Answer:
3
Step-by-step explanation:
Find the raised power (exponent) that is greatest in value in order to find the degree of a polynomial. In this example, the highest power is 3, so that is the degree of the polynomial.
hope this helps!
The average cost of 2 storybooks was 2.45. One of the books cost 2.80. Find the cost of the other book
Answer:
The answer is simply 26,25/3 which gives that each book costed 8,75 dollars assuming of course that all books have the same price.
Paul has a standard deck of cards. What is the probability that he will choose a 2?
Answer:
Step-by-step explanation:
The deck is divided into 4 different kinds of cards
clubsdiamondsHeartsSpadesEach kind of card has a 2
So there are 4 twos in a standard deck of cards.
Answer:
P(2) = 4/52P(2) = 1/13P(2) = 0.07692NO LINKS!!!! Exponential Growth and Decay Part 2
Problem 4
a = 10800 = initial populationb = 1 + r = 1 + (-0.025) = 0.975 is the decay factorThe template of [tex]y = a*b^x[/tex] becomes [tex]y = 10800*0.975^x[/tex] to represent the exponential function.
x = number of years since 2002y = populationWe want to know when the population reaches half of 10800, so we want to know when the population is 10800/2 = 5400
Plug in y = 5400 and solve for x.
[tex]y = 10800*0.975^x\\\\5400 = 10800*0.975^x\\\\0.975^x = 5400/10800\\\\0.975^x = 0.5\\\\\log(0.975^x) = \log(0.5)\\\\x\log(0.975) = \log(0.5)\\\\x = \log(0.5)/\log(0.975)\\\\x \approx 27.377851\\\\x \approx 28\\\\[/tex]
I rounded up to the nearest whole number because x = 27 leads to y = 5452, which is not 5400 or smaller.
Luckily, x = 28 leads to y = 5315 which gets over the hurdle of being 5400 or smaller.
Add 28 years onto the starting year 2002 and we get to 2002+28 = 2030
The population reaches half of its original amount in the year 2030.
Answers:The exponential function is [tex]y = 10800*0.975^x[/tex]It takes 28 years to get to half the population. This occurs in the year 2030============================================================
Problem 5
a = 28750 = starting value for the carb = 1 + r = 1 + (-0.12) = 0.88 = decay factorIf the car loses 12% of its value each year, then it keeps the remaining 88%
Plug those values into [tex]y = a*b^x[/tex].
We find the equation is [tex]y = 28750*0.88^x[/tex] where,
x = number of years since 2012y = car's valueReplace y with 10,000 and solve for x.
[tex]y = 28750*0.88^x\\\\10000 = 28750*0.88^x\\\\0.88^x = 10000/28750\\\\0.88^x \approx 0.347826\\\\\log(0.88^x) \approx \log(0.347826)\\\\x\log(0.88) \approx \log(0.347826)\\\\x \approx \log(0.347826)/\log(0.88)\\\\x \approx 8.261168\\\\x \approx 9\\\\[/tex]
Like in the previous problem, we round up so we clear the hurdle.
Adding 9 years onto 2012 gets us to 2012+9 = 2021
Answers: The function is [tex]y = 28750*0.88^x[/tex]It takes about 9 years, and it occurs in the year 2021Answer:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Question 4Given:
a = 10,800b = decrease of 2.5% = 0.975x = time (in years)y = populationAs the population is decreasing by 2.5% each year, the population will be 100% - 2.5% = 97.5% of the previous year. Therefore, the base is 0.975.
Final equation: [tex]\large \text{$ y=10800(0.975)^x $}[/tex]
Half of population: 10800 ÷ 2 = 5400
[tex]\large \begin{aligned}y & =5400\\\implies 10800(0.975)^x & =5400\\(0.975)^x & = \dfrac{5400}{10800}\\(0.975)^x & = 0.5\\\ln (0.975)^x & = \ln 0.5\\x \ln 0.975 & = \ln 0.5\\x & = \dfrac{\ln 0.5}{\ln 0.975}\\x & = 27.377785123\end{aligned}[/tex]
2002 + 27.37785... = 2029.37785...
Therefore, the population will reach half during 2029 (by 2030).
Question 5Given:
a = 28,750b = decrease of 12% = 0.88x = time (in years)y = value (in dollars)As the value is decreasing by 12% each year, the value will be 100% - 12% = 88% of the previous year. Therefore, the base is 0.88.
Final equation: [tex]\large \text {$ y=28750(0.88)^x $}[/tex]
Find when the car is worth $10,000:
[tex]\large \begin{aligned}y & = 10000\\\implies 28750(0.88)^x & = 10000\\(0.88)^x & = \frac{10000}{28750}\\(0.88)^x & = \frac{8}{23}\\\ln (0.88)^x & =\ln \left(\frac{8}{23}\right)\\x \ln (0.88) & =\ln \left(\frac{8}{23}\right)\\x & =\dfrac{\ln \left(\frac{8}{23}\right)}{\ln (0.88)}\\x & = 8.26116578\end{aligned}[/tex]
2012 + 8.26116578.. = 2020.26116578..
Therefore, the value of the car will reach $10,000 during 2020 (by 2021).
What is the solution to the given inequality? 1/2-1/4x>-1/4
Answer:
x ≤ 3
Step-by-step explanation:
[tex]\dfrac{1}{2}-\dfrac{1}{4}x \geq -\dfrac{1}{4}[/tex]
Subtract 1/2 from both sides:
[tex]\implies \dfrac{1}{2}-\dfrac{1}{4}x-\dfrac{1}{2} \geq -\dfrac{1}{4}-\dfrac{1}{2}[/tex]
[tex]\implies -\dfrac{1}{4}x \geq -\dfrac{3}{4}[/tex]
Multiply both sides by 4:
[tex]\implies -\dfrac{1}{4}x \cdot 4 \geq -\dfrac{3}{4} \cdot 4[/tex]
[tex]\implies -x \geq -3[/tex]
Divide both sides by -1 (remembering to flip the sign):
[tex]\implies \dfrac{-x}{-1} \geq \dfrac{-3}{-1}[/tex]
[tex]\implies x \leq 3[/tex]
Can some one help me???
The unknown sides of the right angle triangle using trigonometric ratios are as follows;
PR = 13.2 units
RQ = 17.6 units
What is a right angle triangle?
A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sides of the triangle can be found using trigonometric ratios.
Therefore,
sin 37° = opposite / hypotenuse
sin 37° = PR / 22
cross multiply
PR = 22 sin 37
PR = 22 × 0.60181502315
PR = 13.2399305093
PR = 13.2 units
cos 37 = adjacent / hypotenuse
cos 37 = RQ / 22
RQ = 22 cos 37
RQ = 17.569981221
RQ = 17.6 units
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What is the value of x in the equation 5x+ 3 = 4x?
A.-3
B.- 1/3
C.1/3
D.3
Answer:
-3
Step-by-step explanation:
5•-3=-15
4•-3=-12
-15+3=-12
Find the 60th term of the following sequence.
8, 16, 24. ...
Answer:
Step-by-step explanation:
Remark
You want the 60th term of the arithmetic (?) sequence given.
Formula
L = a + (n - 1)*d
Givens
L = ?
a = 8
d = 8
n = 60
Solution
L = 8 + (60 - 1)*8
L = 8 + 60*8 - 8
L = 480
Answer
The 60th term is 480
Answer:
Step by step explanation :
As we know
[tex]\:\bf\boxed{an\:=\:a\:+\:(n\:-\:1)\:d}[/tex]
where,
an = the nth term in the sequence
n = the term
d = common difference
a = first term of the AP.
Here,
an = a60
n = 60
d = 16 - 8 = 8
a = 8
Now,
[tex]\:\mathsf{a60\:=\:8\:+\:(60\:-\:1)(8)}[/tex]
=> [tex]\:\mathsf{a60\:=\:8\:+\:(59)(8)}[/tex]
=> [tex]\:\mathsf{a60\:=\:8\:+\:472}[/tex]
=> [tex]\:\bf{a60\:=\:480}[/tex]
Therefore the 60th term of the AP is 480.
Which of these expressions can be used to calculate the monthly payment for
a 30-year loan for $195,000 at 6.6% interest, compounded monthly?
O A.
$195 000 0.0055 (1+0.0055) 360
(1+0.0055)300 +1
OB.
$195 000 0.0055 (1+0.0055) 360
(1+0.0055) 300-1
O C.
$195 000 0.0055(1-0.0055)300
(1-0.0055) 300-1
Answer:
B
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
PMT = monthly paymentP = loan amounti = interest rate per month (in decimal form)n = term of the loan (in months)Given:
P = $195,000i = 6.6% = 0.066n = 12 × 30 = 360[tex]\implies \sf PMT=\dfrac{195000(0.066)(1+0.066)^{360}}{(1+0.066)^{360-1}}[/tex]
Question 2 of 10
Which of the following geometric objects occupy one dimension?
Check all that apply.
A. Line
B. Triangle
C. Plane
D. Segment
E. Ray
F. Point
A. Line
D. Segment
E. Ray
Step-by-step explanation:Math dimensions include length, width, and height (in that order). The dimension that an object occupies is dependent on how many different measurements, aka dimensions, an object has.
0th Dimension
The first dimension is actually the zeroth dimension. This dimension includes objects that do not have any measurements. A point does not have a length because it only occupies one spot on a plane.
The 0th dimension includes:
Point1st Dimension
The next dimension, the 1st dimension, has only length. This means the object can travel across the x-axis, but it can only go in one direction.
The 1st dimension includes:
LineSegementRay2nd Dimension
For this question, the last dimension is the 2nd dimension. The 2nd dimension has both length and width. This means that the object occupies both the x and y-axis.
The 2nd dimension includes:
TrianglePlane3rd Dimension
The 3rd dimension is not included in the question or the answer choices but is still important. The 3rd dimension has length, width, and height. This occupies the x, y, and z-axis and cannot be graphed on a regular geometric plane. The 3rd dimension is graphed in a geometric space.
The 3rd dimension includes:
CubePrismAn electric bulb is sold in a box measuring 5 cm by 4 cm by 4 cm. If the shopkeeper receives them in a carton measuring 50 cm by 20 cm by 20 cm, how many bulbs would be packed in one carton ?
Answer:
250
Step-by-step explanation:
Bulb box and carton both are of cuboidal shape.
For bulb box the dimensions are:
l = 5 cm, w = 4 cm, h = 4 cm[tex]V_{Bulb\: box} =lwh[/tex][tex]\implies V_{Bulb\: box} =5(4)(4)[/tex][tex]\implies V_{Bulb\: box} =80\: cm^3[/tex]For Carton the dimensions are:
l = 50 cm, w = 20 cm, h = 20 cm[tex]V_{Carton} =lwh[/tex][tex]\implies V_{Carton} =50(20)(20)[/tex][tex]\implies V_{Bulb\: box} =20,000\: cm^3[/tex]To find the number of bulbs packed in the carton, divide the [tex]V_{Carton}[/tex] by [tex] V_{Bulb\: box}[/tex]
[tex] Number \:of \:bulbs =\frac{V_{Carton}}{V_{Bulb\: box}}[/tex][tex] \implies Number \:of \:bulbs =\frac{20,000}{80}[/tex][tex] \implies Number \:of \:bulbs = 250[/tex]So, 250 bulbs will be packed in one carton.
A salesman earns $4 commission on all the merchandise that he sells. Last month he sold $9000
worth of merchandise. How much commission (in dollars) did he earn last month?
Answer:
2250
Step-by-step explanation:
In this problem, you do 9000/4 because he earns $4 commissions, and that will give you 2250.
Please help with this! I have to reflect over the x axis by the way
Answer:
T' = (-8, 8)
U' = (2, 8)
V' = (-8, 7)
Step-by-step explanation:
reflection over x axis means we change the sign of the y coordinate and nothing else
T = (-8, -8)
y coordinate = -8, change the sign to get 8
T' is thus (-8, 8)
U = (2, -8)
y coordinate = -8, y' = 8
U' = (2, 8)
V = (-8, -7)
y' = 7
V' = (-8, 7)
In this equation f(x) = 3x -15, what is y if x is 9?
*
Answer:
y = 12
Step-by-step explanation:
To solve this equation... The function is basically:
y = 3x - 15
So by substituting in x=9:
y = 27 - 15 = 12.
y = 12
Hope this helps.
Answer:
y = 12
Step-by-step explanation:
f(x) = y, so to find y, we jut need to substitute 9 for all the x-values in the equation:
f(9) = 3(9) - 15
Simplify:
f(9) = 27 - 15
f(9) = 12
Since f(x) = y
y = 12 when x is 9
Hope this helped!
Y=4x+1 function rule table
Answer:
the table of the function is below
Step-by-step explanation:
Which statement about the graph of the quadratic function is NOT true?
Answer:
2nd option
Step-by-step explanation:
the graph has a minimum value of - 6 ( U ) not a maximum
Answer:
2nd option
Step-by-step explanation:
The graph has a minimum of -6, hence the 2nd option, which states the maximum is 3 is incorrectA rectangular prism and its net are shown below.
(All lengths are in feet.)
The volume of the rectangular prism is 180 ft³, From the net of the prism, A = 10 feet, B = 4 feet, C = 6 feet and D = 3 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The volume of the rectangular prism = length * width * height = 10 * 6 * 3 = 180 ft³
From the net of the prism, A = 10 feet, B = 4 feet, C = 6 feet and D = 3 feet.
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ctions: Write your answer in the box. Do not use spaces
What is the value of the following expression if x 22: "five times a number
decreased by 2"?
Answer:
5x - 2
Step-by-step explanation:
if x is your number its 5 lots of your number - 2
PLEASE HELP ME! Find the 10th term of the geometric sequence that has a1 = 400 and A2 = 200.
Answer:
I believe the answer is 0.7813
Step-by-step explanation:
Find the difference between 400 and 200, as they are first and second terms. This is going to be 0.5 since it is being divided.
The formula is: a∨n=a∨1(r)^(n-1)
n= the number of the sequence you are looking for
r=0.5
a∨1=400
a∨2=200
400(0.5)^(10-1)
Juanita must buy 50 plastic ducks for a game at the carnival. The ducks are sold in packages of 6. What is the LEAST number of packages Juanita should buy?
Answer:
9
Step-by-step explanation:
The least number of packages she should buy is 9 because 9 x 6 is 54 so she would have 4 extra ducks but she would still have enough for the carnival game
Which answer best describes the complex zeros of the polynomial function? f(x)=x^3−3x^2+16x−48
A The function has three nonreal zeros.
B The function has three real zeros.
C The function has two real zeros and one nonreal zero.
D The function has one real zero and two nonreal zeros.
Using the Factor Theorem, it is found that the correct option regarding the complex zeros of f(x) is given by:
D The function has one real zero and two nonreal zeros.
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.
In this problem, the function is given by:
f(x) = x³ - 3x² + 16x + 48.
Using a calculator, the roots are given by:
[tex]x_1 = -1.89767, x_2 = 2.44884 + 4.39288i, x_3 = 2.44884 - 4.39288i[/tex]
The first root is real, while the second and third are complex(nonreal), hence option D is correct.
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Laurie says that 2+3 x 2+3= 13. Ray says that 2+3 x 2+3= 11. Who is correct
Answer:
Ray
Step-by-step explanation:
Ray is correct . Have a nice day :)
if mÃc=170° Find mLB
Answer:
∠ B = 85°
Step-by-step explanation:
the inscribed angle B is half the measure of its intercepted arc AC , then
∠ B = [tex]\frac{1}{2}[/tex] × 170° = 85°
7) What is the area of the figure below?
12 cm
13 cm
20 cm
21 cm
Answer:
65,520
Step-by-step explanation:
12x13x20x21=64,520
PLS HELP
Find the value of x and y.
Answer:
x= 27.71281 = 16√3
y= 13.85641 = 8√3
Step-by-step explanation:
hope it helps :)
Convert 4 3/5 to a fraction greater than one
Answer:
23/5
Step-by-step explanation:
* means multiply
4 3/5
5 * 4 = 20
20 + 3 = 23
23/5
Answer:
[tex]\frac{23}{5}[/tex]
Step-by-step explanation:
The type of fraction we are dealing with is called a mixed fraction
In order to convert this fraction into a fraction greater than 1, we will have to convert it into an improper fraction
So we keep the denominator
Multiply the whole number by the denominator and add that to the numerator
The area of a rectangle is 24 cm² and the perimeter is 22 cm .What is the lenth and width of this rectangle?
Step-by-step explanation:
length × width = 24
2×length + 2×width = 22
length + width = 11
length = 11 - width
this we use in the first equation again :
(11 - width) × width = 24
11×width - width² = 24
width² - 11×width + 24 = 0
the general solution to an quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = width
a = 1
b = -11
c = 24
and so we get
width = (11 ± sqrt((-11)² - 4×1×24))/2×1) =
= (11 ± sqrt(11² - 96))/2 = (11 ± sqrt(121-96))/2 =
= (11 ± sqrt(25))/2 = (11 ± 5)/2
width1 = (11 + 5)/2 = 16/2 = 8 cm
width2 = (11 - 5)/2 = 6/2 = 3 cm
and teenaged to this is then
length1 = 11 - width1 = 11 - 8 = 3 cm
length2 = 11 - width2 = 11 - 3 = 8 cm
so, it is clear. one dimension has to be 8 cm, and the other one 3 cm. it does not matter which is which.
find x. not sure what it is
Answer:
x=29°
Step-by-step explanation:
angle measure of circular arc=180-122=58°
x=1/2×58=29°
A circular swimming pool has a radius of 8
feet. Which measurement is closest to the area
of the swimming pool in square feet?
Answer: 706.5
Step-by-step explanation:
no promisees that its right
How would you solve this without a calculator?
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form:
[tex]1351+780\sqrt{3}[/tex]
Decimal Form:
2701.99962990
Thus, 2,701 is your answer
Consider that x = 1.5 and y = 3. Which statement is true about x + y?
Answer:
x + y = 4.5
Step-by-step explanation:
x + y = 1.5 + 3 = 4.5
