Answer:
0.28
Step-by-step explanation:
Depreciation Expense per mile:
= (Cost of delivery truck - Salvage value) ÷ Expected miles driver
=(33000-2760)÷108000=0.28 per mile
A line contains the point (4, 5) and has a slope of -2.
Which point is also on the line?
(5,7)
(6,2)
(5,3)
(4.1)
Answer: (5,3)
Step-by-step explanation:
Substituting into point-slope form, the equation of the line is
[tex]y-5=-2(x-4)[/tex]
Which rearranges as follows:
[tex]y-5=-2x+8\\\\y=-2x+13[/tex]
To determine if a point lies on a line, you can see if its coordinates satisfy the equation.
Of all the options, only (5,3) works.
Cos3A ×cos2A =cos A ×cos 2A -sin4A×sin A=prove it
Answer:
Step-by-step explanation:
cosA×cos 2A-sin4A×sinA
=cosAcos2A-2sin2Acos2A sin A
=cos 2A(cosA-2sin2AsinA)
=cos 2A(cosA-2×2sinAcosAsin A)
=cos2A×cosA(1-4sin²A)
=cos 2AcosA(1-4(1-cos²A))
=cos2A×cosA(1-4+4cos²A)
=cos 2A(-3cosA+4cos³A)
=cos 2A(4cos³A-3cosA)
=cos 2A×cos3A
For the equation 2x - y = 1, if x = 0, then y = ?
Answer:
y= -1
Step-by-step explanation:
(2) (0) − y = 1
0 + − y = 1
(−y) + (0) = 1
−y = 1
Step 2: Divide both sides by -1
Y = −1
Could someone show me a step by step process on how to do this problem? Calculus 2
The arc length is given by the definite integral
[tex]\displaystyle \int_1^3 \sqrt{1 + \left(y'\right)^2} \, dx = \int_1^3 \sqrt{1+9x} \, dx[/tex]
since by the power rule for differentiation,
[tex]y = 2x^{3/2} \implies y' = \dfrac32 \cdot 2x^{3/2-1} = 3x^{1/2} \implies \left(y'\right)^2 = 9x[/tex]
To compute the integral, substitute
[tex]u = 1+9x \implies du = 9\,dx[/tex]
so that by the power rule for integration and the fundamental theorem of calculus,
[tex]\displaystyle \int_{x=1}^{x=3} \sqrt{1+9x} \, dx = \frac19 \int_{u=10}^{u=28} u^{1/2} \, du = \frac19\times\frac23 u^{1/2+1} \bigg|_{10}^{28} = \boxed{\frac2{27}\left(28^{3/2} - 10^{3/2}\right)}[/tex]
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality. The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that to ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥. Be sure to use decimal numbers in your answer (such as using 0.40 for 40%). __________
Answer:
yes yes yes yes yes Yes Yes you are cute
Find the surface area of a sphere with radius 15 in
radius -15
Surface Area of a sphere =4πr^2
=4x22/7x15x15
=19800/7
=2828.57
i. 749x98+749 x2 ii. 62 x 999 +4795 iii. 736 x 97 iv. 258 x 1008
solve these using distributive property
pls help if u know
Step-by-step explanation:
I= 74810
II=66733
III=71392
iv=239904
In the diagram, is parallel to. Also, is drawn such that the length of is half the length of. If sin A = 0.5, then what is sin E?
sinE is 0.5
What are similar triangles?
Two triangles will be similar if the angles are equal (corresponding angles), and sides are in the same ratio or proportion (corresponding sides). Similar triangles may have different individual lengths of the sides of triangles, but their angles must be equal and their corresponding ratio of the length of the sides must be the same.
Clearly, given triangle AFB and triangle DFE are similar.
We know that Similar Triangles have the same corresponding angle
We can find sinE as show below:
From diagram clearly
∠A=∠E
and ∠B=∠D
Since, ∠A=∠E
Taking sin on both sides
sinA=sinE
Give, sinA=0.5
sinA=sinE=0.5
⇒ sinE=0.5
Hence, sinE is 0.5
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What is the measure of
angle x?
Enter your answer in the box.
X =
Answer:
x = 48°
Step-by-step explanation:
Complementary angles
Angles that sum to 90°.
Vertical Angle Theorem
When two straight lines intersect, the vertical angles are congruent (equal).
Therefore, angle x is equal to the angle that is complementary to 42°.
To find x, subtract 42° from 90°:
⇒ x = 90° - 42°
⇒ x = 48°
what is the area of the figure bellow?
Answer:
The area of the figure is C. 48.5 cm²
Evaluate the following expression at x = 3 and y = -4. 7x - 3y + 2.
provide your answer below:
Answer:
35
Step-by-step explanation:
first, you look at 7x, from the previous equation, you know that x=3, so you take 7x3=21 then you evaluate -3y. as you did with x on the last one you will look at the equation for y and see that it's -4. A negative times a negative is a positive, so -4x(-3)= 12. Then you add them all together, since 12 is a positive, the equation would now look like 21+12+2. After adding all three numbers together, you get 12.
What is the solution of the inequality shown
below?
c+3>8
Answer:
c > 5
Step-by-step explanation:
The properties of equality can be used to solve inequalities. Attention needs to be paid to ordering.
ApplicationWe can subtract 3 from both sides to solve this.
c +3 > 8 . . . . . . given
c +3 -3 > 8 -3 . . . . subtract 3 from both sides
c > 5 . . . . . . . . . simplify
The solution is c > 5.
__
Additional comment
Adding or subtracting a value to a number on a number line is equivalent to shifting it right or left. It does not change ordering.
Multiplying or dividing by a positive number is equivalent to expanding or compressing the distance from zero. It does not change ordering.
Multiplying or dividing by a negative number reflects the value across the origin, in addition to expanding or compressing the distance from zero. This reflection reverses the left-right ordering. For example, -2 < -1, but 2 > 1. (Both numbers multiplied by -1.)
As long as you're aware of the effect on ordering, you can use any of the properties of equality to solve inequalities.
A normal population has a mean u = 31 and standard deviation = 10. What proportion of the population is less than 30?
The proportion of the population exists less than 30 then
(x< 30) = 0.986.
How to estimate the proportion of the population that exists less than 30?To estimate the z-score using the formula, z = (x - µ)/σ
Where, x be the randomly chosen values = 30
µ be the mean = 31
σ be the standard deviation = 10
Proportion of the population that exists less than 18 = P(x < 30)
Plug in the values into z = (x - µ)/σ, to get z-score.
Substitute the values in the above equation, we get
z = (30 - 31)/10
z = -1/10 = -0.1
Therefore, the value of z = - 0.1.
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An insurance provider states that their customers save at least, on average, 300 dollars per year by switching to them, with a standard deviation of 150 dollars. Before we decide to switch to the new company and go through all of the hassle, we want to test the claim. So, we go out and sample 64 individuals who switched to the new insurance company and found them to have saved an average of 255 dollars per year. Do we have enough evidence at the α = 0.05 level to state that the insurance provider is false in their claim? Discussion Prompts Answer the following questions in your initial post: What are the hypotheses based on the words given in the problem? Should we use a Z or T distribution in this case? What is our Z or T statistic? What is the P-value? Based on your p-value and alpha, what conclusion will we make? Based on your results, would you switch to this company? Explain why or why not (Note: this can go beyond the use of statistics, but statistical analysis can help our decisions)
The solution to the question is mathematically given as
1)
H0: M [tex]\geqslant[/tex] 300
H0: M [tex]\geqslant[/tex] 300
2)
Z distribution.
3)
z=-2.4
4)
P=0.0082
5)
"H0" is rejected as a hypothesis with a level of significance of 0.05.
What is the hypothesis ?Generally, the equation for is mathematically given as
Solutions
we have, [tex]$u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}[/tex]
(1):
H0: M [tex]\geqslant[/tex] 300 dollars; customers save at least 300 dollars per year by switching to them.
H0: M [tex]\geqslant[/tex] 300 dollars:
(This is a left-tailed test)
(2):
when [tex]\sigma[/tex] is known, we use the Z test. we use Z distribution.
(3):
[tex]\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}[/tex]
(4):
[tex]Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082[/tex]
(5):
In conclusion, Since p-value = 0·0082 <0.05
This is statistically significant at the 0.05 level.
We thus "Refect H0" using a threshold of significance of 0.05.
"H0" is rejected as a hypothesis with a level of significance of 0.05.
There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.
Therefore, we would not consider making the transition to this firm.
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what is the greatest number that can divide 13,17 and 21 and have one as a remainder
Answer:
4
Step-by-step explanation:
this is the same question as what number can divide
13-1 = 12, 17-1 = 16 and 21-1 = 20 and has 0 remainder ?
the greatest number that can do that is 4.
we can easily see that, but formally, let's do prime factorization :
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 2 no
3 ÷ 3 = 1 finished
12 = 2×2×3
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1 finished
16 = 2×2×2×2
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 2 no
5 ÷ 3 no
5 ÷ 5 = 1 finished
20 = 2×2×5
so, the largest common factor is the combination of the longest streaks per factor they have in common.
they only have 2s in common.
and the longest common streak is 2×2 = 4.
hence the answer
(5.01 LC) A square is shown below. which expression can be used to find the area, in square units, of the Shaded triangle in the Square?
(answer options are in picture)
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
where s = side length.
If a diagonal is drawn to create 2 halves, then area of each half is 8.
So, The area of a square = 1/2 ( 4 · 4 ) = 16.
If a square has a side length of 4, then the area of the square is 16.
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
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PLEASE HELP ASAP !!!!
Which functions have a range of {y e R-00 < y < ∞0}?
O f(x) = -4x + 11
Of(x) = x - 8
O
f(x) = 2x+3
O f(x) = -(x + 1)² - 4
O
f(x)
f(x) = x²
x² + 7x9
Answer:
Options 1 and 2
Step-by-step explanation:
Correct. The range of all linear functions without a restricted domain is the set of all real numbers.Correct. The range of all linear functions without a restricted domain is the set of all real numbers.Wrong. The exponential cannot take negative values.Wrong. Quadratics do not have a range that is the set of real numbers.Wrong. Quadratics do not have a range that is the set of real numbers.Write down the answer for Q 7 and 8
The answers to the given addition operations are
7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46
8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72
Addition operationFrom the question, we are to add the given numbers
7. 6 Hundredths add to 4 tenths add to 6 ones is equal to
6 Hundredths = 0.06
4 tenths = 0.4
6 ones = 6
Thus, we get
0.06 + 0.4 + 6 = 6.46
8. 82 Hundredths add to 9 tenths add to 4 tens is equal to
82 Hundredths = 0.82
9 tenths = 0.9
4 tens = 40
Thus, we get
0.82 + 0.9 + 40 = 41.72
Hence, the answers to the given addition operations are
7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46
8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72
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a dust mite is 400 pm long under a microscope, it looks 100,000 pm long. what magnification scale was used
Answer: 250:1
Step-by-step explanation:
Divide the measurement of appearance by the actual measurement.
[tex]100,000/400=250[/tex]
The magnification scale is 250:1. The scale is used by a 250X magnifying lense.
Throughout this course, you have examined how real-world scenarios can be modelled using quadratic functions, exponential functions, trigonometric ratios sinusoidal functions, and sequences and series. Part A:- In this task, you will be creating unique real-world problems that can be modelled using the functions that we have learned. You may use real-world scenarios that we have examined throughout the course, but your problem should be created by you and have a unique description. Choose three (3) of the five (5) topics below and create a real-world scenario related to each of the three. 1. Exploring Quadratic Functions to Find Zeros or the Vertex; 2. Exponential Growth or Decay; 3. Using Trigonometric Ratios to Solve Three Dimensional Problems; 4. Representing Periodic Behaviour with Sinusoidal Functions: 5. Solving Financial Problems using Sequences & Series.
PLEASE SOLVE WITHOUT USING RADINAS
The exponential function is illustrated below.
How to illustrate the example?An exponential function has a growth factor or 3.76. What is the percentage growth rate?
The growth factor (b) is given as:
b = 3.76
So, the percentage growth rate (r) is calculated as:
r = b - 1
Substitute known values
r = 3.76 - 1
Evaluate the difference
r = 276%
The way to solve Financial Problems using Sequences & Series will be:
The first salary that Mr James earn is 10000 and there is a yearly increase of 2000. Find his salary in the 5th year. This will be:
= a + (n - 1)d
= 1000 + (5 - 1)2000
= 10000 + (4 × 2000)
= 10000 + 8000.
= 18000
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A restaurant manager has the option of a 30-year loan of $417,000 at an annual interest rate of 3.85% or the same interest rate but on a loan for 15 years.
(a)
Calculate the monthly payment for each loan. (Round your answers to the nearest cent.)
30-year $
15-year $
(b)
Calculate the savings in interest by using the 15-year loan. (Round your answer to the nearest cent.)
$
(c)
The term of the 15-year loan is one-half the term of the 30-year loan. Is the monthly payment for the 15-year loan twice that of the 30-year loan?
Yes
No
(d)
Is the interest savings for the 15-year loan more or less than one-half of the interest paid on the 30-year loan?
more
less
a) The monthly payment for each loan is as follows:
30-year $1,954.93
15-year $3,053.25
b) The savings in interest by using the 15-year loan is $154,189,20 ($286,774.20 - $132,585).
c) No. the monthly payment for the 15-year loan is not twice that of the 30-year loan as the loan term.
d) The interest savings for the 15-year loan are more than one-half of the interest paid on the 30-year loan.
How are the calculations for periodic payments done?The calculations for the monthly payments, including interests can be carried out using an online finance calculator, as follows:
30-year Loan:N (# of periods) = 360 months (12 x 30 years)
I/Y (Interest per year) = 3.85%
PV (Present Value) = $417000
FV (Future Value) = $0
Results:
PMT = $1,954.93
Sum of all periodic payments = $703,774.80 ($1,954.93 x 360)
Total Interest = $286,774.20 ($703,774.80 - $417,000)
15-year Loan:N (# of periods) = 180 months (12 x 15 years)
I/Y (Interest per year) = 3.85%
PV (Present Value) = $417000
FV (Future Value) = $0
Results:
PMT = $3,053.25
Sum of all periodic payments = $549,585 ($3,053.25 x 180)
Total Interest = $132,585 ($549,585 - $417,000)
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HELPPPP PLSSSSSSSSS!!!!!!!!??!
Answer:
(3+3) x (3+1)
Step-by-step explanation:
nice
We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.
Solution :» (1 + 3) × (3 + 3)
» (4) × (6)
» 24
Here's our answer..!!
Can someone help me with a step by step process of how to solve this? Calculus 2
If you fix a point on the curve in the given interval, and revolve that point about the [tex]x[/tex]-axis, it will trace out a circle with radius given by the function value [tex]y[/tex] for that point [tex]x[/tex]. The perimeter of this circle is then [tex]2\pi(8\sqrt x) = 16\pi \sqrt x[/tex].
The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].
So, the surface area is given by the definite integral
[tex]\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}[/tex]
Which of the following options have the same value as 5\%5%5, percent of 353535?
Answer:
[tex]\frac{5}{100}\times35[/tex]
[tex]0.05\times35[/tex]
Step-by-step explanation:
Given:
Which of the following options have the same value as 5% 35, percent of 35?
Following Options:
[tex]5 \times 35[/tex]
[tex]\frac{5}{100}\times35[/tex]
[tex]0.5\times0.35[/tex]
[tex]0.05\times35[/tex]
[tex]\frac{5}{10}\times35[/tex]
Solve:
[tex]5[/tex] % [tex]= 0.05=\frac{5}{100}[/tex]
Thus the following options:
[tex]5 \times 35[/tex] [ False x ]
5 does not equal 5%
[tex]\frac{5}{100}\times35[/tex] [True √ ]
[tex]5[/tex]% [tex]=\frac{5}{100}[/tex]
[tex]0.5\times0.35[/tex] [ False x ]
[tex]0.5 = 0.50[/tex]
[tex]0.05\times35[/tex] [True √ ]
[tex]5[/tex]% [tex]= 0.05=\frac{5}{100}[/tex]
[tex]\frac{5}{10}\times35[/tex] [ False x ]
[tex]\frac{5}{10}=0.50[/tex]
Therefore, the options [B] [tex]\frac{5}{100}\times35[/tex] and [D] [tex]0.05\times35[/tex] is True.
Kavinsky
NO LINKS!!! Please help me with this problem
Answer:
9
Step-by-step explanation:
To find the rate of change we use the formula
f(x2) - f(x1)
------------------
x2 -x1
f(x) = 9x
x2 = 9 and x1 = 0
f(x2) = 9( 8) = 72
f(x1) = 9(0) =0
The rate of change is
72 - 0
------------
8-0
72
----
8
9
The rate of change is 9
Answer:
9
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given:
f(x) = 9xinterval: 0 ≤ x ≤ 8Therefore:
a = 0b = 8Substitute the given values into the average rate of change formula:
[tex]\begin{aligned}\implies \dfrac{f(8)-f(0)}{8-0} & = \dfrac{9(8)-9(0)}{8-0}\\\\& = \dfrac{72-0}{8-0}\\\\& = \dfrac{72}{8}\\\\& = 9\end{aligned}[/tex]
Therefore, the average rate of change of the function f(x) over the interval 0 ≤ x ≤ 8 is 9.
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find the value of x,y in the given figure with reasons.
Answer:
answer
x= 40°
Step-by-step explanation:
x= 40° [ base angle of isocles triangle]
Find d²y/dx² for implicitly in terms of x and y
xy-1=2x+y²
The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].
What is the second derivative of an implicit equation?
In this problem we have a function in implicit form, that is, an expression of the form: f(x, y, c) = 0, where c is a constant. Then, we should apply implicit differentiation twice to determine the second derivative of the function:
Original expression
x · y - 1 = 2 · x + y²
First derivative
y + x · y' = 2 + 2 · y · y'
(x - 2 · y) · y' = 2 - y
y' = (2 - y) / (x - 2 · y)
Second derivative
y' + y' + x · y'' = 2 · (y')² + 2 · y · y''
2 · y' - 2 · (y')² = (2 · y - x) · y''
y'' = 2 · [y' - (y')²] / (2 · y - x)
y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]]
The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].
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P=2(L+W) Solve for W
Answer:
W = (P -2L)/2
Step-by-step explanation:
P = 2(L + W) Distribute the 2
P = 2L + 2W Subtract 2L from both sides
P - 2L = 2W Divide both sides by 2
(P-2L)/2 = W
please help!!
maths functions
Answer:
The Co-ordinate of C is (4/3, -1/2)
Step-by-step explanation:
We have two equation one is of straight line equation which is:
y=2x-3 (i)
Other equation is of quadratic function which is:
y=-3x^2+5 (ii)
Put the value of y from equation (i) in equation (ii)
So, we have:
2x-3=-3x^2+5
3x^2+2x-8=0
By factorization:
3x^2+6x-4x-8=0
3x(x+2)-4x(x+2)=0
(x+2)(3x-4)=0
x+2=0 ; 3x-4=0
x=-2 ; x=4/3
Put first x=-2 in equation (i)
y=2(-2)-3
y=-4-3
y=-7
Now Put x=4/3 in equation (i)
y=2(4/3)-3
y=8/3-3
y=-1/2
So, we have two Order pair One is (-2 , -7) and Second one is (4/3 , -1/2)
Hence the Co-ordinate of C is:
C=(4/3 , -1/2)
Answer:
Point C: (3, 3)
Point D: (3, -22)
Step-by-step explanation:
If the distance between points C and D is 25 units, the y-value of point D will be 25 less than the y-value of point C. The x-values of the two points are the same.
Therefore:
[tex]\textsf{Equation 1}: \quad y=2x-3[/tex]
[tex]\textsf{Equation 2}: \quad y-25=-3x^2+5[/tex]
As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:
[tex]\implies 2x-3-25=-3x^2+5[/tex]
[tex]\implies 3x^2+2x-33=0[/tex]
[tex]\implies 3x^2-9x+11x-33=0[/tex]
[tex]\implies 3x(x-3)+11(x-3)=0[/tex]
[tex]\implies (x-3)(3x+11)=0[/tex]
[tex]\implies x=3, -\dfrac{11}{3}[/tex]
From inspection of the given graph, the x-value of points C and D is positive, therefore x = 3.
To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:
[tex]\begin{aligned} \textsf{Point C}: \quad 2x-3 & =y\\2(3)-3 & =3\\ \implies & (3, 3)\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Point D}: \quad -3x^2+5 & = y \\ -3(3)^2+5 & =-22\\ \implies & (3, -22)\end{aligned}[/tex]
Therefore, point C is (3, 3) and point D is (3, -22).
The function f(x) is shown in the graph
f(a)
Which type of function describes ((x)?
© Exponential
O Logarithmic
O Rational
O Polynomial
Answer:
the function is an exponential funtion.
Step-by-step explanation:
learned it