 pm = 61 ounces
The amount of oil at 12 noon is 64.33 ounces.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.
At 2 p.m., the amount of oil left in the lantern is 63 ounces.
At 5 p.m., the amount of oil left in the lantern is 61 ounces.
This means,
Amount of oil burnt in the lantern from 2 pm to 5 pm.
= 63 ounces - 61 ounces
= 2 ounces
Now,
3 hours = 2 ounces
2 hours = 1.33 ounces
1 hour = 0.67 ounces
Now,
The number of hours from 12 noon to 2 pm.
= 2 hours
So,
The amount of oil at 12 noon.
= 63 + 4/3
= (189 + 4) / 3
= 193/3 ounces
Thus,
The amount of oil at 12 noon is 65 ounces.
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Help me please, geometry
Answer:
x = 19.5 (nearest tenth)
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angle
O is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Use the cos ratio to find the measure of the altitude (the perpendicular drawn from the vertex of the triangle to the opposite side):
[tex]\implies \cos(47^{\circ})=\dfrac{a}{18}[/tex]
[tex]\implies a=18\cos(47^{\circ})[/tex]
Now use the sin ratio to the the measure of side x:
[tex]\implies \sin(39^{\circ})=\dfrac{a}{x}[/tex]
[tex]\implies x=\dfrac{a}{\sin(39^{\circ})}[/tex]
[tex]\implies x=\dfrac{18\cos(47^{\circ})}{\sin(39^{\circ})}[/tex]
[tex]\implies x=19.50671018[/tex]
Therefore, x = 19.5 (nearest tenth)
the table shows the length of time in hours ,some children spent watching tv last week
The histogram of the distribution plotted on the y - axis and the interval for the length of time on the x - axis is attached below.
How to denote the histogram?The first bar denotes the length of time between 0 and 10 having a frequency of 8. The second bar denoted the interval between 10 and 15 with a frequency of 15
The third bar denoted the interval between 15 and 20 with a frequency of 10. The fourth bar denoted the interval between 20 and 30 with a frequency of 11
Therefore, the histogram of the distribution is attached below.
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Evaluate.
-|a+b| 2-c when a=1 2/3 b=-1 ,and c= -3 Enter your answer as a simplified fraction in the box.
Step-by-step explanation:
-| 12/3 - 1| 2-(-3)
-|12-3/3|5
-5|9/3|
-5|3|
-5×3 & -5×-3
-15 & 15
I think it is the answer
What is the following answer to 2+2
Answer:
well the answer is 4 have a good day
how many lines of symmetry does the following figure have ?
Answer:
1
Step-by-step explanation:
It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.
Answer: 1
College students (ages 18-26) tend to make decisions which are
tentative (more short-range) and support a desire for autonomy.
a result of a greater sense of commitment and stability.
more permanent choices.
College students (ages 18-26) tend to make decisions that are tentative (more short-range) and support a desire for autonomy. This depicts more permanent choices.
How to illustrate the information?
It should be noted that values are a compass that helps us make decisions and choices.
Choices characterize the stage of life we are in. For example 18-26 ages tend to make tentative choices, later 27-31 ages tend to make permanent choices, and ages 32-42 people make stable choices.
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A bag of 20 marbles consists of 5 blue marbles, 4 red marbles and 9 yellow marbles. You draw a marble out of the bag, put it back then draw out another marble. Calculate the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw? Write your answer a percentage to the nearest hundredth.
The probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total marbles = 20
Number of blue marbles = 5
P(blue) = 5/20
P(blue∩blue) = P(blue)×P(blue)
= (5/20)(5/20)
= 25/400
= 1/16
= 0.0625 ≈ 0.063
Thus, the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.
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A building casts a shadow of 40 feet on the ground. A wooden figure of a man is placed on the building and casts a shadow an additional 10 feet beyond the building's shadow. What is the height of the man?\
The height of the man from the given question is; 37.5 ft
How to solve trigonometric ratios?This question will form a triangle where;
Height of building = 30 ft
Height of man = h ft
Initial height of shadow = 40 ft
Additional height of shadow = 10 ft
Using similarity theorem, we have;
h/30 = (40 + 10)/40
h/30 = 5/4
h = (30 * 5)/4
h = 37.5 ft
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Recently, a random sample of 2534 year olds was asked, "How much do you currently have in savings, not including retirement savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings.
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively
How to determine the mean?The table of values is given as:
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Rewrite the table to include the class midpoint and the frequency
x f
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\bar x = 233.331775701[/tex]
Approximate
[tex]\bar x = 233.3[/tex]
Hence, the approximation of the mean is 233.3
How to determine the standard deviation?The standard deviation is calculated as:
[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\sigma = 229.82[/tex]
Hence, the approximation of the standard deviation is 229.82
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Larry Mitchell invested part of his $36,000 advance at 7% annual simple interest and the rest at 2% annual simple interest. If his total yearly interest from both
accounts was $1,970, find the amount invested at each rate.
The amount invested at 7% is $
The amount invested at 2% is $
The amount invested at each rate
Investment at 7% = $25000
Investment at 2% = $11,000
What is investment?Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation.
Given:
Larry Mitchell invested = $36,000 at 7% annual simple interest
the rest at 2% annual simple interest.
Total investment = 36000
let the investment at 7% is x
then, invested at 2% = 36000 - x
Total interest earned = $1,970
Simple interest = principal * rate * time
Investment at 4%:
(x * 0.07) + [(36000 - x) * 0.02] = 1970
0.07x + 720 - 0.02x= 1970
0.05x = 1970-720
0.05x = 1250
x= 25000
Hence,
Investment at 7% = $25000
Investment at 2% = $36,000 - $25000 = $11,000
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Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time.
The recursive function that gives the number of books Ashley has at any time is
=
, starting at
.
The recursive formula would be: 100 - XN = B.
What is Recursive formula?
When a function calls itself and uses its own previous terms to define its subsequent terms, it is called a recursive function. It is the technical recursive function’s definition, i.e., a recursive function builds on itself.
X: represents how many weeks
N: represents books per week
B: represents books she has at anytime
So the recursive formula would be: 100 - XN = B
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1) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches.
a)
What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
b)
If a random sample of twenty-six 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
c)
Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
!) The probability in part (b) is much higher because the mean is larger for the x distribution.
!!) The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
!!!) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
!!!!) The probability in part (b) is much higher because the mean is smaller for the x distribution.
!!!!!) The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
2) Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean = 66 and estimated standard deviation = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
a)
What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
b)
Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
!) The probability distribution of x is approximately normal with x = 66 and x = 45.
!!) The probability distribution of x is approximately normal with x = 66 and x = 22.50.
!!!) The probability distribution of x is approximately normal with x = 66 and x = 31.82.
!!!!) The probability distribution of x is not normal.
c) What is the probability that x < 40? (Round your answer to four decimal places.)
d) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
e) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
f) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?
Yes
NO
g) Explain what this might imply if you were a doctor or a nurse.
!) The more tests a patient completes, the weaker is the evidence for lack of insulin.
!!) The more tests a patient completes, the stronger is the evidence for lack of insulin.
!!!) The more tests a patient completes, the weaker is the evidence for excess insulin.
!!!!) The more tests a patient completes, the stronger is the evidence for excess insulin.
Answer:
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 4 inches.
(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
z1 = (70-71)/4 = -0.25
z2 = (72-71/4 = 0.25
P(70<X<72) = p(-0.25<z<0.25) = 0.1974
Answer: 0.1974
(b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
z1 = (70-71)/(4/sqrt(13)) = -0.9014
z2 = (72-71/(4/sqrt(13)) = 0.9014
P(70<X<72) = p(-0.9014<z<0.9014) = 0.6326
Answer: 0.6326
please mark me the brainiest
