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We have two trains that leave Mexico City at the same time, one to the east and the other to the west. The train that travels to the west is 10 mph slower than the other train. The diagram of the problem is:
The combined velocity is:
[tex]V_T=v+v-4=2v-4[/tex]The equation that relates the distance D between the trains and the time after t hours is:
[tex]D=V_T\cdot t[/tex]If after 1.5 hours the trains are 171 miles apart, then using the equation above:
[tex]\begin{gathered} 171=V_T\cdot1.5 \\ V_T=\frac{171}{1.5} \\ V_T=114 \\ 2v-4=114 \\ 2v=118 \\ v=59\text{ mph} \end{gathered}[/tex]Now, the speeds are:
[tex]\begin{gathered} \text{East}\colon59\text{ mph} \\ \text{West}\colon55\text{ mph} \end{gathered}[/tex]
Related Questions
Travis scored 18 points in the first basketball game of the season. He scored 3 fewer point in the second game than in the first game. find the total number of point Travis scored in the first and second games.
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Let's call the number of points scored in the first game A and the number of points scored in the second game B:
A = 18
since he scored 18 points in the first
B = A -3 = 18 - 3 = 15
B = 15
since he scored 3 fewer point in the second
The total number of point is
A + B = 18 + 15 = 33
Jacob drove 78 miles in 2 2/3 hours. If he drove at a constant rate, how far did he travelin one hour? Enter your answer as a whole number, proper fraction, or mixednumber in simplest form.
Answers
In order to calculate the distance travelled in one hour, we can divide the total number of miles by the amount of time required for that number of miles:
[tex]\text{speed}=\frac{78}{2\frac{2}{3}}=\frac{78}{(2+\frac{2}{3})}=\frac{78}{\frac{6}{3}+\frac{2}{3}}=\frac{78}{\frac{8}{3}}=78\cdot\frac{3}{8}=\frac{39\cdot3}{4}=\frac{117}{4}[/tex]So in one hour, the distance travelled is 117/4 miles.
Converting this value into a mixed number, we have:
[tex]\frac{117}{4}=\frac{116}{4}+\frac{1}{4}=29+\frac{1}{4}=29\frac{1}{4}[/tex]--------
Done!
Do you have any questions about the answer?
I need help with this practice problem solving The subject is pre trigonometry
Answers
Answer:
[tex]\theta=\frac{2\pi}{3}+\pi\cdot n[/tex]Step-by-step explanation:
Find the general solution for:
[tex]\begin{gathered} 3\cot \theta=-\sqrt[]{3} \\ \text{ Divide both sides by 3} \\ \cot \theta=-\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Now, for the general solution, it is known that for
[tex]\begin{gathered} \cot (\frac{\pi}{6})=\sqrt[]{3} \\ \text{Then,} \\ \theta=\frac{2\pi}{3}+\pi\cdot n \end{gathered}[/tex]Passing through (-2, 8) and PERPENDICULAR to y = 2x + 5
Answers
the equation of the line is,
y = 2x + 5
the slope of the line is m = 2
the slope of the line perpendicular to y = 2x + 5 is ,
m = -1/2
it is passing through (-2,8)
so the equation of the line is
[tex]y-8=(-\frac{1}{2})(x-(-2))[/tex][tex]\begin{gathered} y-8=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]thus the equation of the line is,
y = -1/2 x + 7
what is a solution to the inequality below [tex] \sqrt{x} \ \textgreater \ 6[/tex]
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Answer:
C. x > 36
Explanation:
Taking the square of both sides gives
[tex](\sqrt[]{x})^2=6^2[/tex][tex]x>36[/tex]Therefore, looking at the answer choice, we see that choice C is the correct one.
Instructions: For the given polynomial, select eachstatement that applies regarding end behavior.
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Solution:
Given:
[tex]f(x)=-x^4-21x^2-2x+3[/tex]To get the end behaviour of the polynomial, we plot the function using a graphing calculator and see how it behaves.
The function is graphed as shown in the image below,
From the image above, the vertex of the curve shows a rise towards the left.
Hence, the end behaviour is that it rises to the left.
this is 50 points help me out k
Answers
Answer: It is 45
Step-by-step explanation:
you have 5 four and the number is 4
Triangle ABC has vertices A(1,3), B(2,5), and C(5,3). What are the coordinates of B after the translation described by the rule T(1,4)?B =
Answers
Answer:
B' (3, 9)
Explanation:
Given the coordinates of vertices of a triangle A(1,3), B(2,5), and C(5,3), if the triangle is translated by T(1, 4), the coordinates of the new triangle will be expressed as:
A' = (1, 4) + A(1, 3)
A' = (1+1, 4+3)
A' = (2, 7)
B' = (1, 4) + B(2, 5)
B' = (1+2, 4+5)
B' = (3, 9)
C' = (1, 4) + C(5, 3)
C' = (1+5, 4+3)
C' = (6, 7)
From the calculation above, it can be seen that the coordinates of B after translation is B' (3, 9)
At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a
randomly selected loan agent closes on a randomly selected day has the probability distribution below.
4
5 6
P(x) 0.05 0.10 0.22 0.30 0.18 0.12 0.03
X
1
2
3
At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan
agent on a randomly selected day.
Which is the mean of X?
Which is the mean of Y?
V
Which is the standard deviation of X?
7
which is the standard deviation of Y
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The mean of X is E(X)=$3.94
The mean of Y is E(Y)=$347
The standard deviation of X is $1.4129
The standard deviation of Y is $220.645
What is meant by mean and standard deviation?The mean is the set of two or more numbers' mathematical average. It is possible to calculate two different types of means: the arithmetic mean and the geometric mean. Add the numbers in a set together and divide by the total number of numbers in the set to find the arithmetic mean.
Standard deviation, which is the square root of the means of the squared deviations from the arithmetic mean, is also known as root-mean square deviation. To quantify the risks associated with an investment instrument, standard deviation is used in finance.
The computation is shown below:
Y = a +bX
where,
Y = money earned by a randomly chosen
a = $150
b = $50
X = number of loan
Now,
E(X) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)
=$3.94
E(X) =$3.94
Therefore, mean of X is $3.94
Now,
E(y) = $150 + ($50 × 3.94)
= $347
E(y) =$347
Therefore, mean of Y is $347
Variance=∑[tex]P_{i}[/tex]([tex]X_{i}[/tex]-μ)
=0.43218+0.37636+0.194392+0.00108+0.202248+0.509232+0.280908
=1.9964
Standard deviation=√variance
=√1.9964
=1.4129
Therefore, the standard deviation of X is $1.4129
Y=a+bX
Y=$150+($50×1.4129)
Y=$220.645
Therefore, the standard deviation of X is $220.645
To know more about standard deviation and mean, visit:
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simplify 7.5y⁴ • 9y²
Answers
Answer:
67.5y⁶.
Explanation:
Given the expression:
[tex]7.5y^4\times9y^2[/tex]First, reorder the terms:
[tex]=7.5\times9\times y^4\times y^2[/tex]Next, combine like terms:
[tex]\begin{gathered} =67.5\times y^4\times y^2 \\ =67.5\times y^{4+2} \\ =67.5\times y^6 \\ =67.5y^6 \end{gathered}[/tex]The simplified form is 67.5y⁶.
help with more than 1 question pls and ty if nkt i will report u its not fair
Answers
SOLUTION
9.
[tex]\begin{gathered} (x+10)^2\text{ = ( x + 10 ) ( x + 10 )} \\ =x^2\text{ + 10 x + 10x + 100} \\ =x^2\text{ + 20 x + 100} \end{gathered}[/tex]10.
[tex]\begin{gathered} (x-10)^2\text{ = ( x - 10 ) ( x - 10 )} \\ =x^2\text{ -10 x - 10 x + 100} \\ =x^2\text{ - 20 x + 100} \end{gathered}[/tex]11. ( x + 10 ) ( x - 10 ) ( Difference of two squares)
[tex]\begin{gathered} x^2\text{ - 10 x + 10 x - 100} \\ =x^2\text{ - 100} \end{gathered}[/tex](x squared -9x -7) -(7x squared +2x +3) Find the difference
Answers
ANSWER
[tex]-6x^2-11x-10[/tex]EXPLANATION
We want to find the difference between the two expressions:
[tex](x^2-9x-7)-(7x^2+2x+3)[/tex]To do this, we will subtract like terms from one another.
That is:
[tex]x^2-7x^2-9x-2x-7-3[/tex]Simplifying the expression, we have:
[tex]-6x^2-11x-10[/tex]That is the answer.
Hello I need help with this problem for my home work here’s a picture
Answers
The Solution:
Given:
We are required to find the equivalent of the given expression.
Simplifying the given expression, we get:
[tex]4x^2\sqrt{5x^4}\cdot3\sqrt{5x^8}=4x^2\times x^2\sqrt{5}\times3x^4\sqrt{5}[/tex][tex]=4x^2\times x^2\times3x^4\times\sqrt{5}\times\sqrt{5}=4x^4\times3x^4\times5=60x^8[/tex]Therefore, the correct answer is [option B]
Charlie is saving money to buy a game. So far he has saved $20, which is one-fourth of the total cost of the game. how much does the game cost?
Answers
Let 'x' represent the cost of the game.
Therefore, one-fourth of the total cost of the game is
[tex]\begin{gathered} \frac{1}{4}\text{ of x=20} \\ \frac{1}{4}x=20 \end{gathered}[/tex]Evaluate for x
[tex]x=20\times4=80[/tex]Hence, the total cost of the game is $80.
27. The following chart represent the cost, Cd), in dollars, of a pizza in relation to its diameter, d, in inches. What is the average rate of change in cost from an 8 in to a 16 in pizza. d Cd) 8 2.51 103.93 125.65 147.70 16 10.05
Answers
The average rate of change is the ratio of the absolute change in one quantity divided by the absolute change in another quantity. Usually, the first one is dependent on the second one.
An 8 in pizza costs $2.51.
A 16 in pizza costs $10.05.
The absolute change in the cost is:
[tex]10.05-2.51=7.54[/tex]The absolute change in the diameter is:
[tex]16-8=8[/tex]Then, the average rate of change of the cost with respect to the diameter is:
[tex]\frac{7.54}{8}=0.9425[/tex]Therefore, to the nearest hundredth, the average rate of change in the cost from an 8in to a 16 in pizza, is:
[tex]0.94[/tex]Given the equation of the straight line AB is 3x+KY=8 where k is a constant. the straight line AB is parallel to the straight line connecting the point P(-1, 6) with the point Q(5, -3). Find the value of k then calculate the x-intercept of the straight line AB
Answers
If we have two parallel lines, than their slopes must be the same.
One way of comparing slopes of linear equations is to write them in the slope-intercept form:
[tex]y=mx+b[/tex]In this form, m is the slope and b is the y-intercept.
So, let's write the first equation in this form:
[tex]\begin{gathered} 3x+ky=8 \\ ky=-3x+8 \\ y=-\frac{3}{k}x+\frac{8}{k} \end{gathered}[/tex]To find the value of k, we can find the slope of the parallel line and compair it to the slope in this equation.
The slope of a line given two points on it can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]Since we have points (-1, 6) and (5, -3), we can calculate the slope of the parallel line:
[tex]m=\frac{-3-6}{5-(-1)}=\frac{-9}{5+1}=-\frac{9}{6}=-\frac{3}{2}[/tex]Since both lines are parallel, their slopes are the same.
We know that the slope of the first line is -3/k and the second line is -3/2, so, since they are parallel:
[tex]\begin{gathered} -\frac{3}{k}=-\frac{3}{2} \\ -3\cdot2=-3\cdot k \\ 2=k \\ k=2 \end{gathered}[/tex]Since we have the value for k, we can substitute it into the equation for AB:
[tex]\begin{gathered} y=-\frac{3}{k}x+\frac{8}{k} \\ y=-\frac{3}{2}x+\frac{8}{2} \\ y=-\frac{3}{2}x+4 \end{gathered}[/tex]To find the x-intercept, we can see that it happens when the value of y is equal to 0, so we can plug in y = 0 and find the value of x:
[tex]\begin{gathered} y=0 \\ 0=-\frac{3}{2}x+4 \\ \frac{3}{2}x=4 \\ x=\frac{2}{3}\cdot4 \\ x=\frac{8}{3} \end{gathered}[/tex]So, the value of k is 2 and the x-intercept is 8/3.
Given the image, if AB is a semicircle and DB = 70 degrees, what is the measure of ACD?
Answers
Continuing from there, since it’s a semi circle, the total angle is 180 degrees. Therefore, ACD = (180 - 70)degrees.
Answer => 110 degrees
Hint - Look at the semi circle as a protractor. It’s exactly like that. If one side is 70, then the other is 110.
3.Which equation does not describe the line? Place the red X on the one that does not belong x y 10 y = 2x + 4 ce 6 4, y + 0 = 2(x + 2) 2 10 -8 -6 -4 2 0 2+ 2 4 6 8 10 y + 4 = 2(x + 0) 4+ 6+ 8+ y - 4 = 2(x + 0) 107
Answers
step 1
Find the equation of the graph
Find the slope
take the points
(-2,0) and (0,4)
m=(4-0)/(0+2)
m-4/2
m=2
step 2
Find the equation of the line in point slope form
point (-2,0) and m=2 ------> y-0=2(x+2)
point (0,4) and m=2 ------> y-4=2(x-0)
Find the equation in slope intercept form
y=mx+b
we have
m=2
b=4 (given)
y=2x+4
therefore
1 point The following expression represents monthly growth. What is the yearly rate of growth? (1.04)^m
Answers
(1.04)^m
m= Months
One year has 12 months_
(1.04)^12 = 1.60
0.60 = yearly rate of growth
A school wants to put a bond in the next election, they call this bond Measure K. Before puttingthe bond on the ballot, they want to see how much support they would have from voters in thecounty. They select a random sample of voters in the county, and find a 90% confidence intervalfor the proportion of voters in this county who would vote yes. In order to do this, they neededto use:(Multiple choice)O 1 proportion (z) confidence intervalO 1 proportion (2) hypothesis testO 2 proportion (z) confidence intervalO 2 proportion (2) hypothesis test
Answers
A school wants to put a bond in the next election, they call this bond Measure K.
They select a random sample of voters in the county and find a 90% confidence interval for the proportion of voters in this county who would vote yes.
Recall that a hypothesis test is used when we want to test an assertion or a claim.
For the given case, there is no assertion or any claim so this is definitely not a hypothesis test.
This is in fact a confidence interval since we are interested in the proportion of voters in this county who would vote yes.
The confidence interval would give us a fair estimate of the true population proportion of voters in this county who would vote yes.
Now coming to whether is it a 1 proportion or 2 proportion confidence interval.
Notice that there is only 1 proportion for the given case that is the proportion of voters in this county who would vote yes.
Therefore, the need to use "1 proportion (z) confidence interval"
For a standard normal distribution, find:P(Z > -1.79)Express the probability as a decimal rounded to 4 decimalplaces.
Answers
Given the probability:
[tex]P(Z>-1.79)[/tex]To find this probability, you have to use the tables for the standard normal distribution. These tables show the accumulated probability for the Z-distribution, this means that you can find the probability up to a determined Z-value. To find the probability above a determined Z-value you have to use the complementary probability, that is:
[tex]P(Z>-1.79)=1-P(Z\leq-1.79)[/tex]- First, use the Z-table to find the accumulated probability until Z=-1.79, the Z-value is negative, so you have to use the left entry of the table:
In the first column, you will find the first two digits of the Z-value, and in the first two, you will find the third digit of the Z-value, and in the body of the table, all accumulated probabilities are listed.
Cross the corresponding row and column to find the accumulated probability:
Then the accumulated probability until -1.79 is:
[tex]P(Z\leq-1.79)=0.0367[/tex]Now that you found the accumulated probability, you can use the complement to find the probability above -1.79
[tex]\begin{gathered} P(Z>-1.79)=1-P(Z\leq-1.79) \\ P(Z>-1.79)=1-0.0367 \\ P(Z>-1.79)=0.9633 \end{gathered}[/tex]Define Miller for the perimeter P of a rectangle with length L and width W is p equals 2L + 2W. which of the following is the formula for the length of a rectangle in terms of the perimeter and width.a.l equals B- W / 2 b.l equals b + W / 2 c.l equals P -2 W / 2 d.l equals p + 2 W / 2
Answers
P = 2L + 2W ok
2L = P - 2W
L = (P - 2W)/2 This is the correct answer
I think it's letter C
Problem 2.
4x - 4 > 12
4x > 12 + 4
4x > 16
x > 16/4
x > 4 This is the correct choice
find the new price after the markup given. round to the nearest cent if necessary. $145 marked up 175%
Answers
Answer:
Explanation:
Given that the initial/cost price is;
[tex]\text{ \$145}[/tex]It was then marked up 175%.
The new price can be calculated using the formula;
[tex]\begin{gathered} S=C+r(C) \\ S=(1+r)C \\ \text{where;} \\ S=\text{ new price} \\ C=\text{ cost price} \\ r=\text{markup percent in fraction} \end{gathered}[/tex]Given;
[tex]\begin{gathered} C=\text{ \$145} \\ r=\frac{175\text{\%}}{100\text{\%}} \\ r=1.75 \end{gathered}[/tex]substituting:
[tex]\begin{gathered} S=(1+r)C \\ S=(1+1.75)\times\text{ \$145} \\ S=2.75\times\text{ \$145} \\ S=\text{ \$398.75} \end{gathered}[/tex]Therefore, the new price is;
[tex]undefined[/tex]Simplify the following: -(3z)²
Answers
We have the following general rule for exponents:
[tex](a\cdot b)^n=a^n\cdot b^n[/tex]Then, in this case we have:
[tex]-(3z)^2=-(3^2\cdot z^2)=-9z^2[/tex]therefore, the simplifed expression is -9z²
What is the area of the circle if CY= 5.4 mm
Answers
Given
The diameter is given XY = 5.4 mm.
Explanation
To determine the area of circle,
Use the area of circle formula.
[tex]A=\pi(r)^2[/tex]Find the radius, using the relation between diameter and radius.
[tex]d=2r[/tex]Substitute the diameter in the relation.
[tex]\begin{gathered} 5.4=2r \\ r=2.7mm \end{gathered}[/tex]Now substitute the radius in the area of circle formula.
[tex]\begin{gathered} A=(2.7)^2\pi \\ A=7.29\pi mm^2 \end{gathered}[/tex]Answer
Hence the area of circle is
[tex]7.29\pi mm^2[/tex]The correct option is C.
In a survey of 100 people, 7 out of every 25 said that Abraham Lincoln was the greatest U.S President. What percent of people surveyed does this represent?
Answers
28%
EXPLANATION
Percentage of people surveyed that said Abraham Lincoln was the greatest U.S president is;
[tex]=\frac{7}{25}\times100[/tex][tex]=\text{ 28 \%}[/tex]Part A: A landscape service charges costumers a one-time fee and an hourly rate of $15. For 3 hours of work m, it charges $75 Write the equation in point-slope formHow much does the landscape service charge for 20 hours
Answers
The hourly rate is the slope m, and we're given the point (3,75)
Now, using the point-slope form:
[tex]y-75=15(x-3)[/tex]Now, let's put it in the slope-intercept form (clear y):
[tex]\begin{gathered} y-75=15x-45 \\ \rightarrow y=15x+30 \end{gathered}[/tex]For 20 hours of service,
[tex]\begin{gathered} y=15(20)+30 \\ \rightarrow y=330 \end{gathered}[/tex]The service would charge $330
solve for theta. Enter answer only round to the tenth
Answers
ANSWER:
[tex]\theta=62.73\text{\degree}[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the value of the angle by means of the trigonometric ratio sine which is the following
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{opposite = 24} \\ \text{hypotenuse = 27} \end{gathered}[/tex]Replacing and solving for the angle:
[tex]\begin{gathered} \sin \theta=\frac{24}{27} \\ \theta=\arcsin (\frac{24}{27}) \\ \theta=62.73\text{\degree} \end{gathered}[/tex]18. What is the value of f(-2) for the function f(x) = 2(3Y"?A12fca=acze33B118С.29D. 18
Answers
Given the function:
[tex]f(x)=2(3)^x[/tex]To find f(-2), substitute x for -2 in the function.
[tex]f(-2)=2(3)^{-2}[/tex]Solving further using law of indicies, we have:
[tex]\begin{gathered} f(-2)\text{ = }\frac{2}{3^2} \\ \\ f(-2)\text{ = }\frac{2}{9} \end{gathered}[/tex]ANSWER:
[tex]\frac{2}{9}[/tex]find the missing angletan x= 0.9004
Answers
We are told that the tangent of an angle x is equal to 0.9004. In order to solve this equation for x we can use the arctangent function that has this property:
[tex]\tan^{-1}(\tan x)=x[/tex]Then we can apply the arctangent to both sides of our equation:
[tex]\begin{gathered} \tan^{-1}(\tan x)=\tan^{-1}0.9004 \\ x=\tan^{-1}0.9004 \end{gathered}[/tex]So our angle is the arctangent of 0.9004 which can be found using a calculator. However calculators oftenly work with radians and we need to express x in degrees. In order to transform the result from radians to degrees we have to perform the following operation:
[tex]x=\tan^{-1}0.9004\cdot\frac{360}{2\pi}=41.999872^{\circ}[/tex]AnswerWheter we round to the nearesth tenth, hundreth or thousanth the answer is 42°.