Answer:
348.331 ft/s237.498 mi/hStep-by-step explanation:
There are two parts to this problem:
compute the speed from distance and timeexpress it in appropriate units.As you can learn from any speed limit sign, speed is in units of distance per time--miles per hour in the US. To compute speed, you divide distance by time.
If we were to use the given numbers directly, dividing distance in miles by time in seconds, our speed would have units of miles per second. In order to change the units to the ones asked for by the problem statement, we need to make one of two conversions.
For the first part, we need to convert miles to feet, so our speed is in feet per second instead of miles per second. For the second part, we need to convert seconds to hours, so the speed is in miles per hour.
__
Any units conversion can be done using a conversion factor that is a fraction that has a value of 1. That is, its numerator is equal to its denominator.
For the conversion from miles to feet, we want to cancel units of miles and leave units of feet. The operation on units looks like ...
[tex]\dfrac{miles}{second}\times\dfrac{feet}{mile}=\dfrac{feet}{second}[/tex]
The units of miles in the numerator cancel the units of miles in the denominator, so we're left with feet per second, as we want. In order to make the conversion factor have a value of 1, it must be ...
(5280 ft)/(1 mi) . . . . . . numerator equal to denominator
(a) Express the speed in ft/s:
(2.5 mi)/(37.895 s) × (5280 ft)/(1 mi) = 2.5·5280/37.895 ft/s ≈ 348.331 ft/s
__
(b) For the conversion to miles per hour from miles per second, we need to cancel the units of seconds in the denominator and replace them with hours. The conversion factor for that is ...
(3600 s)/(1 h) . . . . . . numerator equal to denominator
(2.5 mi)/(37.895 s) × (3600 s)/(1 h) = 2.5·3600/37.895 mi/h ≈ 237.498 mi/h
Between what two consecutive integers is √151
1) 11 and 12
2) 9 and 10
3) 12 and 13
4) 14 and 15
Answer:
The answer to your question is: 3) between 12 and 13
Step-by-step explanation:
Just get the square root of 151, and compare your result with the options.
√ 151 = 12.28
Then, the only possibility is (3) 12 and 13.
Which of the following is a concern about globalization? A. The possibility of promoting child labor B. Less jobs in exporting industries C. Less variety in consumer goods D. Higher prices for consumer goods
Answer:
A
Step-by-step explanation:
A: The possibility of promoting child labor is a concern about globalization
What is the volume of a right rectangular prism when the height is 11 m and the area of the square base is 9m 2 ?
Answer:
The answer to your question is: 99 m²
Step-by-step explanation:
Data
height = 11 m
area of the square base = 9 m²
Formula
Volume of a right rectangular prism = area of the base x height
= 11 x 9 substitution
= 99 m²
Can you please answer this?
Part A: What is the solution to the pair of equations represented by g(x) and p(x)?
Part B: Write any two solutions for p(x).
Part C: What is the solution to the equation g(x) = f(x)? Justify your answer.
Answer:
A. (1, -1)
B. (1, -1), (2, 0)
C. x = 0
Step-by-step explanation:
A graph is a plot of all the points that are solutions to an equation.
Part A:
A point will be a solution to two equations if it is a point of intersection of their graphs. The one point that is a solution to both p(x) and g(x) is the one point where their graphs intersect: the red and blue lines cross at (1, -1).
__
Part B:
Any other point on the graph p(x) will be another solution of it. One that is near to the point of intersection with g(x) is the point where p(x) crosses the x-axis: (2, 0). Of course, the solution listed in Part A is also a solution to p(x).
__
Part C:
The point where the graph of g(x) crosses the graph of f(x) is (0, 3). The x-value that makes g(x) = f(x) is x=0. That is the solution to this equation. (We don't really care what the values of f(0) and g(0) are--just that they are equal.)
I need help on this one ASAPP
Answer:
At most 5 --> x ≤ 5
Larger than 5 --> x > 5
Below 5 --> x < 5
Not less than 5 --> x ≥ 5
Step-by-step explanation:
I learned how to figure this out like this: "The smaller number eats the bigger one", since the symbols "<" and ">" looks like an open mouth.
The symbols "≥" and "≤" mean that it is larger or equal to the number shown.
In the first case, it means that the number that represents "x" could be any up to the number 5 (including it). And in the last case, it means that the number that represents "x", could be any starting from 5(including it).
Help me ASAP PLEASE
Answer:
4. Functions: 1, 2, 4, 5, 7, 8, 11, 12
5. y = -1/2x+5/2, x ≤ -1; 2x +1, x > -1.
y = 2, x < 0; x, 0 ≤ x ≤ 3; 3 x > 3.
Step-by-step explanation:
4. A list of ordered pairs is a function of no x-values are re-used. In (3) and (6), the value x=2 is used more than once.
A graph represents a function if it passes the "vertical line test." A vertical line cannot intersect the graph in 2 or more points. (9) and (10) both fail that test.
If the relation is not listed here as being "not a function," then it is one of the answers to question 4.
__
5. The first step in writing the equation of a piecewise function is to identify the pieces. These are generally bounded by points of discontinuity--jumps in the function value, or changes in the slope of lines.
The second step is to identify the section of the function that boundary points belong to. Solid dots are part of the function definition; open circles are not.
Left Graph
The left piece ends at x=-1. There is a solid dot attached to the left piece, so its definition will be for the domain x ≤ -1. That line has slope -1/2, since is drops 1 unit for each 2 to the right. If extended, it would intersect the y-axis at y = 2 1/2 = 5/2. So, the piece on the left is y = -1/2x + 5/2 for x ≤ -1.
The right piece starts at x=-1, but does not include that point. It has a rise of 2 for each 1 to the right, so its slope is 2. It crosses the y-axis at y=1, so the piece on the right is y = 2x + 1 for x > -1.
You can use the method of your textbook author to combine theses pieces into one equation. The method shown above is one way to do it.
__
Right Graph
This graph has a discontinuity at x=0 and a change in slope at x=3. It can be described by 3 pieces. The point at x=0 does not belong to the left piece, but goes with the middle piece.
The left piece of the function is the constant 2, so has the equation y = 2 for x < 0.
The middle piece has a slope of 1 and a y-intercept of 0, so has the equation y = x for 0 ≤ x ≤ 3.
The point at x=3 belongs to both the middle piece and the right piece, so can be part of both function definitions, if you like. Generally, it is better form to include any given x-value in only one of the pieces of the function. So the equation for the right piece can be y = 3 for x > 3.
For the following situation determine what type of sampling was used. A research company believes teens today are getting less than the recommended hours of sleep. The company takes a list of 2000 teen volunteers and assigns each volunteer a number. A random number generator is used to select 350 individuals to take part in a sleep survey.
Answer: Simple random sampling.
Step-by-step explanation:
A simple random sample is basically a subset (with size n) from the entire population, where the chance of getting selected for each element is equal.
Given :A research company believes teens today are getting less than the recommended hours of sleep. The company takes a list of 2000 teen volunteers and assigns each volunteer a number. A
A random number generator is used to select 350 individuals to take part in a sleep survey.
It is a simple random sampling because the researcher selected participants randomly such that the chance to get selected for each of them remains same.
The perimeterof a parralelagram is 60 meters. The width of the parralelgram is 6 meters less than its length. Find the length and width of the paralelogram
Answer:
The answer to your question is:
length = 12
width = 6
Step-by-step explanation:
Perimeter of a parallelogram = 2 length + 2 width
We know that width = length - 6
So
60 = 2 length + 2(length -6)
60 = 2 length + 2 length - 12
60 - 12 = 4 length
48 = 4 length
length = 48/4 = 12 meters
width = length - 12
= 12 - 6
= 6
Answer:
12
6
Step-by-step explanation:
An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. The standard deviation of completion times is 1.6 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 33 completion times under new management was taken. The sample had a mean of 11.2 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.
Let [tex]\mu[/tex] be the population mean.
Null hypothesis : [tex]\mu=12[/tex]
Alternative hypothesis : [tex]\mu<12[/tex]
Since Alternative hypothesis is left tailed so , the test is a left tailed test.
Given : n=33 > 30 , so we use z-test.
Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
i.e. [tex]z=\dfrac{11.2-12}{\dfrac{1.6}{\sqrt{33}}}\approx-2.87[/tex]
Using z-value table,
P-value for left tailed test =[tex]P(z<-2.87)=0.0020524[/tex]
Since , the p-value (0.0020524) is less than the 0.05 level of significance, it means we reject the null hypothesis.
Therefore, we have enough evidence to support the claim that the mean completion time has decreased under new management.
Which is the range of the function f(x) =One-seventh(9)x?
a: all real numbers
b: all real numbers less than 0
c:all real numbers greater than 0
d: all real numbers less than or equal to 0
Answer:
Option c: all real numbers greater than 0
Step-by-step explanation:
we have
[tex]f(x)=\frac{1}{7}(9^{x})[/tex]
This is a exponential function of the form
[tex]f(x)=a(b^{x})[/tex]
where
a is the initial value (y-intercept)
b is the base
r is the rate
b=(1+r)
In this problem we have
a=1/7
b=9
r=b-1 ----> r=9-1=8 -----> r=800%
using a graphing tool
see the attached figure
The domain is the interval ------> (-∞,∞)
The domain is all real numbers
The range is the interval ---------> (0,∞)
The range is all real numbers greater than zero
Answer: all real numbers greater than 0
Step-by-step explanation:
Range is the set of y values for which the function is defined using a graphing tool
The domain is the interval ----> (-∞,∞) All real numbers
For all positive and negative values for x the value of y is always positive
The range is the interval ---->(0,∞)
All real numbers greater than 0
Match the following:a. When two variables change in the same direction, one remaining larger than the other by the same factor b. To insert between neighboring points or estimate by taking an average of known values c. A relationship between two variables in which the product remains constant. When one variable increases the other decreases in proportion so that the product is unchanged 1. direct relationship2. interpolate 3. inverse relationship
Answer:
a. When two variables change in the same direction, one remaining larger than the other by the same factor - direct relationship
b. To insert between neighboring points or estimate by taking an average of known values - interpolate
c. A relationship between two variables in which the product remains constant. When one variable increases the other decreases in proportion so that the product is unchanged - inverse relationship
Jill and Marcy go to an ice cream store where they have the option of getting a smoothie in either a cylindrical or rectangular container. The cylinder has a height of 8 cm and a radius of 8 cm. The rectangular container has a height of 8 cm, a length of 8 cm, and a width of 5 cm. Jill purchased the cylindrical container and Marcy purchased the rectangular container. Who got the larger smoothie, and what was its volume?
Answer: Jill got the larger smoothie and its volume is 1609.14 cubic cm.
Step-by-step explanation:
Since we have given that
Jill purchased the cylindrical container.
Height of container = 8 cm
Radius = 8 cm
So, volume of cylindrical container would be
[tex]\pi r^2h\\\\=\dfrac{22}{7}\times 8\times 8\times 8\\\\=1609.14\ cm^3[/tex]
Marcy purchased the rectangular container.
Height of container = 8 cm
Width = 8 cm
Length = 8 cm
so, volume of rectangular container would be
[tex]l\times b\times h\\\\=8\times 8\times 8\\\\=512\ cm^3[/tex]
Hence, Jill got the larger smoothie and its volume is 1609.14 cubic cm.
Can someone please help?
60 ≥ 35 + 5t
-35 -35
25 ≥ 5t
5 5
t≤5
his mistake was that he used ≤ for at least instead of using ≥. so at end, when I solved, I saw that Sven should spend 5 minutes or less on each scale.
Can anyone double check my work for me?
Answer:
They're are all correct.
Step-by-step explanation:
I went each of them carefully. They are all correct.
PLEASE HELP!!!
The density of lead is 11.34 g/cm^3 and the density of aluminum is 2.69 g/cm^3. Find the radius of lead and aluminum spheres each having a mass of 50 kg.
Answer:
You have to replace x for each density
Step-by-step explanation:
Density = Mass / Volumen
1,000 g = 1 kg
1,000,000 cm^3 = 1 m^3
g/cm^3 = 1000 kg/m^3
Using density as x
[tex]volumen \: = \frac{50000}{x} \\ volumen \: sphere \: = 4\pi {r}^{3} \\ 4\pi {r}^{3} = \frac{50000}{x} \\ r = \sqrt[3]{ \frac{50000}{4\pi {x}^{} } } [/tex]
Density can be defined as the mass per unit volume of a given substance.
The formula is given as:
Density = Mass / volume
The radius of the Aluminum sphere is 16.43cm and the radius of the Lead sphere is 10.17 cm
The density of lead is 11.34 g/cm³.The density of aluminum is 2.69 g/cm³.Mass of lead and Aluminum = 50kgStep 1: Convert the masses of Lead and Aluminium from kg to g1 kg = 1000g
50kg = ?
Cross Multiply
50kg × 1000g/ 1 kg
= 50,000g
The mass of lead and Aluminum is 50,000g
Step 2: Find the Volume and radius of AluminiumThe density of Aluminum is 2.69 g/cm³.
Mass of Lead is 50,000g
Volume = Mass/ Density
Volume of Aluminum = 50,000g/ 2.69 g/cm³
Volume of Aluminium = 18587.360595 cm³
The Volume of the Aluminum Sphere = 18587.360595 cm³
The formula to find the radius is given as
(3V/4π)[tex]^{1/3}[/tex]
= (3 × 18587.360595/ 4π)[tex]^{1/3}[/tex]
The radius of the lead sphere = 16.43 cm
Step 3: Find the Volume and radius of LeadThe density of lead is 11.34 g/cm³.
Mass of Lead is 50,000g
Volume = Mass/ Density
Volume of Lead = 50,000g/ 11.34 g/cm³
Volume of Lead = 4409.1710758 cm³
The Volume of a Lead Sphere = 4409.1710758 cm³
The formula to find the radius is given as
(3V/4π)[tex]^{1/3}[/tex]
= (3 × 4409.1710758/ 4π)[tex]^{1/3}[/tex]
The radius of the lead sphere = 10.17 cm
Therefore, the radius of the Aluminum sphere is 16.43cm and the radius of the Lead sphere is 10.17 cm.
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A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.
- Reject the null hypothesis with either a one-tailed or a two-tailed test
- Fail to reject the null hypothesis with a one-tailed test but reject with two tails
- Reject the null hypothesis with a one-tailed test but fail to reject with two tails
- Fail to reject the null hypothesis with either a one-tailed or a two-tailed test
Answer:
Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.
Step-by-step explanation:
We are given the following information:
n = 16
[tex]t_{statistic} = 1.94[/tex]
[tex]\alpha = 0.05[/tex]
Now,
Right One-tail Test
[tex]t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753[/tex]
[tex]t_{stat} > t_{critical}[/tex]
We reject the null hypothesis in this case.
Two-tail Test
Now, [tex]t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = \pm 2.131[/tex]
[tex]-2.131 < t_{stat} < 2.131[/tex]
We accept the null hypothesis in this case.
Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.
The correct decision for this hypothesis test is to reject the null hypothesis with a one-tailed test but fail to reject with two tails.
Explanation:To make a decision in a hypothesis test, we compare the t statistic to the critical value. In this case, the t statistic is 1.94. Since the treatment is expected to increase scores and the sample mean shows an increase, we are conducting a one-tailed test. Looking at the critical value for a = 0.05 for a one-tailed test using the t15 distribution, we find that it is 1.753. Since the t statistic (1.94) is greater than the critical value (1.753), we reject the null hypothesis. Therefore, the correct decision for this hypothesis test is to reject the null hypothesis with a one-tailed test but fail to reject with two tails.
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x+2y=-5
y=x+2
solve x and y
Solve for d. 6(d+1)−2d=54 Enter your answer in the box. d =
Answer:
The answer to your question is: d = 12
Step-by-step explanation:
6(d+1)−2d=54
Expand 6d + 6 -2d = 54
6d - 2d = 54 - 6
Simplify 4d = 48
d = 48 / 4
Result d = 12
The cubed root of a number
A computer maker receives parts from three suppliers, S1, S2, and S3. Fifty percent come from S1, twenty percent from S2, and thirty percent from S3. Among all the parts supplied by S1, 5% are defective. For S2 and S3, the portion of defective parts is 3% and 6%, respectively. (a) What portion of all the parts is defective? (b) A customer complains that a certain part in her recently purchased computer is defective. What is the probability that it was supplied by S1?
Answer:
a) 4.9 % of all parts is defective or 0.049 of the total parts.
b) 0.5102 is the probability that the defective part was supplied by S1
Step-by-step explanation:
N is the total number of parts from supplier S1, S2 and S3.
N1 = 0.5*N is the total number of part supplied by S1
N2 = 0.2*N is the total number of part supplied by S2
N3 = 0.3*N is the total number of part supplied by S3
a) if Nd1 is the number of defective parts from supplier S1, Nd2 is the number of defective parts from supplier S2 and Nd3 is the number of defective parts from supplier S3, the the total defective parts Nd is:
Nd = Nd1 + Nd2 + Nd3, where
Nd1 = 0.05*N1 = 0.05*0.5*N = 0.025*N,
Nd2 = 0.03*N2 = 0.03*0.2*N = 0.006*N,
Nd3 = 0.06*N3 = 0.06*0.3*N = 0.018*N,
Then Nd = Nd1 + Nd2 + Nd3 = 0.049*N, so Nd/N = 0.049
b) [tex]P(S1 \vert d) = \frac{P(S1,d)}{P(d)} = \frac{P(d \vert S1)}{P(d)} = \frac{0.05*0.5}{0.049} \approx 0.5102[/tex]
for the last expression I used the Bayes tehorem.
[tex]P(S1 \vert d)[/tex] is the probability that occur S1 given that d (defective) is true. This a conditional probability.
see at https://en.wikipedia.org/wiki/Bayes%27_theorem
The overall defect portion from all suppliers is 4.9%. If a part is defective, the probability that it was supplied by S1 is approximately 51.02%.
Explanation:To determine what portion of all the parts is defective, we calculate a weighted average of the defect rates based on the supplier portion contributions. The calculation is as follows:
S1's contribution to the overall defect rate: 50% * 5% = 2.5%S2's contribution to the overall defect rate: 20% * 3% = 0.6%S3's contribution to the overall defect rate: 30% * 6% = 1.8%The overall defect rate is the sum of these contributions, which is [tex]2.5 + 0.6 + 1.8 = 4.9%.[/tex]
For part (b), the probability that the defective part was supplied by S1 can be found using Bayes' theorem:
If a part is defective, the probability of it being from S1 is the probability that S1 provided a defective part over the probability that any part is defective. This probability is ([tex]0.50 * 0.05) / 0.049 = 0.025 / 0.049 \approx 0.5102 or 51.02%.[/tex]
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Hailey paid \$13$13dollar sign, 13 for 1\dfrac3{7} \text{ kg}1 7 3 kg1, start fraction, 3, divided by, 7, end fraction, space, k, g of sliced salami. What was the cost per kilogram of salami? \$
Answer:
The answer is 9.10, ($9.10).
Step-by-step explanation:
Oh just to let you know that other answer (joke) was such a loser joke.
PLZ HURRY IT'S URGENT!!
The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 12 square inches. What are the length and width?
Which equation models this problem?
w – (4 + w) = 12
w + (4 + w) = 12
w(4 + w) = 12
4 • w = 12
Answer:
The equation that models this problem is w(4 + w) = 12
Step-by-step explanation:
we know that
The area of a rectangle is
[tex]A=LW[/tex]
we have
[tex]A=12\ in^2[/tex]
so
[tex]12=LW[/tex] -----> equation A
[tex]L=W+4[/tex] ----> equation B
substitute equation B in equation A and solve for W
[tex]12=(W+4)W[/tex]
therefore
The equation that models this problem is w(4 + w) = 12
Answer:
The answer is w(4+w)=12
Step-by-step explanation:
State whether each function is a linear function. Explain.
1. y = 3x
2. y =- 2+5x
3. 2x + y= 10
4. f(x) = 4x^2
5. -3/x + y = 15
6. x + y + 8
Answer:
The answer is below
Step-by-step explanation:
1. y = 3x is a linear function because it doesn't have any power
2. y =- 2+5x is a linear function because it doesn't have any power
3. 2x + y= 10 is a linear function because it doesn't have any power
4. f(x) = 4x^2 it isn't a linear function because x is elevated to a power
5. -3/x + y = 15 is a linear function because it doesn't have any power
6. x + y + 8 is a linear function because it doesn't have any power
The first, second, third and sixth functions are linear functions, as they comply with the standard linear function format, y = mx + c. The fourth and fifth functions are not linear because they do not follow this standard format.
Explanation:A linear function is a function whose graph is a straight line. The general form of a linear function is y = mx + c, where m is the slope of the line, and c is the y-intercept.
y = 3x is a linear function, as it can be rewritten in the general form y = mx + c by considering m as 3 and c as 0. y =- 2+5x is also a linear function. Here, the slope m is 5 and the y-intercept c is -2. 2x + y= 10 can be rearranged as y = -2x + 10, which is a linear function with m = -2 and c = 10. f(x) = 4x^2 is not a linear function as the x term is raised to the power of 2, making it a quadratic function. -3/x + y = 15 is not a linear function as it includes an x term in the denominator. x + y + 8 is a linear equation. If this equation is rearranged in the format y = mx + c, it becomes y = -x - 8. Here, m = -1 and c = -8.Learn more about linear function here:
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A 12-cm-long thin rod has the nonuniform charge density λ(x)=(2.0 nC/cm)e−|x|/(6.0 cm), where x is measured from the center of the rod. What is the total charge on the rod? Hint: This exercise requires an integration. Think about how to handle the absolute value sign
Answer:
the total charge is
[tex]Q=24(1-\exp(-1))nC\approx15.171nC[/tex]
Step-by-step explanation:
Since x is measured from the center, that means that x=0 is the center so the edges of the rod correspond to x=-6 and x=6. that meas that the total charge can be calculated as
[tex]Q=\int^{6}_{-6}2\exp\left(\frac{-|x|}{6}\right)dx[/tex]
separating the integral from -6 to 0 and from 0 to 6, taking into account that |x|=-x for x<0 and |x|=x for x >=0, we get[tex]Q=\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx+\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx[/tex]
using the substitution x=-u in the first integral we get[tex]\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx=-\int^{0}_{6}2\exp\left(\frac{-u}{6}\right)du=\int^{6}_{0}2\exp\left(\frac{-u}{6}\right)du[/tex]
which is the same as the first integral. Thus, the total charge is given by
[tex]Q=2\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx[/tex]
integrating we get
[tex]Q=4(-6\exp\left(\frac{-x}{6}\right))\big|^{6}_{0}=-24(\exp(-6/6)-\exp(0))=24(1-\exp(-1))[/tex]
The total charge is Q= 15.171nC.
Calculations and Parameters:Since x is measured from the center, that means that x=0 is the center.
So, the edges of the rod correspond to
x=-6 and x=6.
That means that the total charge can be calculated as
[tex]Q= \int\limits^6_ 6 2 exp(-|x|/6)dx[/tex]
separating the integral from -6 to 0 and from 0 to 6,
Taking into account that
|x|=-x for x<0
and |x|=x for x >=0
Thus, the total charge is given by:
[tex]Q= 2\int\limits^6_0 2exp (-x/6), dx[/tex]
When we integrate, we get:
Q= 24(1- exp(-1))nC ≈
15.171nC
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You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture?a 4 inch
Answer:
1.333 is more close to 1.5 than 1.25 .
Step-by-step explanation:
We are given:
You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture.
First divide 6 by 4: we get,
6/4 = 1.5 inches
This is the ratio to achieve.
Now divide 20 by 16
20/16 = 10/8
10/8 = 5/4
5/4 = 1.25 inches
Now divide 24 by 18
24/18 = 12/9
12/9 = 4/3
4/3 = 1.333 inches
1.333 is more close to 1.5 than 1.25 .
Evaluate the expression (4x^3)^2 for x=2
A.128
B.512
C.256
D. 1024
Answer:
d:) 1024
Step-by-step explanation:
Evaluate (4 x^3)^2 where x = 2:
(4 x^3)^2 = (4×2^3)^2
Multiply each exponent in 4×2^3 by 2:
4^2 (2^3)^2
Multiply exponents. (2^3)^2 = 2^(3×2):
2^(3×2)×4^2
4^2 = 16:
2^(3×2)×16
3×2 = 6:
2^6×16
2^6 = (2^3)^2 = (2×2^2)^2:
(2×2^2)^2 16
2^2 = 4:
(2×4)^2 16
2×4 = 8:
8^2×16
8^2 = 64:
64×16
| | 6 | 4
× | | 1 | 6
| 3 | 8 | 4
| 6 | 4 | 0
1 | 0 | 2 | 4:
Answer: 1024
Two cars, a Porsche Boxster and a Toyota Scion XB, are traveling in the same direction, although the Boxster is 115.0 m behind the Scion. The speed of the Boxster is 26.0 m/s and the speed of the Scion is 18.9 m/s. How much time does it take for the Boxster to catch the Scion? [Hint: What must be true about the displacement of the two cars when they meet?]
Answer:
16.197 seconds
Step-by-step explanation:
the time and the final place fot both cars is the same.
for the Boxster we have
X = Vboxster . T
being
X the distancance from the initial place of the Boxter to the meeting point
Vboxster the speed of the Boxster (26m/s)
T the time
and for the Scion
X = Xo + Vscion . T
Being
Xo the initial point of the Scion (115m)
X the distancance from the initial place of the Boxster to the meeting point
Vscion the speed of the Scion (18.9 m/s)
T the time
Xo + Vscion . T = Vboxster . T
Xo = Vboxster . T - Vscion . T
Xo = (Vboxster - Vscion) . T
Xo/(Vboxster - Vscion) = T
115m/ (26-18.9) m.s-1 = T
16.197 s = T
Answer:
a)t = 16.2s : time it takes for the Boxster to catch the Scion
b)The displacement of the Boxster (db) is 115 m more than the displacement of the Scion(ds)
db =ds+115
Step-by-step explanation:
Conceptual analysis
We apply the formula for constant speed movement:
v= d/t Formula (1)
v = speed in m/s
d: distance in m
t: time in s
Problem development
The time of Scion (ts) is equal time of Boxster (tb)
t (s) =tb=t
The displacement of the Boxster is 115 m more than the displacement of the Scion
db =ds+115
we apply formula (1 )car kinematics :
Scion kinematics
18.9=ds/t
t =ds /18.9 Equation (1)
Boxster kinematics
26=db/t
26=(ds+115)/t
t=(ds+115)/26 Equation (2)
Equation (1) = Equation (2)
ds /18.9 =(ds+115)/26
18.9(ds+115)= 26 ds
18.9ds+18.9*115=26 ds
2173.5= 26 ds-18.9ds
2173.5=7.1ds
ds =2173.5÷7.1
ds=306.12m
We replace ds=306.12m in the equation (1)
t =306.12÷18.9
t = 16.2s
In 1997, Superman’s cape from the 1978 movie Superman was sold at an auction. The winning bid was $17,000. Question 1 Write an inequality that represents the amounts of all the losing bids. Let b represent the amount of a bid.
The inequality to represent the losing bids can be written as:
b < 17000.
The winning bid for Superman's cape from the 1978 movie was $17,000.
To represent the amounts of all the losing bids, we need to write an inequality that indicates bids that are less than $17,000.
Let "b" represent the amount of a bid.
The inequality to represent the losing bids can be written as:
b < 17000
This inequality states that any bid "b" that is less than $17,000 would be a losing bid. The symbol "<" signifies "less than."
So, any bid amount smaller than $17,000 falls into the category of losing bids.
To learn more on inequality click:
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The inequality representing all losing bids for Superman's cape is b < 17,000, where b is the amount of any losing bid. Bidders must consider auction strategies and valuations to avoid overbidding and the winner's curse.
The question involves creating an inequality to represent the losing bids in an auction where Superman's cape was sold for $17,000. The variable b is introduced to represent the amount of any losing bid. The inequality that represents all the losing bids would be b < 17,000. since any bid that is less than $17,000 would not win the auction.
describe the graph of a function g by observing the graph of the base function f ?
Answer:
Choice 3 is your answer
Step-by-step explanation:
The format of the function when you move it side to side or up and down is
f(x) = (x - h) + k,
where h is the side to side movement and k is up or down. The k is easy, since it will be positive if we move the function up and negative if we move the function down from its original position.
The h is a little more difficult, but just remember the standard form of the side to side movement is always (x - h). If our function has moved 3 units to the left, we fit that movement into our standard form as (x - (-3)), which of course is the same as (x + 3). Our function has moved up 5 units, so the final translation is
g(x) = f(x + 3) + 5, choice 3 from the top.
The width of a singles tennis court is 75% of the width of a doubles court. A doubles court Is 36 feet wide. How wide is a singles court Is 36 feet wide. How wide is a singles court
Answer:
width of a singles court = 27 feet
Step-by-step explanation:
Width of a doubles tennis court = 36 feet
Width of a singles tennis court = 75% of 36
[tex]width = 75\% \times 36 \\ width = \frac{75}{100} \times 36 \\ width = \frac{3} {4} \times 36 \\ width = \frac{108}{4} = 27[/tex]