Answer:
C(4,6)
Step-by-step explanation:
the x turns into its opposite when reflected across y same thing for y when reflected across x
Answer:
c. (4, 6)
Step-by-step explanation:
The rule of an reflection about the y-axis is: [tex]A(x,y)\rightarrow A'(-x,y)[/tex]
Apply the rule to point (-4, 6):
[tex]\frac{(-4,6)\rightarrow\boxed{(4,6)}}{(x,y)\rightarrow(-x,y)}[/tex]
Option C should be the correct answer.
Century Roofing is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.)
Question Completion:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Answer:
Century Roofing
Project's NPV is: ($6,578)
Step-by-step explanation:
a) Data and Calculations:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)
Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700
PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)
NPV = Cash inflow minus Cash outflow
= $158,422 - $165,000
= ($6,578)
Negative NPV
b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value. It becomes a present cash outflow. Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.
3
BO
Evaluate the function f(x) = x2 + 4x + 1 at the given values of the independent variable and simplify.
a. f(6)
b. f(x +9)
c. f(-x)
Answer:
a) f(6)=(6)^2+4(6)+1=65
b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117
f (-x)=(-x)^2-4x+1
coefficient of 8x+7y
Answer:
8
Step-by-step explanation:
Identify the exponents on the variables in each term, and add them together to find the degree of each term.
8x→1
7y→1
The largest exponent is the degree of the polynomial.
1
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient of a polynomial is the coefficient of the leading term.
____________________________________________________________
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient in a polynomial is the coefficient of the leading term.
8
List the results.
Polynomial Degree: 1
Leading Term: 8x
Leading Coefficient: 8
Hope This Helps!!!
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
algebra pyramid please answer !! be the first to be marked as a brainliest .
Answer:
The first pyramid:
63x
39x 24x
23x 16x 8x
The second pyramid:
162x
82x 80x
4x 78x 2x
The third pyramid:
12a+2b
9a+b 3a+b
9a b 3a
The fourth pyramid:
-19a
-5a -14a
3a -8a -6a
Step-by-step explanation:
All that an alegbra pyramid is is adding the two terms below it.
So you can see how I added the terms that lied below each number, such as in number 1: I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.
Hope this helped!
Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).
Answer:
The work done by the force is 42.4 Joules
Step-by-step explanation:
The force F = 7 pounds
angle to the horizontal that the force acts ∅ = 30°
The object is moved a distance d = 7 feet
The coordinate (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.
The work done by this force = F cos ∅ x d
==> 7 cos 30° x 7
==> 7 x 0.866 x 7 = 42.4 Joules
A human factor expert recommends that there be atleast 9 square ft of floor space in a classroom for every student in the class. Find the min space required for 49 students
13,226 divided by 29
13226/29= 456.068965517
A type of related samples design in which participants are observed more than once is called a
A. repeated measures design
B. matched pairs design
C. matched samples design
D. both matched pairs design and matched samples design
Answer:
Option A (repeated measures design) is the correct option.
Step-by-step explanation:
Researchers as well as statisticians vary in terms of methods used mostly for repetitive measurements. Besides illustration, repeated models of measurements are however recognized as repeated analyzes of variance measurements, standardized considerations of measurements, or layouts of objects throughout them.The other three options are not related to the given instance. So that alternative A would be the correct choice.
Which expression is equal to (1+6i)−(7+3i) ?
Answer:
- 6+3iStep-by-step explanation:
[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]
Find the indicated complement. A certain group of women has a 0.12% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
Answer:
the probability will be 0.
Step-by-step explanation:
0.12%= 0.0012= 3/2500.
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answer:
The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 100[/tex]
The percent of people who write this exam obtain scores between 350 and 650
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]
[tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]
[tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]
From the z-table [tex]P(Z < -1.5 ) = 0.066807[/tex]
and [tex]P(Z < 1.5 ) = 0.93319[/tex]
=> [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]
=> [tex]P(350 < X 650 ) = 0.866[/tex]
Therefore the percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
5/7 minus 2/9 please
Answer:
[tex]\large \boxed{31/63}[/tex]
Step-by-step explanation:
5/7 - 2/9
Make denominators equal by LCM.
(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)
45/63 - 14/63
Subtract fractions since denominators are equal.
(45 - 14)/63
31/63
Answer:
[tex]\frac{31}{63}[/tex]
Step-by-step explanation:
Find the LCM of 7 and 9: 63Find how much we increased each number to get to 63: we increased 7 by 9, and we increased 9 by 7Multiply the numerators by the corresponding increase numbers: 5 × 9 = 45, and 2 × 7 = 14Put the new numerators over the new denominators, so it looks like this: [tex]\frac{45}{63}[/tex] and [tex]\frac{14}{63}[/tex] Finally, subtract one from the other and here's what you get: [tex]\frac{31}{63}[/tex]Therefore, the answer is [tex]\frac{31}{63}[/tex].
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?
Answer:
8.8 pounds
Step-by-step explanation:
Given the following :
Combined weight loss which occurred within a week = 28 kg
Number of days in a week = 7 days
1 kilogram (kg) = 2.2 pounds
Combined weight loss in pounds that occurs within a week:
Weight loss in kg × 2.2
28kg * 2.2 = 61.6 pounds
Assume weight loss occurred at a constant rate :
Weight lost by the group per day :
(Total weight loss / number of days in a week)
(61.6 pounds / 7)
= 8.8 pounds daily
Answer:
88
Step-by-step explanation:
Found the answer and I am doing the quiz rn lel
A new fast-food firm predicts that the number of franchises for its products will grow at the rate dn dt = 6 t + 1 where t is the number of years, 0 ≤ t ≤ 15.
Answer:
The answer is "253"
Step-by-step explanation:
In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:
Given:
[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]
[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]
integrate the above value:
[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]
When the value of n=1 then t=0
[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]
so the value of n is:
[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]
when we put the value t= 15 then,
[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]
Compute the least-squares regression line for the given data set. Use a TI-84 calculator. Round final answers to four decimal places, as needed.
x 5 7 6 2 1
y 4 3 2 5 1
Regression line equation: ŷ = _______ + _______ x.
Answer:
Y = 2.843+ 0.037 X
Step-by-step explanation:
Let the equation of the straight line to be fitted to the data , be Y = a+b X where a and b are to be evaluated. The normal equations fro determining a and b are
∑Y = na +b ∑X
∑XY = a∑X + b∑X²
We now calculate ∑X, ∑Y , ∑X², and ∑XY
X Y XY X²
5 4 20 25
7 3 21 49
6 2 12 36
2 5 10 4
1 1 1 1
21 15 64 115
Thus the normal equation becomes
5a + 21b =15
21a +115b = 64
Solving these two equations simultaneously we get
105 a + 441b = 315
105a + 575b = 320
134b= 5
b= 0.037 , a= 2.843
Hence the equation for the required straight line is
Y = 2.843+ 0.037 X
name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)
Answer:
Step-by-step explanation:
Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.
- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.
∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]
- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.
∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]
- Angles having the same relative positions at the point of intersection are the corresponding angles.
∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]
- Co interior angles are the angles between the parallel lines located on the same side of the transversal.
∠4 and ∠5, ∠3 and ∠6 [Co interior angles]
- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.
∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]
Determine if the process appears to be within statistical control. If not, state the reason why not.
a. It does not appear to be within statistical control because there is an upward shift.
b. It appears to be within statistical control.
c. It does not appear to be within statistical control because there is an upward trend.
d. It does not appear to be within statistical control because there is increasing variation.
Answer:
c. It does not appear to be within statistical control because there is an upward trend.
Step-by-step explanation:
Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.
What is the measure of FEG?
A. 30 degrees
B. 40 degrees
C. 50 degrees
D. 70 degrees
Please include ALL work!! <3
Answer:
C. 50 degrees
Step-by-step explanation:
Because 6x + 5x = 110° and x = 10
5×10 = FEG 50°
Find the measure of A.
A. 50
B. 70
C. 100
D. 90
Answer:
D
Step-by-step explanation:
I don't know how to eliminate the wrong answers.
Two line segments which have one end at a diameter and the other end meeting at a common point, make a 90 degree angle.
A is made that way, so A is 90 degrees.
Answer:
Step-by-step explanation:
I believe it is 90
Find an exact value of sin(17pi/12)
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\frac{(17)(3.141593)}{12}[/tex]
= [tex]\frac{53.407075}{12}[/tex]
= [tex]4.45059[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
I have an answer and explanation but I can't type so search up the question you asked and you should get an answer and explanation from s0cratic.
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
Given the following hypotheses: H0: μ = 490 H1: μ ≠ 490 A random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9. Using the 0.01 significance level:
a.) State the decision rule.
b.) Compute the value of the test statistic.
c.) What is your decision regarding the null hypothesis?
Answer:
We conclude that the population mean is equal to 490.
Step-by-step explanation:
We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490 {means that the population mean is equal to 490}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490 {means that the population mean is different from 490}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_1_4[/tex]
where, [tex]\bar X[/tex] = sample mean = 495
s = sample standard deviation = 9
n = sample of observations = 15
So, the test statistics = [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= 2.152
The value of t-test statistics is 2.152.
Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that the population mean is equal to 490.
A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles. Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.
Compute the linear speed on the surface of the planet at 30 degrees north latitude.
Answer:
The velocity is [tex]v = 886.96 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
The period of each revolution is [tex]T = 1\ day = 24 \ hours[/tex]
The angle is [tex]\theta = 30^o[/tex]
The radius is [tex]r = 3387.5 \ miles[/tex]
Generally the linear speed is mathematically represented as
[tex]v = w * r[/tex]
Where [tex]w[/tex] is the angular speed which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 *3.142 }{24}[/tex]
[tex]w = 0.2618 \ rad/s[/tex]
Thus
[tex]v = 0.261833 * 3387.5[/tex]
[tex]v = 886.96 \ m/s[/tex]
Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked.Required:a. What is the (approximate) probability that X is at most 30?b. What is the (approximate) probability that X is less than 30?c. What is the (approximate) probability that X is between 15 and 25 (inclusive)?
Answer:
(a) The probability that X is at most 30 is 0.9726.
(b) The probability that X is less than 30 is 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.
Step-by-step explanation:
We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.
Let X = the number among these that are nonconforming and can be reworked
The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).
Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.
Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).
So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22
and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]
= 4.42
So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])
(a) The probability that X is at most 30 is given by = P(X < 30.5) {using continuity correction}
P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726
The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.
(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5) {using continuity correction}
P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554
The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5) {using continuity correction}
P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852
P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)
= 1 - 0.9554 = 0.0446
The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.
Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.
Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.
Answer:
Its 10x^2+12
Step-by-step explanation:
Answer:
-10X^2+12
Step-by-step explanation:
A passenger train traveled 180 miles in the same amount of time it took a freight train to travel 120 miles. The rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
Answer:
The passenger train is moving at 45 miles per hour
Step-by-step explanation:
Let the amount of time it took the two trains to travel the distance = t.
Since the two trains traveled the distance at the same time,
Rate of the passenger train =[tex]\frac{180}{t}[/tex]
Rate of the freight train = [tex]\frac{120}{t}[/tex]
Where t is in hours.
From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as
[tex]\frac{120}{t}= \frac{180}{t}-15[/tex]
from the above equation, we can now get our value for t as
[tex]\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours[/tex]
We have our time of travel for the two trains as 4 hours.
The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour
Carla drove her truck 414 miles on 18 gallons of gasoline. How many miles did she drive per gallon?
Answer:
23 miles per gallon
Step-by-step explanation:
414 miles = 18 gallons
=> 18/18 gallons = 414/18 miles
=> 1 gallon = 23 miles
So, she drove 23 miles per gallon.
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years
Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
