Places A and B are 100km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 10 hours and if they move in opposite directions, they meet in 1 hour and 40 minutes. Find the speeds of the cars.
Answers
Answer:
Speed of the first car = x = 35km/hr
Speed of the second car = 25km /hr
Step-by-step explanation:
The calculation of speeds of the cars is given below:-
Assume that the speed of the 1st car which is opening from A = x km/hr
and assume the Speed of the 2nd car which is starting from B
= y km/hr
As we know that
Time = Distance ÷ Speed
So, the distance lies between two places i.e. A and B are
80km d = 80 km
1. now when the car moves in the similar direction
So, the corresponding speed of them = (x + y)km/hr
Time = 8hr
d = 80km
\(8 = \frac{80}{(x + y)}\\\\x + y = \frac{80}{8}\\\\x + y = 10 ..... (i)\)
2. when two cars moving in the inverse direction,
So, the corressponding speed = (x - y) km / hr
Time = 1 hr 20 minutes
That means
= (1 + 20 ÷ 60) hr
= (80 ÷ 60)
= 4/3 hr
d = 80km
Now
4 ÷ 3 = 80 ÷ (x -y)
x -y = (80 × 3) ÷ 4
x - y = 60 ..... (ii)
Now, we will sum equation 1 and equation 2 we will get
2x = 70
x = 35
now, Put x = 35 in (i) we will get
y = 25
Speed of the first car = x = 35km/hr
Speed of the second car = 25km /hr
Related Questions
Please help. It is an easy maths question I am just dum
Answers
2. Triangle Area Formula=base x height / 2
3. We get 60 as the area when u plug the numbers into the formula.
4. Since there is another triangle in the back it’s also 60 so then it’s 120.
5. Then we do length times width for the two rectangles.
6. When completing the equation you get 130.
7. Since you have another rectangle the same length you add another 130 making it 260.
8. Lastly, the base same thing length times width.
9. The answer for that is 240.
10. Now u add everything 240+260+120=620.
ANSWER:620 cm^2
sketch the following waveforms a) r(t 2)-r(t-2)v
Answers
It seems like you're asking to sketch the waveforms for the function a) r(t 2) - r(t - 2)v, where r(t) is the unit step function and v(t) is the unit ramp function.
The waveform of r(t 2) represents a unit step function stretched by a factor of 2 along the time axis. It means that the step will occur at t = 0.5 instead of t = 1.
The waveform of r(t - 2)v represents the product of a delayed unit step function and a unit ramp function. The unit step function is delayed by 2 units, so it starts at t = 2. The ramp function starts at t = 0, but since it's multiplied by the delayed unit step function, the ramp only starts rising at t = 2.
To find the overall waveform, subtract the second waveform (r(t - 2)v) from the first waveform (r(t 2)). The resulting waveform will be a combination of the two, with a step function occurring at t = 0.5 and a ramp function starting at t = 2, but the ramp will have a decreasing effect on the waveform.
Unfortunately, I cannot visually sketch the waveform for you. However, you can use this description to draw it on a graph or use a graphing tool to visualize the waveform.
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In Houston, Texas, at the spring equinox (March 21), there are 12 hours and 9 minutes of sunlight. The longest and shortest day of the year varies from the equinox by 1h 55 min . The amount of sunlight during the year can be modeled by a sine function.
c. Write a function that relates the number of days away from the spring equinox to the variation in hours of sunlight in Houston.
Answers
In Houston, Texas, the variation of sunlight during the year can be modeled by the sine function. Given that there are 12 hours and 9 minutes of sunlight during the spring equinox, and the longest and shortest day varies from the equinox by 1 hour and 55 minutes. Therefore, the variation of hours of sunlight in Houston, Texas, can be modeled using the sine function as follows: \(f(x) = Asin(B(x - C)) + D\)
where; A is the amplitude of the sine function, which is given by (Max - Min) / 2A = (Max - Min) / 2
= (13h 4m - 10h 14m) / 2 = 1h 25mB is the period of the sine function, which is given by 2π / B = 365 days
B = 2π / 365 ≈ 0.017
C is the horizontal shift of the function, which corresponds to the day of the year when the maximum or minimum daylight occurs. Since the longest and shortest day of the year varies from the equinox by 1 hour and 55 minutes, then the maximum and minimum daylight will occur on June 20th and December 22nd, respectively. Therefore, the horizontal shift can be found as follows:
C = 80D is the vertical shift of the function, which is the average daylight duration throughout the year.
Since there are 12 hours and 9 minutes of sunlight during the spring equinox, the vertical shift can be found as follows: \(D = (Max + Min) / 2\)
= (13h 4m + 10h 14m) / 2
= 11h 39m
Putting all the values together,
f(x) = Asin(B(x - C)) + D = 1h 25m
sin(0.017(x - 80)) + 11h 39m.
Therefore, this is the function that relates the number of days away from the spring equinox to the variation in hours of sunlight in Houston.
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The x-component of a force on a 15-g golf ball by a golf club versus time is plotted in the attached figure.
Find the x-component of the impulse, in newton-seconds, during the following interval: [0, 50 msec]
Find the x-component of the impulse, in newton-seconds, during the following interval: [50 msec, 100 msec]
Find the change in the x-component of the momentum, in kilogram meters per second, during the following interval: [0,50 msec]
Find the change in the x-component of the momentum, in kilogram meters per second, during the following interval: [50 msec, 100 msec]
Answers
Answer: LOOK below
Step-by-step explanation:
How many significant figures would this calculation have if it were completed: \[ (9.04-8.23+21.954+81.0) \times 3.1416 \]
A) 3 B)4 C)5 D)6
Answers
The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.
To determine the number of significant figures in a calculation, we follow the rules for significant figures:
1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.
Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).
Now, multiplying this result by \(3.1416\) gives \(329.5719744\).
The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.
According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.
Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.
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PART 2: Use the numbers you created to write a system of equations. Kassim and Yehia go to the movie theater and purchase refreshments for their friends. Kassim spends a total of $4 2 bags of popcorn and 2 drinks. Yehia spends a total of $3 for 2 bags of popcorn and 1 drinks. on
a) Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Equation 1
Equation 2:
Answers
Answer: hope this helps you
EXAMPEL :
Jacob and Zachary go to the movie theatre and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks.
Step-by-step explanation:
let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:
2p + 3d = 18.25
4p + 2d = 27.50
From this, we can use substitution or elimination to solve:
For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.
For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.
I'll be using elimination in this case:
-2(2p + 3d = 18.25) --> -4p - 6d = -36.50
-4p - 6d = -36.50
4p + 2d = 27.50
-4d = -9.00
d = 2.25
4p + 2 * 2.25 = 27.50
4p + 4.50 = 27.50
4p = 23.00
p = 5.75
Now let's check our answer:
2 * 5.75 + 3 * 2.25 = 18.25
11.50 + 6.75 = 18.25
18.25 = 18.25
So drinks cost $2.25 and popcorn $5.75
Simplify the expression.
16-4 [3+2 divide (9-7)]
Answers
Answer:
0
Step-by-step explanation:
16-4 (3+2÷2)
16-4 (3+1)
16-4×4
16-16
0 ans.
Solve for x. Assume that lines which appear to be diameters are actually diameters.
Answers
The value of x in the circle is - 6.
How to find angles in a circle?The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
Therefore, let's find the value x using the relationship between the central angle and the arc angle as follows:
-24x + 7 = 151
subtract 7 from both sides of the equation
-24x + 7 - 7 = 151 - 7
-24x = 144
divide both side of the equation by -24
x = 144 / -24
x = -6
Therefore,
x = -6
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What theorem explains why ∠4 ≅ ∠8?
Which angle pairs are same-side interior angles? List all angle pairs.
Answers
The theorem that explains why ∠4 ≅ ∠8 is the Alternate Interior Angles Theorem. The same side interior angles pair are ∠3 and ∠5, and ∠4 and ∠8.
Alternate Interior Angles theorem states that if two parallel lines are intersected by a transversal, then the alternate interior angles formed are congruent.
The same-side interior angles are the angles that are on the same side of the transversal and inside the two parallel lines. In the given diagram, the same-side interior angle pairs are ∠3 and ∠5, and ∠4 and ∠8.
All the angle pairs formed by the intersection of the two parallel lines and the transversal are
Corresponding angles are ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8
Alternate interior angles are ∠3 and ∠5, ∠4 and ∠8
Alternate exterior angles are ∠1 and ∠7, ∠2 and ∠6
Vertical angles are ∠3 and ∠4, ∠5 and ∠6, ∠1 and ∠2, ∠7 and ∠8
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What is the measure of 1?
A.15
B.35
C.37
D.79
Answers
Answer:
we have
1+2=180(being co-interior angle)
2x+5+3x-10=180
5x-5=180
5x=180+5
x=185/5=37
m<1=2x+5=2×37+5=74+5=79
The diameter of a circle increased from 25cm to 25.8cm. Find the percentage increase in its circumference.
Answers
Answer:
3.1% increase
Step-by-step explanation:
Diameter1=25cm
Radius1=12.5cm
Circumference1=2x22/7x12.5
Diameter2=25.8cm
Radius2=12.9cm
Circumference2=2x22/7x12.9
% increase =Circumference2-Circumference1/Circumference2 x 100%= 2x22/7x12.9-2x22/7x12.5 / 2x22/7x12.9 x100%
12.9-12.5/12.9 x 100%
0.4/12.9 x 100%
4/129 x 100%
3.1%
Describe the translation that maps ABCD onto A’B’C’D’
Answers
On a test called the MMPI-2, a score of 30 on the Anxiety Subscale is considered
very low. Felipe participates in a yoga group at his gym and decides to give this
subscale to 18 people in his yoga group. The mean of their scores is 35.2, with a standard deviation of 10.4. He wants to determine whether their anxiety scores are statistically equal to 30.
What are the groups for this one-sample t-test?
What is the null hypothesis for this one-sample t-test?
What is the value of "?
Should the researcher conduct a one- or two-tailed test?
What is the alternative hypothesis?
What is the value for degrees of freedom?
What is the t-observed value?
What is(are) the t-critical value(s)?
Based on the critical and observed values, should Felipe reject or retain the null
hypothesis? Does this mean that his yoga group has scores that are above 30, below 30, or
statistically equal to 30?
What is the p-value for this example?
What is the Cohen’s d value for this example?
If the " value were dropped to .01, would Felipe reject or retain the null hypothesis?
Calculate a 42% CI around the sample mean.
Calculate a 79% CI around the sample mean.
Calculate a 95% CI around the sample mean.
Answers
The MMPI-2 test is used for the assessment of psychopathology and personality of patients.
It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.
A score of 30 or less is usually considered very low.
The questions are answered by the patient, usually in a clinical or research setting.
A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.
The following are the parameters of the one-sample t-test:Groups:
18 participants
Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30
Type of test: One-tailed test
Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.
Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734
Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5
If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).
For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13
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Isolate f variable! Solve the equation algebraically! Show work!!
42 = 6f
Answers
Answer:
f=7
Step-by-step explanation:
42=6f
/6 /6
42/6=7
You divide 6 from 42, which leaves you with 7=f.
Find m∠XYZ in the figure if ∠XYZ and ∠PQR are supplementary angles.
Question 5 options:
A)
83°
B)
7°
C)
97°
D)
173°
Answers
Answer: C
Step-by-step explanation:
Supplementary angles add up to 180
x + 83 = 180
x= 97
List the 5 ways we can show that two triangles are congruent.
Answers
Answer:
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. If any two angles and the included side are the same in both triangles, then the triangles are congruent.
(side, side, side) we have two triangles with all three sides equal. ...
(side, angle, side) ...
(angle, side, angle) ...
(angle, angle, side) ...
(hypotenuse, leg)
Step-by-step explanation:
this is crazy lol
At a store, a shirt has a regular price of "x" dollars. During a sale, the price of the shirt is discounted by 30%. The expression 0.7x describes the discounted price, in dollars, of the shirt. Which expression also describes the discounted price, in dollars, of the shirt?
Answers
Have a good day
to show that RQP ≅ PSR by SSS, what must be the value of x?
Answers
Answer:
The answer is 5
Step-by-step explanation:
If you do 2x+3=4x-7, it will get you x=5
The required value of x is 5 units to show that RQP ≅ PSR by SSS.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
We have been given that
RQP ≅ PSR by SSS
SSS stands for the Side-Side-Side criterion.
According to this, two triangles are congruent if the three sides of a triangle are equal to the corresponding sides of the other triangle.
As per the given figure,
⇒ QR = PS
⇒ 2x+3 = 4x-7
⇒ 4x - 2x = 7 + 3
⇒ 2x = 10
⇒ x = 10/2
⇒ x = 5
Therefore, the required value of x is 5 units.
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identify the zeros of the polynomial function .
Answers
Step-by-step explanation:
To start, every term has an
x
in common, so we can factor that out. Doing this, we get
x
(
x
2
+
x
−
42
)
=
0
What I have in blue can be factored by a thought experiment. What two numbers have a sum of
1
and a product of
−
42
?
After some trial and error, we arrive at
−
6
and
7
. Thus, this business can be factored as
x
(
x
−
6
)
(
x
+
7
)
=
0
We can leverage the zero product property here, setting all three terms equal to zero. As our zeroes, we get
x
=
0
,
x
=
6
, and
x
=
−
7
A cake weights 900 g. Paul cuts it in 4 pieces. The biggest piece weighs as much as the 3 other pieces weigh together. What is the weight of the biggest piece?
Answers
Answer:500 g
Step-by-step explanation:
NEED HELP ASAP PLS ^^
Rearrange this equation
y+x=2
Answers
Answer:
y=-x+2
Step-by-step explanation:
y+x-x=2+x
y=-x+2
The sum of two numbers is twenty-four. Four less than three times the
smaller is twelve less than twice the larger. Find the
two numbers.
can you please give me the equation for this tyyyy
Answers
With the help of two variable equations, the two numbers are 8 and 16.
How to solve the system of equations?There are three ways to solve equations-
1. Substitution method
2. Elimination method
3. Graphing method.
Now, let the number be x and y.
Therefore, the sum of two numbers is twenty-four, x+y= 24
Now, given that,
3x-4=2y-12
3x-2y=-8
2y-3x=8
Now, substituting the value of y in the equation
2(24-x)-3x=8
40=5x
x=8
Therefore, the two numbers are 8 and 16.
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The sum of the lengths of the sides of triangle ABC is 25 in . The lengths of sides overline AB and overline BC are 9 inches and 8 inches . Find the length of side overline AC and classify the triangle.
Answers
Answer:
AC = 8 The classification is isosceles
Step-by-step explanation:
helpppp i’ll give that crown thing
Answers
Answer:
N K Q
Step-by-step explanation:
feng earned a score of 81 on exam a that had a mean of 76 and a standard deviation of 10. he is about to take exam b that has a mean of 300 and a standard deviation of 50. how well must feng score on exam b
Answers
To determine how well Feng must score on exam B, we can use z-scores and the concept of standard deviations.
First, let's calculate the z-score for Feng's score on exam A:
z-score = (x - mean) / standard deviation
z-score for exam A = (81 - 76) / 10 = 0.5
This means that Feng's score on exam A is 0.5 standard deviations above the mean of exam A.
To find out how well Feng must score on exam B, we need to calculate the equivalent score in terms of z-scores for exam B.
x = mean + (z-score * standard deviation)
x = 300 + (0.5 * 50) = 325
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Can please someone help me ASAP? It’s due today!! I will give brainliest if it’s all correct.
Please do part a, b, and c
Answers
The probability of selecting 2 cards that are consonants is 3/10 or 0.3.
What is the sample space?The sample space is the set of all possible outcomes when two cards are randomly selected without replacement from a pile of cards labeled with the letters A, E, R, S, and T. There are 5 cards in the pile, so there are 5 ways to select the first card. After the first card is selected, there are only 4 cards left, so there are 4 ways to select the second card. Therefore, the sample space has 5 x 4 = 20 possible outcomes.
Sample space: {AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
Part B: The favorable outcomes are the outcomes where both cards are consonants. The consonants in the pile are R, S, and T, so there are 3 ways to select the first consonant. After the first consonant is selected, there are only 2 consonants left, so there are 2 ways to select the second consonant. Therefore, there are 3 x 2 = 6 favorable outcomes.
Favorable outcomes: {RS, RT, SR, ST, TR, TS}
Part C: The probability of selecting 2 cards that are consonants is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 6 / 20
Probability = 3 / 10
Therefore, the probability of selecting 2 cards that are consonants is 3/10 or 0.3.
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Sarah works as a nanny and charges different rates for working during the week and the weekend. One week, she earned 902.50 working 45 hours, of which 5 hours were during the weekend. The following week she earned 1045 working 50 hours, of which 10 hours were during the weekend. What does Sarah charge per hour, in dollars, for working during the week?
Answers
Sarah's charges per hour for working during the week will be $9.5.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.
Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be
45x + 5y = 902.5 ...1
50x + 10y = 1045
25x + 5y = 522.5 ...2
Subtract equation 2 from equation 1, then we have
45x - 25x = 902.5 - 522.5
20x = 380
x = 19
And the value of y will be
25 (19) + 5y = 522.5
475 + 5y = 522.5
5y = 47.5
y = 9.5
Sarah's charges per hour for working during the week will be $9.5.
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How many types of traders are there in a derivative security
market and who are they?
Answers
In a derivative security market, there are typically four types of traders:
Hedgers: Hedgers are market participants who use derivatives to manage or offset risks associated with their underlying assets. They enter into derivative contracts to protect themselves from potential adverse price movements.
Speculators: Speculators are traders who take on risk in the hopes of making a profit from price movements in derivative securities. They do not have an underlying exposure to the asset but engage in derivative trading solely for speculative purposes.
Arbitrageurs: Arbitrageurs seek to exploit price discrepancies between related assets in different markets. They simultaneously buy and sell similar assets or derivatives in different markets to take advantage of price differentials.
These categories are not mutually exclusive, and individuals or entities may engage in multiple roles simultaneously or switch between them depending on market conditions and their investment objectives.
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The Cambridge Study in Delinquint Development was undertaken in North London (U.K.) to investigate the links between criminal behavior in young men and the socioeconomic factors of their upbringing (Farrington 1994). A cohort of 395 boys was followed for about 20 years, starting at the age of 8 or 9. All of the boys attended six schools located near the research office.
Number of convictions Frequency
0 265
1 49
2 21
3 19
4 10
5 10
Required:
a. What type of table is this?
b. How many variables are presented in this table?
c. How many boys had exactly two convictions by the end of the study?
d. What fraction of boys had no convictions?
e. Display the frequency distribution in a graph. Which type of graph is most appropriate? Why?
Answers
a. This is a frequency distribution table.
b. The table presents two variables: the number of convictions and the frequency of boys with that number of convictions.
c. According to the table, 21 boys had exactly two convictions by the end of the study.
d. The table shows that 265 boys had no convictions, which represents the fraction of boys with no convictions.
a. The given table is a frequency distribution table. It presents the number of convictions as one variable and the frequency of boys with that number of convictions as another variable.
b. In this table, two variables are presented. The first variable is the number of convictions, ranging from 0 to 5, and the second variable is the frequency, which represents the number of boys with each specific number of convictions.
c. According to the table, the frequency for boys with exactly two convictions is 21. Therefore, 21 boys had exactly two convictions by the end of the study.
d. The frequency distribution table shows that the number of boys with no convictions is 265. To determine the fraction of boys with no convictions, we divide the frequency of boys with no convictions by the total number of boys in the cohort: 265 / 395 = 0.6709, or approximately 67.09%. Thus, about 67.09% of boys in the study had no convictions.
e. To display the frequency distribution in a graph, a bar graph is the most appropriate choice. A bar graph will represent the number of convictions on the x-axis and the frequency on the y-axis. Each bar's height will correspond to the frequency of boys with a specific number of convictions, allowing for a visual representation of the distribution.
The given table is a frequency distribution table presenting the number of convictions and the corresponding frequency of boys in the Cambridge Study in Delinquent Development. It provides insights into the distribution of convictions among the cohort of boys studied. By analyzing the table, we can determine the number of boys with specific convictions, calculate fractions, and visualize the frequency distribution using a bar graph.
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Find the area of the shape.
Answers
Answer:
\( area \: of \: trapezium = \: \frac{1}{2} (a + b) \times h\)
Therefore, 1/2 (9 +17)*8
Therefore, 1/2(26)*8
Therefore, 13*8
Therefore, 104
Your answer is 104ft²