Answer:
Step-by-step explanation:
Answer to question 1:
On average do part-time students spend less than 20 hours per work on academic work and assignments ?
Answer to question 2:
On average do students work greater than 50 hours a week ?
Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
Answer:
Step-by-step explanation:
-4 is a root for 3 times and 1 is root for once
so (x+4)^3 * (x-1) is part of f(x)
the constant term there is 4^3*(-1)=-64
so there is a multiplier of 320/-64=-5
f(x) = -5 * (x+4)^3 * (x-1)
Find the values of the sine, cosine, and tangent for ZA C A 36ft B
24ft
Find the values of the sine, cosine, and tangent for ∠A
a. sin A = [tex]\frac{\sqrt{13} }{2}[/tex], cos A = [tex]\frac{\sqrt{13} }{3}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
b. sin A = [tex]3\frac{\sqrt{13} }{13}[/tex], cos A = [tex]2\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{3}{2}[/tex]
c. sin A = [tex]\frac{\sqrt{13} }{3}[/tex], cos A = [tex]\frac{\sqrt{13} }{2}[/tex], tan A = [tex]\frac{3}{2}[/tex]
d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex], cos A = [tex]3\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
Answer:d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex], cos A = [tex]3\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
Step-by-step explanation:The triangle for the question has been attached to this response.
As shown in the triangle;
AC = 36ft
BC = 24ft
ACB = 90°
To calculate the values of the sine, cosine, and tangent of ∠A;
i. First calculate the value of the missing side AB.
Using Pythagoras' theorem;
⇒ (AB)² = (AC)² + (BC)²
Substitute the values of AC and BC
⇒ (AB)² = (36)² + (24)²
Solve for AB
⇒ (AB)² = 1296 + 576
⇒ (AB)² = 1872
⇒ AB = [tex]\sqrt{1872}[/tex]
⇒ AB = [tex]12\sqrt{13}[/tex] ft
From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of [tex]12\sqrt{13}[/tex] ft (43.27ft).
ii. Calculate the sine of ∠A (i.e sin A)
The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e
sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex] -------------(i)
In this case,
Ф = A
opposite = 24ft (This is the opposite side to angle A)
hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)
Substitute these values into equation (i) as follows;
sin A = [tex]\frac{24}{12\sqrt{13} }[/tex]
sin A = [tex]\frac{2}{\sqrt{13}}[/tex]
Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]
sin A = [tex]\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]
sin A = [tex]\frac{2\sqrt{13} }{13}[/tex]
iii. Calculate the cosine of ∠A (i.e cos A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e
cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex] -------------(ii)
In this case,
Ф = A
adjacent = 36ft (This is the adjecent side to angle A)
hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)
Substitute these values into equation (ii) as follows;
cos A = [tex]\frac{36}{12\sqrt{13} }[/tex]
cos A = [tex]\frac{3}{\sqrt{13}}[/tex]
Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]
cos A = [tex]\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]
cos A = [tex]\frac{3\sqrt{13} }{13}[/tex]
iii. Calculate the tangent of ∠A (i.e tan A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e
tan Ф = [tex]\frac{opposite}{adjacent}[/tex] -------------(iii)
In this case,
Ф = A
opposite = 24 ft (This is the opposite side to angle A)
adjacent = 36 ft (This is the adjacent side to angle A)
Substitute these values into equation (iii) as follows;
tan A = [tex]\frac{24}{36}[/tex]
tan A = [tex]\frac{2}{3}[/tex]
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis: y=x6, y=1 about y=6.
Answer:
mehoimehoihoi
Step-by-step explanation:
Consider the proportion
8
k
=
5
2.7
Answer:
4.32 = k
Step-by-step explanation:
8/k = 5/2.7
We can solve using cross products
8* 2.7 = 5k
21.6 = 5k
Divide each side by 5
21.6/5 = k
4.32 = k
Answer: 5k = 21.6 and k = 4.32
there you go have a good day bye
Step-by-step explanation:
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir
bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
ОА.
3.25x + 13.50 S 40
OB.
3.25x + 13.50 240
Oc.
13.50x +3.25 S 40
OD.
13.50x +3.25 2 40
Answer:
A. 3.25x + 13.50 ≤ 40
The number of bracelets is x. It's a variable.
The 13.50 is a constant.
The total needs to be less than or equal to 40 because that's all the money he has.
Answer:
3.25x + 13.50 ≤ 40
Step-by-step explanation:
For this problem, you have to directly make the equation. Using the givens, it shows that he has only 40 dollars, and wants to buy only one hat for 13. 50. He wants to buy his friends braclets 3.25, but since you dont know how many friends its for, you will leave it as x.
There is only 40 dollars so you will use: ≤
The answer will be:
3.25x + 13.50 ≤ 40
Hope this helps.
what are all the factos of 36
Hi there!
»»————- ★ ————-««
I believe your answer is:
{1, 2, 3, 4, 6, 9, 12, 18, 36}
»»————- ★ ————-««
Here’s why:
A factor is a whole number that is multiplied by another to have a product have another number.
⸻⸻⸻⸻
The Factors Are:
1 (1 * 36 = 36)2 (2 * 18 = 36)3 (3 * 12 = 36)4 (4 * 9 = 36)6 (6 * 6 = 36) 9 (9 * 4 = 36)12 (12 * 3 = 36)18 (18 * 2 = 36)36 (36 * 1 = 36)⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
A.109
B.87
C.98
D.69
Answer:
hey what's
Step-by-step explanation:
a question wow okay the answer is
A trucking company buys 25,275 gallons of gasoline. The federal excise tax is $0.195 per gallon. Find the amount of excise tax due. (Round your answer to the nearest cent if necessary)
Answer: 5,055
Step-by-step explanation
multiply the amount of gallons purchased by tax and round up
$4928.625 is the answer.
An Excise tax is an indirect tax, usually paid by the manufacturer or retailer of the product. then passes along in the price of the product to the consumer.
Amount of gasoline = 25,375 gallons.
The Excise tax = $0-195/gallon.
The amount of Excise tax dece = 25.875 X $0.195
= $4928.625
Se the amount of Excise tax due for 25975 gallons of gasoline is $ 4928.625
what is Excise tax?Excise tax is generally a tax levied on the sale of a particular good or service or for a particular purpose. State excise taxes are usually levied on the sale of gasoline, air tickets, heavy trucks, road tractors, tanning beds, tires, cigarettes, and other goods and services.
Excise can be used to charge prices for externalities or to discourage the consumption of goods by others. They can also be used as royalties to generate income from people who use certain government services. Income should be used to maintain those government services.
Learn more about excise tax here:https://brainly.com/question/2871942
#SPJ2
heeeeeeeeeeeeelp meee
Answer: i need the formula and i got you.
Step-by-step explanation:
in the pair of triangle, write the similarity statement and identify the postulate of theorem that justifies the similarity.
Answer:
ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem
ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem
Step-by-step explanation:
First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.
Second set :
[tex]\frac{EG}{RQ}[/tex] = [tex]\frac{10}{12}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{EF}{RF}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{FG}{FQ}[/tex] = [tex]\frac{20}{24}[/tex] = [tex]\frac{5}{6}[/tex]
Which parabola opens upward?
y = 2x – 4x^2 – 5
y = 4 – 2x^2 –5x
y = 2 + 4x – 5x^2
y = –5x + 4x^2 + 2
Answer:
D) y = –5x + 4x^2 + 2
Step-by-step explanation:
You can tell by the first number being positive or negative. To check use Desmo graphing calculator and enter your equation for next time.
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened?
Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 and standard deviation of 18 . Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. a. Around what percentage of adults in the USA have stage 2 high blood pressure
Answer:
The percentage of adults in the USA have stage 2 high blood pressure=98.679%
Step-by-step explanation:
We are given that
Mean, [tex]\mu=120[/tex]
Standard deviation, [tex]\sigma=18[/tex]
We have to find percentage of adults in the USA have stage 2 high blood pressure.
[tex]P(x\geq 160)=P(Z\geq \frac{160-120}{18})[/tex]
[tex]P(x\geq 160)=P(Z\geq \frac{40}{18})[/tex]
[tex]P(x\geq 160)=P(Z\geq 2.22)[/tex]
[tex]P(x\geq 160)=1-P(Z\leq 2.22[/tex]
[tex]P(x\geq 160)=0.98679[/tex]
[tex]P(x\geq 160)=98.679[/tex]%
Hence, the percentage of adults in the USA have stage 2 high blood pressure=98.679%
Which graph shows the solution to the system of linear inequalities?
y>2/3x+3
y ≤ -1/3x+2
Answer:
Graph 2 which has both solid and dashed line
Step-by-step explanation:
Given the linear inequalities :
y>2/3x+3 - - - (1)
y ≤ -1/3x+2 - - - (2)
One quick observation that can be made from the two graphs is the type of line used to plot the two linear inequalities;
Inequalities that uses either the < or > sign are plotted using a dashed line while inequalities with makes use of ≤ or ≥ are plotted using the solid line. Therefore we can conclude that the graph which uses both the solid line and the dashed line to represent the linear inequality conditions is the correct choice.
Find a vector equation and parametric equations for the line The line through the point (2, 2.4, 3.5) and parallel to the vector 3i 1 2j 2 k
Answer:
The vector equation
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Step-by-step explanation:
Given
[tex]Point = (2,2.4,3.5)[/tex]
[tex]Vector = 3i + 2j - k[/tex]
Required
The vector equation
First, we calculate the position vector of the point.
This is represented as:
[tex]r_0 = 2i + 2.4j + 3.5k[/tex]
The vector equation is then calculated as:
[tex]r = r_o + t * Vector[/tex]
[tex]r = 2i + 2.4j + 3.5k + t * (3i + 2j - k)[/tex]
Open bracket
[tex]r = 2i + 2.4j + 3.5k + 3ti + 2tj - tk[/tex]
Collect like terms
[tex]r = 2i + 3ti+ 2.4j + 2tj+ 3.5k - tk[/tex]
Factorize
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation is represented as:
[tex]x = x_0 + at\\y = y_0 + bt\\z = z_0 + ct[/tex]
Where
[tex]r = (x_0 + at)i +(y_0 + bt)j+(z_0 + ct)k[/tex]
By comparison:
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-4, 7) (6, -33) (10, -105)
HELP PLZ
Answer:
[tex]y= -x^{2} -2x+15[/tex]
Step-by-step explanation:
[tex]y= -x^{2} -2x+15[/tex]
If 128x is a perfect square number what is the least value of x
Please answer the question fast
Answer:
in a square all sides are equal so x has to equal
128
Hope This Helps!!!
six options. Each of these six options leads to a menu with four options. For each of these four options, three more options are available. For each of these three options, another three options are presented. If a person calls the 800 number for assistance, how many total options are possible
Answer:
Hence the total number of possible options available to a person who calls the 800 number is 216.
Step-by-step explanation:
Given that the caller 10 800 telephone system has six options. For each of these four options, three more options are available. For each of these three options, another three options are presented.
Hence the total number of possible options available to a person who calls the 800 number = [tex]6 \times 4 \times 3 \times 3 = 216[/tex].
[tex]3x+7=12-2x;1[/tex]
Step-by-step explanation:
[tex]3x + 7 = 12- 2x \\ 3x + 2x = 12 - 7 \\ 5x = 5 \\ x = \frac{5}{5} \\ x =1[/tex]
the first term of an arithmetic sequence is -5, and the tenth term is 13. find the common difference
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Equivalent question: Find the slope of line going through points (1,-5) and (10,13).
Line points up vertically and subtract. Then put 2nd difference on top of first difference.
(1,-5)
(10,13)
---------'subtracting
-9, -18
So the slope of the line gong through point's (1,-5) and (10,13) is -18/-9=2.
The common difference of an arithmetic sequence whose first term is -5 and whose tenth term is 13 is 2.
Melanie has D dimes and Q quarters. She has no less than $4 worth of coins altogether. Write this situation as an inequality.
Step-by-step explanation:
D(.10) + Q(.25) = 4
I think
Answer:
D(.10) + Q(.25) = 4
Step-by-step explanation:
The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 13.3 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
Answer:
0.96784
Step-by-step explanation:
17-13.3/2
=1.85
p(x<1.85)
=0.96784
The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
Mean [tex]\mu[/tex]=13.3 minutes
Standard deviation[tex]\sigma[/tex]=2 minutes
What is a z-score?The value of the z-score tells you how many standard deviations you are away from the mean.
So, the z-score of the above data
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{17-13.3}{2}[/tex]
[tex]z=1.85[/tex]
From the standard normal table, the p-value corresponding to z=1.85
Or, p(x<1.85)=0.9678 or 96.78%
Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
To get more about the z-score visit:
https://brainly.com/question/25638875
What is 70% less than 55?
Answer:
100-70=30 so
55*0.3=16.5
Hope This Helps!!!
Answer:
Answer :
70% less than 55 is
16.5
Y=2x-8 and intercept at (-4,-1)
Answer:
y=2x+7
Step-by-step explanation:
y=2x-8
2 is the gradient.
-4 is x
-1 is y
-1=2(-4)+c
-1=-8+c
-1+8=c
c=7
therefore,
y=2x+7
Help asap please!!..
Answer:
9x² - 4/3x + ¼
Step-by-step explanation:
(3x - ½)²
(3x - ½)(3x -½)
9x² - ⅔x - ⅔x + ¼
9x² - 4/3x + ¼
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours. Find the probability of a bulb lasting for at most 528 hours. Round your answer to four decimal places.
Answer:
0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours.
This means that [tex]\sigma = 15, \mu = 520[/tex]
Find the probability of a bulb lasting for at most 528 hours.
This is the p-value of Z when X = 528. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{528 - 520}{15}[/tex]
[tex]Z = 0.533[/tex]
[tex]Z = 0.533[/tex] has a p-value of 0.7031
0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.
In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
Answer:
Probability[Number of people from church] = 0.26 (Approx.)
Step-by-step explanation:
Given:
Total number of adult in survey = 1,033
Missing information:
Number of people from church = 269
Find:
Probability[Number of people from church]
Computation:
Probability of an event = Number of favourable outcomes / Number of total outcomes
Probability[Number of people from church] = Number of people from church / Total number of adult in survey
Probability[Number of people from church] = 269 / 1,033
Probability[Number of people from church] = 0.2604
Probability[Number of people from church] = 0.26 (Approx.)
PLEASE HELP ME ASAP GIVING 10+ POINTS
The actual height of the building shown in the model is 150 feet What is the actual width of the building shown in the model?
Answer:
60 ft
Step-by-step explanation:
The answer has to be in feet units
Now that we know the height is 5 cm equivalent to 150 feet, what is the width of the building in feet units
5 cm = 150 ft
Rule: multiply cm by 30 to get the ft
2 cm = ?
2 cm × 30 = 60 ft
2 cm = 60 ft
Find the value of x (please)
9514 1404 393
Answer:
(a) 21
Step-by-step explanation:
The product of the lengths to the near and far circle intercepts are the same for the two lines. For the tangent, the near and far intercepts are the same point, so we have ...
(36)(36) = (27)(27+x)
48 = 27+x . . . . . . . . . . divide by 27
x = 21 . . . . . . . . subtract 27
Not sure what to pick
Answer:
option d is correct answer
Answer:
Step-by-step explanation:
D looks good
