Answer:
The position of the particle is described by [tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]
Step-by-step explanation:
The position function is obtained after integrating twice on acceleration function, which is:
[tex]a(t) = 2\cdot t + 5[/tex], [tex]\forall t \geq 0[/tex]
Velocity
[tex]v(t) = \int\limits^{t}_{0} {a(t)} \, dt[/tex]
[tex]v(t) = \int\limits^{t}_{0} {(2\cdot t + 5)} \, dt[/tex]
[tex]v(t) = 2\int\limits^{t}_{0} {t} \, dt + 5\int\limits^{t}_{0}\, dt[/tex]
[tex]v(t) = t^{2}+5\cdot t + v(0)[/tex]
Where [tex]v(0)[/tex] is the initial velocity.
If [tex]v(0) = -5[/tex], the particular solution of the velocity function is:
[tex]v(t) = t^{2} + 5\cdot t -5, \forall t \geq 0[/tex]
Position
[tex]s(t) = \int\limits^{t}_{0} {v(t)} \, dt[/tex]
[tex]s(t) = \int\limits^{t}_{0} {(t^{2}+5\cdot t -5)} \, dt[/tex]
[tex]s(t) = \int\limits^{t}_0 {t^{2}} \, dt + 5\int\limits^{t}_0 {t} \, dt - 5\int\limits^{t}_0\, dt[/tex]
[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + s(0)[/tex]
Where [tex]s(0)[/tex] is the initial position.
If [tex]s(0) = 6[/tex], the particular solution of the position function is:
[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]
Answer:
Position of the particle is :
[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex]
Step-by-step explanation:
Given information:
The particle is moving with an acceleration that is function of:
[tex]a(t)=2t+5[/tex]
To find the expression for the position of the particle first integrate for the velocity expression:
AS:
[tex]V(t)=\int\limits^0_t {a(t)} \, dt\\v(t)= \int\limits^0_t {(2.t+5)} \, dt\\\\v(t)=t^2+5.t+v(0)\\[/tex]
Where, [tex]v(0)[/tex] is the initial velocity.
Noe, if we tale the [tex]v(0) =-5[/tex] ,
So, the velocity equation can be written as:
[tex]v(t)=t^2+5.t-5[/tex]
Now , For the position of the particle we need to integrate the velocity equation :
As,
Position:
[tex]S(t)=\int\limits^0_t {v(t)} \, dt \\S(t)=\int\limits^0_t {(t^2+5.t-5)} \, dt\\S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+s(0)[/tex]
Where, [tex]S(0)[/tex] is the initial position of the particle.
So, we put the value [tex]s(0)=6[/tex] and get the position of the particle.
Hence, Position of the particle is :
[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex].
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Two trains leave New York at the same time heading in opposite directions. Train A travels at 4/5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A? Can you pls help me fast
=============================================
Work Shown:
x = speed of train A
y = speed of train B
"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y
distance = rate*time
d = x*7
d = (4/5)y*7 = (28/5)y represents the distance train A travels
d = y*7 = 7y represents the distance train B travels
summing those distances will give us 693
(28/5)y + 7y = 693
5*( (28/5)y + 7y ) = 5*693
28y + 35y = 3465
63y = 3465
y = 3465/63
y = 55
Train B's speed is 55 mph
4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph
Train A's speed is 44 mph
"An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 260 engines and the mean pressure was 4.2 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.02 will be used. Determine the decision rule. Enter the decision rule."
Answer:
H₀ is accepted, we don´t have evidence to claim valves produces more than 4,1 pounds/square inch
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 4.1
Population standard deviation σ = 0,9
Sample size n = 260
Sample mean μ = 4,2
Level of significance 0,02 α = 0,02 form z-table we find z score
z(c) = 2,05 (critical value)
Test hypothesis
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ > μ₀
Is a one tail-test ( to the right. Values have a mean over the population mean)
z(s) = ( μ - μ₀ )/ σ /√n
z(s) = 4,2 - 4,1 / 0,9/√260
z(s) = 0,1 *16,1245 / 0,9
z(s) = 1,7916
To compare z(s) and z(c)
z(s) < z(c)
Then z(s) is in the acceptance region, we accept H₀
In circle O, radius OQ measures 9 inches and arc PQ measures 6π inches. Circle O is shown. Line segments P O and Q O are radii with length of 9 inches. Angle P O Q is theta. What is the measure, in radians, of central angle POQ?
Answer:
2π/3 radStep-by-step explanation:
To get theta, we will apply the formula for calculating the length of an arc as shown;
Length of an arc = theta/360 * 2πr
theta is the central angle (required)
r is the radius of the circle
Given r = 9 inches and length of the arc PQ = 6π in
Substituting this given values into the formula to get the central angle theta;
6π = theta/360 * 2πr
Dividing both sides by 2πr
theta/360 = 6π/2πr
theta/360 = 3/r
theta/360 = 3/9
theta/360 = 1/3
cross multiplying;
3*theta = 360
theta = 360/3
theta = 120°
Since 180° = π rad
120° = x
x = 120π/180
x = 2π/3 rad
Hence the measure of the central angle in radians is 2π/3 rad
If while playing Blackjack if you receive the 6 of hearts and the 8 of diamonds, what are the odds that you will bust if you hit? (If you receive another card what are the odds that their sum will add to 22 or higher with Aces counting as 1 and royal cards counting as 10?)
Answer:
Winning odd = 3.4
Loosing odd = 4.3.
Step-by-step explanation:
So, from this particular Question or problem we have the following data or information or parameters which is going to aid or help us in solving this particular Question;
=> Given 6 of hearts and the 8 of diamonds.
We know that there are 8 types of cards.
Also, we know that the total number of the cards is equal to fifty-two(52).
From cards of six(6) to ten(10) a bust will surely occur.
Therefore, 8 × 4 / 52= 32/52 = 0.62.
If an ace is pulled, then the chance of winning bis surely 4 out of 52 deck of cards.
Giving you a Winning odd = 3.4 and a
Loosing odd = 4.3.
What formula could you use to help find the area of the given triangle?
Answer:
Since it is a right triangle, you can use pythagorean theorem to find the missing side.
Step-by-step explanation:
¿Qué interés produce s/ 72,000 al 5% anual en 1 año, 1 mes, 10 días?
Answer: 3,988.8
Usaremos la fómula: I = C * i * n
I = 72 000 * 0.05 * (1 año + 1 mes + 10 día)
I = 72 000 * 0.05 * (1 + 0.08 + 0.0028)
I = 72 000 * 0.05 * 1.108
3,988.8
Step-by-step explanation:
Podemos obtener el interés que produce un capital con la siguiente fórmula:
I = C * i * n
Ejemplo: Si queremos calcular el interés simple que produce un capital de 1.000.000 pesos invertido durante 5 años a una tasa del 8% anual. El interés simple se calculará de la siguiente forma:
I = 1.000.000 * 0,08 * 5 = 400.000
Si queremos calcular el mismo interés durante un periodo menor a un año (60 días), se calculará de la siguiente forma:
Periodo: 60 días = 60/360 = 0,16
I = 1.000.000 * 0,08 * 60/360 = 13.333
Espero te ayude :3
What is 24-(-6) because in confused
Answer:
30
Step-by-step explanation:
24 - (-6)
Apply rule : -(-a) = a
Negative (-) times a negative (-) is positive (+).
24 + 6
= 30
Answer:
-6 is in parentheses because it is a negative number. this prevents the equation from looking like a too long subtraction sign (24--6); therefore it is written as 24 - (-6).
this simplifies to 24 + 6 = 30
to negatives = a positive
hich sequence of transformations could map △ABC to △XYZ? a reflection across line m and a dilation a dilation by One-fourth and a reflection across line m a rotation about C and a dilation a dilation by One-fourth and a translation
Answer:
a dilation by One-fourth and a translation
Step-by-step explanation:
For determining the sequence first we have to find out the scale factor which is shown below:
We can calculate the scale factor to obtain
[tex]= \frac{1.5}{6} \\\\ = \frac{1}{4}[/tex]
Now as we know that the triangle XYZ and the triangle ABC are similar to each other but in the triangle XYZ is smaller in size and it is a shift to upward and right
Therefore the last option is correct
Dion recorded his heart rate as 204 beats in 3 minutes. How many beats does his heart make in 1 minute?
Answer:
68
Step-by-step explanation:
Answer:
The answer is
68 beatsStep-by-step explanation:
To solve this problem we use ratio and proportion
For 3 minutes his heart rate was 204 beats
So 1 minute will be
[tex] \frac{204 \: beats}{3} \times 1[/tex]
= 68 beatsHope this helps you
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 146 students using Method 1 produces a testing average of 51.6. A sample of 180 students using Method 2 produces a testing average of 62.7. Assume the standard deviation is known to be 9.42 for Method 1 and 14.5 for Method 2. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval.
Answer:
The confidence interval is [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 146[/tex]
The second sample size is [tex]n_2 = 180[/tex]
The first sample mean is [tex]\= x_1 = 51.6[/tex]
The second sample mean is [tex]\= x_2 = 62.7[/tex]
The first standard deviation is [tex]\sigma _1 = 9.42[/tex]
The second standard deviation is [tex]\sigma _2 = 14.5[/tex]
Given that the confidence level is 98% then the significance level is mathematically evaluated as
[tex]\alpha = (100 -98 )\%[/tex]
[tex]\alpha = 2 \%[/tex]
[tex]\alpha = 0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
The reason we are obtaining critical value of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
[tex]E = 0.2405[/tex]
The 98% confidence interval is mathematically represented as
[tex](\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E[/tex]
substituting values
[tex](51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405[/tex]
[tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
Assume that y varies directly with x, then solve.
If y=6 when x= 2/3 find x when y=12.
х: /
2×y = 2×6= 12 so 2×x = 2×23 = 43 = 113
Step-by-step explanation:
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Help ! Inductive and deductive reasoning differ in which way? A) Conclusions drawn using deductive reasoning are always false, while conclusions drawn using inductive reasoning are always true. B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid. C) Conclusions drawn using inductive reasoning are always false, while conclusions drawn using deductive reasoning are always true. D) Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
Answer:
B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.
Step-by-step explanation:
Inductive reasoning uses logic and uses more evidence to draw conclusions. In deductive reasoning, WE decide whether a deductive statement is true by assessing the strength of the link between the premises and the conclusion. But some deductive reasoning may appear to make sense without pointing to a truth
Answer:
The answer is D. Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
Step-by-step explanation:
I took the test
What is the degree of the polynomial?
Answer:
2
Step-by-step explanation:
The degree of this polynomial is 2, since a parabola is drawn. A parabola is a graph of a quadratic equation which has the highest degree of 2.
Find the equation of a line that contains the points (−2,2) and (−6,−5). Write the equation in slope-intercept form, using fractions when required.
Answer:
[tex]4y - 7x - 1 = 0[/tex]
[tex]m = \frac{y2 - y1}{x2 - x1?} [/tex]
[tex]m = \frac{ - 5 - 2}{ - 6 - - 2?} [/tex]
[tex]m = \frac{ - 7}{ - 4} [/tex]
[tex]m = \frac{7}{4} [/tex]
[tex]y = m(x - x1) + y1[/tex]
[tex]y = \frac{7}{4} (x + 2) + 2[/tex]
[tex]y = \frac{7}{4} x + \frac{7}{2} + 2[/tex]
[tex]y = \frac{7}{4} x + \frac{11}{2} [/tex]
[tex]4y = 7x + 22[/tex]
[tex]4y - 7x - 22 = 0[/tex]
The equation of the line passing through the point (-2,2) and (-6,-5) is,
y = (-7/4)x +(11/2).
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of a line that contains the points (−2,2) and (−6,−5).
Calculate the slope of the line,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -5-2) / (-6 + 2 )
Slope= 7 / 4
The y-intercept is calculated as,
y = mx + c
2 = (-7/4) x 2 + c
c = 11 / 2
The equation will be written as,
y = mx + c
y = (7 / 4)x + (11/2)
Therefore, the equation of the line passing through the point (-2,2) and (-6,-5) is,
y = (-7/4)x +(11/2).
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Circle the numbers divisible by 2.
320;5,763; 9,308; 5,857;3,219; 5,656; 83,001;53,634
In a soccer league, the ratio of boys to girls is 4 to 6. There are a total of 50 players in the soccer league. Determine how many girls play in the soccer league.
Answer:
30
Step-by-step explanation:
We can call the number of boys 4x and girls 6x so we can write:
4x + 6x = 50
10x = 50
x = 5, therefore the number of girls is 6x = 6 * 5 = 30.
Answer:
30
Step-by-step explanation:
In the ratio 4:6, we can think of this like 4 boys and 6 girls out of 10 team members.
We can find how many girls play by multiplying 6 by 5, since 50 divided by 10 is 5.
6(5) = 30, so 30 girls play in the soccer league.
from $2003$ onward, the number of daily visitors to a website increased by $200\%$ every two years. So, for example, the number of visitors in $2011$ was $200\%$ more than the number of visitors in $2009$.
In what year was the number of daily visitors $800\%$ more than the number of daily visitors in $2003$? Explain, in words, why your answer is correct.
Answer:
2007
Step-by-step explanation:
If the number of visitors was, say, 100 people in 2003, then in 2005 that number would have gone up to 300 people, which is a 200% increase. And that number would have gone up to 900 people in 2007, which is an 800% increase.
Answer:
2007
NOT YOU TRYING TO GET THE AOPS PREALGEBRA 2 ANSWER
I stan though :D
Suppose you invest $15,000 at the age of 35, and agree to start receiving
payments at the age of 45. At age 41, you decide you want to withdraw $5000
from your account. What is the IRS fee you will have to pay? Remember, the
IRS charges 10% if you withdraw before you are 59.5.
A. $500.00
B. $750.00
C. $50.00
D. $250.00
Answer:
A. $500.00
Step-by-step explanation:
IRS popularly known as Internal revenue service charges an IRS fee under the authority of the Federal Law and policy agencies. This implementation of IRS fee is to recuperate the cost of rendering a service to the masses.
From the given information in the question:
Suppose you invest $15,000 at the age of 35 and agree to start receiving payments at the age of 45.
At age 41, you decide you want to withdraw $5000 from your account.
Since the investor is still 41 years of age ; IRS will charge 10% of the withdrawal amount.
IRS fee = 10% of $5000
IRS fee = 0.1 × $5000
IRS fee = $500
Find the unknown side length, x. Write your answer in simplest radical form.
Answer:
Correct option: D
Step-by-step explanation:
In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:
[tex]a^2 = b^2 + c^2[/tex]
Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).
So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:
[tex]x^2 = 40^2 + 42^2[/tex]
[tex]x^2 = 1600 + 1764[/tex]
[tex]x^2 = 3364[/tex]
[tex]x = 58[/tex]
So the correct option is D.
Given: F={(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4,7), (5, 8), (6,9). (7.5))
(F. G) (2) =
10
O 20
O 40
Answer:
(F·G)(2) = 20
Step-by-step explanation:
We assume you want (F·G)(2).
(F·G)(2) = F(2)·G(2)
F(2) = 4 . . . . from the ordered pair (2, 4)
G(2) = 5 . . . .from the ordered pair (2, 5)
So your product is ...
F(2)·G(2) = 4·5 = 20
(F·G)(2) = 20
Subtract the rational expressions: (x/x+2)-(2/x)
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer:
see below
Step-by-step explanation:
Company A f(x) = 15(7x)
Company B g(x) = 100x + 5
If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less False
f Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less True
If Marguerite rents for 1 week, it will cost her the same at either company
A = 105(1) = 105
B = 100(1) +5 = 105 True
If Marguerite rents for 1 week, it will cost her more if she rents from Company A
A = 105(1) = 105
B = 100(1) +5 = 105 False
h(x) = 5x – 5
h(x) = f(x) – g(x)
=15(7x) - ( 100x + 5)
= 105x - 100x -5
= 5x-5 True
h(x) = 5x + 5 False
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
If Marguerite rents for 1 week, it will cost her the same at either company.
h(x) = 5x - 5.
Step-by-step explanation:
Company A: f(x) = 15(7x)
Company B: g(x) = 100x + 5
h(x) = f(x) - g(x)
So, the function h(x) is the difference between Company A's rental and Company B's rental.
h(x) = (15(7x)) - (100x + 5)
= (105x) - (100x + 5)
= 105x - 100x - 5
= 5x - 5
h(x) = 5x - 5.
Let's say that Marguerite rents for 1 week. In Company A, that will cost her 15 * 7 = 105. In Company B, it will cost her 100 + 5 = 105. So, if Marguerite rents for 1 week, it will cost her the same at either company.
Let's say that Marguerite rents for 2 weeks. In Company A, that will cost her 15 * 7 * 2 = 30 * 7 = 210. In Company B, it will cost her 100 * 2 + 5 = 200 + 5 = 205. So, if Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
Hope this helps!
Please help!! Geometry is my weakness!!
Answer:
Hey there!
Opposite angles in a parallelogram must be congruent, so T=R.
Hope this helps :)
Answer:
∠T ≅ ∠R
Step-by-step explanation:
We know that the angles are equal because they are opposite sides in the parallelogram.
Could someone please help me Thank you!!
Answer:
-5/3 -2/5
im pretty sure
Answer:
[tex]5^{7[/tex] or 78125
Step-by-step explanation:
5^2 ( 5^3 · 5^2 )
= 5^2 ( 5^5 ) = 5^7
or, 78125
PLEASE HELP!!! QUICKLY
Practice
Question 1: Choose the number that will complete this Pythagorean triple.
15, 17
Question 2: Choose the number that will complete this Pythagorean triple.
9,
41
Question 3: Choose the number that will complete this Pythagorean triple.
12, 35,
Reset
Submit
Answer:
1. = 8
2. =40
3. =37
Step-by-step explanation:
1. x = √(17² - 15²) = 8
2. x =√(9² +41²) = 40
3. x =√(12² + 35²) = 37
please mark brainliest
Alex has built a garden shed in the shape shown.
(A) Alex plans to paint the outside of the shed, including the roof but not the floor. One can of paint can cover 6m^2 . How many cans of paint will Alex need.
(B)If one can of paint costs $25.50, what will the cost be including 13% tax.
Answer:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
Step-by-step explanation:
As we check the figure, we have a composite figure.
Cuboid on the base and a pyramid on the top of it.
To find the area to be painted, we have 4 rectangular faces of cuboid with dimensions 6m [tex]\times[/tex] 3m.
And 4 triangular faces of pyramid with Base = 6m and Height 5m.
So, total area to be painted = 4 rectangular faces + 4 triangular faces
Area of rectangle = Length [tex]\times[/tex] Width = 6 [tex]\times[/tex] 3 = 18 [tex]m^2[/tex]
Area of triangle = [tex]\frac{1}{2}\times Base \times Height =\frac{1}{2}\times 6 \times 5 = 15\ m^{2}[/tex]
Total area to be painted = 4 \times 18 + 4 \times 15 = 72 + 60 = 132 [tex]m^2[/tex]
A) Area painted by 1 can = 6 [tex]m^2[/tex]
Cans required to paint 132 [tex]m^2[/tex] = [tex]\frac{132}{6} = 22\ cans[/tex]
B)
Cost of 1 can = $25.50
Cost of 22 can = $25.50 [tex]\times[/tex] 22 = $561
Including tax of 13% = $561 + $561 [tex]\times \frac{13}{100}[/tex] = $561 + $72.93 = $633.93
So, the answers are:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
hi there help me please
Hello!
Answer:
Choice 1.
Step-by-step explanation:
We can go through each answer choice and examine whether it represents the question:
1) This does not represent the question because 10% of 6 is 0.6. The question is asking to find a number that 6 = 10% of, not finding 10% of 6.
2) Correct because a number multiplied by 10%, or 0.1, should be equal to 6 to answer the question.
3) Correct because 6 is equivalent to 10% of the answer, which is stated in this answer choice.
4) Correct because 6 should be 10% of the answer.
Therefore, the incorrect choice would be Choice 1.
Multicollinearity may cause problems if the absolute value of the sample correlation coefficient for two of the independent variables exceeds what value? a. .7 b. 1 c. .5 d. .05
Answer: a. .7
Step-by-step explanation:
Multicollinearity means the two or more explanatory variables in a multiple regression model are highly linearly related to each other.
Multicollinearity is a problem because
it weaken the statistical significance of an independent variable. Larger the standard error of a regression coefficient, the less likely it is that this coefficient will be statistically significant.Multicollinearity may cause problems if the absolute value of the sample correlation coefficient for two of the independent variables exceeds 0.7.
So, the correct option is a. .7 .
what is that is the derivative of
x^2-x+3 at the point
x=5
What value of x where
x²-x+3
a minimum?
Answer:
see explanation
Step-by-step explanation:
differentiate using the power rule.
[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus
[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1
x = 5 → 2(5) - 1 = 10 - 1 = 9
To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero
2x - 1 = 0 , then
2x = 1 and
x = [tex]\frac{1}{2}[/tex]
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x) 2. If we multiply a polynomial by a constant, is the result a polynomial? 3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Answer:
1. k=0
2. yes, result is still a polynomial.
3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)
Step-by-step explanation:
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)
for k=0 any polynomial f(x) will reduce f(k) to the constant term.
2. If we multiply a polynomial by a constant, is the result a polynomial?
Yes, If we multiply a polynomial by a constant, the result is always a polynomial.
3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Yes.
If
deg(f+g) < deg(f) and
deg(f+g) < deg(g)
then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.