A motorist travelled from Town A to Town B. After travelling for 1 1/2 hours , he passed
a cyclist travelling at an average speed of 45 Km/h in the opposite direction.
when the motorist reached Town B 2 h later, the cyclist was 30 km away from Town A.
a) Find the average speed of the motorist.
b) Find the distance between Town A and Town B.
Answers
Answer:
the formula: Speed = Distance / Time.
Let's break down the problem into two parts:
a) Find the average speed of the motorist.
Let's assume the average speed of the motorist is "v" km/h.
The distance the motorist traveled in 1 1/2 hours is given by: Distance = Speed × Time = v × (3/2) km.
The distance the cyclist traveled in 1 1/2 hours (opposite direction) is given by: Distance = Speed × Time = 45 × (3/2) km.
Since they passed each other, the sum of their distances should be equal to the distance between Town A and Town B.
So, we can set up the equation: v × (3/2) + 45 × (3/2) = Distance between Town A and Town B.
b) Find the distance between Town A and Town B.
When the motorist reached Town B 2 hours later, the cyclist was 30 km away from Town A.
We can set up the equation: Distance between Town A and Town B = v × 2 + 30.
Now, let's solve the equations:
v × (3/2) + 45 × (3/2) = v × 2 + 30.
Simplifying the equation, we have: (3v + 135)/2 = 2v + 30.
Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 3v + 135 = 4v + 60.
Subtracting 3v from both sides of the equation, we have: v = 75.
Therefore, the average speed of the motorist is 75 km/h.
To find the distance between Town A and Town B, we substitute the value of v into the equation:
Distance between Town A and Town B = v × 2 + 30 = 75 × 2 + 30 = 150 + 30 = 180 km.
Therefore, the distance between Town A and Town B is 180 km.
Related Questions
f(x)=3^x+1 and g(x) = 2x-4, find f(2) - g(-1)
Answers
Answer:
16
Step-by-step explanation:
3^x +1 = f(X)
2x-4 = g(x)
find f(2)-g(-1)
we substitute in function f(X) by value (2), and in function g(X) by value (-1)
1. 3^x +1 becomes 3^2+1 =9+1=10
2. 2(-1)-4= -2-4=-6
then f(2)-g(-1)
= 10-(-6) =10+6=16
Select all the fractions that are equivalent to each other.
(Choose 2)
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Answers
Answer: You should try to multiply and divide try then question me back. But the answers are neither of them.
Step-by-step explanation:
Since the mode is the most frequently occurring data value, it
Select one:
a. is always larger than the mean
b. can never be larger than the mean
c. must have a value of at least two
d. is always larger than the median
e. None of these answers is correct.
Any answer without justification will be rejected automatically.
Answers
The correct answer is option (e): None of these answers is correct.
The statement "the mode is the most frequently occurring data value" is true. However, none of the options provided accurately describes the relationship between the mode and the mean.
The mode and the mean are different measures of central tendency and can have different values. There is no general rule or guarantee that the mode will always be larger or smaller than the mean. The relationship between the mode and the mean depends on the specific dataset and its distribution. Therefore, none of the provided options correctly describes the relationship between the mode and the mean.
11
k
The model below is shaded to represent an expression.
Which expression represents the model?
1 2
3 x 5
A
B
D
1 5
3x2
2
3x5
5
3x 2
Answers
The expression which represents the model is (3 × 2/5). The Option C is correct.
What does a model means?A modeling refers to the process of creating a representation of a real-world scenario to make a prediction or provide insight.
In the given question, it can be observed that the model contains 10 parts in total with a division of 5 each into 2 parts.
Since the division of 2 is made thrice, it gives us:
3 × 2/5
Hence, this makes the third option (3 × 2/5) the correct one.
Note: The full question is attached as picture as below.
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Robert has some nickels and some dimes. He has a maximum of 29 coins worth no less than $2.20 combined. If Robert has 10 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Answers
Robert has 10 nickels, which means he already has 10 coins. We need to find the possible values for the number of dimes he could have.
Let's assume Robert has x dimes.
The value of 10 nickels is 10 * $0.05 = $0.50.
The value of x dimes is x * $0.10 = $0.10x.
The total value of the coins is at least $2.20. So we can write the inequality:
$0.50 + $0.10x ≥ $2.20
Now let's solve this inequality for x:
$0.10x ≥ $2.20 - $0.50
$0.10x ≥ $1.70
x ≥ $1.70 / $0.10
x ≥ 17
Therefore, the possible values for the number of dimes Robert could have are 17 or greater.
So, the comma-separated list of possible values for the number of dimes is: 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
Note: We have considered the maximum limit of 29 coins mentioned in the problem, so any value of x greater than or equal to 17 and less than or equal to 29 would satisfy the given conditions.
Robert's dimes are anywhere between 17 and 19.
Explanation:Nickels
are worth 5 cents, and
dimes
are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.
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I need all the spaces filled in please :)
Answers
Answer:
3x + y = -16
Step-by-step explanation:
Explanation:-
Given a system of equations are
5x+6y =-5
- 2x - 5y = -11
multiply '1' and Adding two system of equtions
+ 1 (5x + 6y = -5)
+ 1 ( -2x - 5y = -11)
3x + y = -16
Final answer:-
5x + 6y = -5
-2x - 5y = -11
3x + y = -16
Factor each polynomial. Look for a GCF first.
2x²-8k-90
O
2 (x-9) (x - 5)
2 (x + 9) (x + 5)
2 (x − 9) (x + 5)
2 (x + 9) (x - 5)
Answers
Answer:
Step-by-step explanation:
First, you could factor 2 out of the whole thing. The result would be 2(x^2-4x-45). Now we find the factors of 45 which are 1, 45, 5, 9, 15, 3. We have to find the pair that adds up to 4, and multiply to get 45. After some guess and check, we can find that 5 and 9 are those numbers. Now we have to get the right signs. Since the result is a negative number for -8k, and -90, the number that is a negative must be less than the other negative. -9<-5, so the answer would be 2(x-9)(x+5)
Find the flaw with the following "proof" that every postage of 3 cents or more can be formed using just 3-cent and 4-cent stamps.Basis Step: We can form postage of 3 cents with a single 3-cent stamp, and we can form postage of 4 cents using a single 4-cent stamp.Inductive Step: Assume that we can form postage of j cents for all nonnegative integers j with j ≤ k using just 3-cent and 4-cent stamps. We can then form postage of k + 1 cents by replacing one 3-cent stamp with a 4-cent stamp or by replacing two 4-cent stamps by three 3-cent stamps.Which of these statements describes a flaw in the proof?
Answers
Answer:
The main flaw of this proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp and a 3 cent postage must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage
Step-by-step explanation:
From the question we are told that
The proof is
Every postage stamp of three cents or more can be formed using just 3 cent and 4 cent stamps.
Basic Step : We can form postage of 3 cents with a single 3 cent stamp and we can form postage of 4 cents using a single four cents tamp
Inductive Step: Assume that we can form postage of j cents for all non negative integers j with j <= k using just 3 cent and 4-cent stamps. We can then form postage of k+1 cents by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps
FLAW IDENTIFICATION
Looking the inductive step, the statement ''by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps '' means that it is possible to use a 3-cent stamp for postage that requires a 4 -cent stamp and this is not correct according the statement in the basic step
Generally the main flaw of this proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp and a 3 cent postage must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage
Write the slope- intercept form of the equation of the line described through (4,5) parallel to y= 1/4x-4
Answers
Answer:
y = 1/4 x + 4
Step-by-step explanation:
1. Because the new equation is parallel to y= 1/4x - 4 => the slope is still the same => New equation : y = 1/4x + b ( b is a number that we'll find now)
2. Put x = 4 and y = 5 in the new equation
=> 5 = (1/4)(4) + b
=> b = 4
3. So then we'll have the new equation that is parallel to y = 1/4x-4
Sandra calculated the height of a cylinder that has a volume of 576 π cubic centimeters and a radios of 8 centimeters. Her work is shown below.
Answers
Answer:
\( \boxed{Height \: of \: cylinder = 9 \: centimeters} \)
Given:
Volume of cylinder = 576π cubic centimeters
Radius of cylinder (r) = 8 centimeters
Step-by-step explanation:
Let the height of cylinder be 'h'
\( = > Volume \: of \: cylinder = \pi {r}^{2} h \\ \\ = > 576 \cancel{\pi} = \cancel{ \pi}( {8}^{2} )h \\ \\ = > 576 = 64h \\ \\ = > 64h = 576 \\ \\ = > h = \frac{576}{64} \\ \\ = > h = 9 \: centimeters \)
Height of cylinder = 9 centimeters
simplify pls do fast
Answers
The sum of the decimal values given is 0.93
Simplifying the decimal values can be done thus :
0.36 + 0.57Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .
0.36*100 = 36
0.57*100 = 57
Adding the whole numbers :
__36
+_57
_____
__93
Dividing the sum by 100 to convert to an equivalent decimal value,
93/100 = 0.93Therefore, the required value is 0.93
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How do I find the answer to this question?
Answers
Answer:
you see
Step-by-step explanation:
Solve the equation
2^2x+1 +5(2^x) -3=0
Please help
Answers
Answer:
The answer is -1
Step-by-step explanation:
2^(2x+1) = 2^2x × 2^1 = 2^2x × 2
after this we can make appointments
2^x = t
and then solve it :)
Pls help me I really need to pass
Answers
Answer:
A. 31 Km
Step-by-step explanation:
\(circumference = 2\pi \:r\)
radius equals the diameter divided by 2
\(r = \frac{d}{2} \)
In this case the diameter is 10, so the radius is 5.
finally,
\(2\pi(5) = 31.415\)
rounded to the nearest whole number gives us
31 Km.
Answer the questions below. Be sure to mark all answers that apply.
(a) Which numbers are divisible by 3?
(b) Which numbers are divisible by 9?
850 127
505
None of these
Answers
Answer:
Step-by-step explanation:
There is none of these numbers are divisible by 9 and the required number is 474 divisible by 3 which the correct answer would be an option (D)
What is the divisibility rule?
The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.
The sum of the digits should be divisible by 9
⇒ 474 : (4+7+4=15, and again, 1+5=6)
This number is not divisible by 9
⇒ 127 : (1+2+7=10, and again, 1+0=1)
This number is also not divisible by 9
⇒ 907 : (9+0+7=16, and again, 1+6=7)
This number is also not divisible by 9
The sum of the digits should be divisible by 3
⇒ 474 : (4+7+4=15, and 15÷3 = 5)
This number is divisible by 3
⇒ 127 : (1+2+7=10, and 10÷3 = 3.333)
This number is not divisible by 3
⇒ 907 : (9+0+7=16, and 16÷3 = 5.333)
This number is not divisible by 3
There is none of these numbers are divisible by 9 and the required number is 474 divisible by 3 which the correct answer would be an option (D)
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The question seems to be incomplete the correct question would be
(a) Which numbers are divisible by 9?
(A). 474
(B). 127
(C). 907
(D). None of these
(b) Which numbers are divisible by 3?
(A). 474
(B). 127
(C). 907
(D). None of these
1) Kelly has 15 blue bracelets and 12 green bracelets. What is the ratio of Kelly’s blue bracelets to green bracelets?
2) Over the winter it snowed 36 days out of 40 days. What is the snow days to days ratio in simple form?
3) The ratio of girls to boys who participated in the quiz bowl was 7:5. There were 42 girls in the competition. How many boys participated?
Answers
1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.
2)The snow days to days ratio is 20:1
3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.
Define ratio?A ratio is a ratio that compares two quantities.A proportion is the difference between two ratios. To write a ratio, do the following: Determine whether the ratio is a part-to-part or a part-to-whole ratio. If necessary, compute the parts and total.The ratio is defined as the division of two numbers or quantities. The ratio is a relationship between the quantities of two or more objects that indicates how much of one is contained in the other. The ratio formula can be used to convert a ratio into a fraction. a:b = a/b is the ratio formula for any two quantities, say a and b.To learn more about ratio refer to:
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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.
2)The snow days to days ratio is 20:1
3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.
Define ratio?
A ratio is a ratio that compares two quantities.A proportion is the difference between two ratios.To write a ratio, do the following: Determine whether the ratio is a part-to-part or a part-to-whole ratio. If necessary, compute the parts and total.The ratio is defined as the division of two numbers or quantities.The ratio is a relationship between the quantities of two or more objects that indicates how much of one is contained in the other.The ratio formula can be used to convert a ratio into a fraction. a:b = a/b is the ratio formula for any two quantities, say a and b.To learn more about ratio refers to:
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mom's florist sells two dozen Rose's for 24.60. First flowers sells 6 Rose's for 7.50 which florist had the lower cost per rose?
Answers
We are to compare the cost of each rose sold by two florists.
Mom's florist sells ( n ) number of roses at a certain price ( S ) as follows:
\(\begin{gathered} n\text{ = 2 dozen roses ( 2}\cdot12=24\text{ )} \\ S\text{ = \$24.60} \end{gathered}\)First florist sells ( k ) number of roses at a certain price ( M ) as follows:
\(\begin{gathered} k\text{ = 6 roses} \\ M\text{ = \$7.5} \end{gathered}\)We will determine the cost price of each rose ( c ) sold by the two florist.
For Mom's florist:
We will take the ratio of the total cost ( S ) and the number of roses sold ( n ) as follows:
\(\begin{gathered} c_1\text{ = }\frac{S}{n} \\ \\ c_1\text{ = }\frac{24.6}{24} \\ \\ c_1=\frac{\text{\$1.025 }}{rose} \end{gathered}\)For First florist:
We will take the ratio of the total cost ( M ) and the number of roses sold ( k ) as follows:
\(\begin{gathered} c_2\text{ = }\frac{M}{k} \\ \\ c_2\text{ = }\frac{7.5}{6} \\ \\ c_2=\frac{\text{\$}1.25\text{ }}{rose} \end{gathered}\)Then we compare the cost prices ( c ) for roses sold by each florist:
\(\begin{gathered} c_1Hence,\(\text{Mom's florist has the lower cost per rose}\)
PLEASE ANSWER NUMBER 2
Answers
Maury and his mom painted the rectangular wall in Maury room Maury painted 1/6 of the wall and his mom painted 1/4 of the wall How much of the wall is still left to paint
Answers
Answer: 7/12
Step-by-step explanation:
1- 1/6 - 1/4
5/6 - 1/4
10/12 - 3/12
7/12 left
Consider the probability statements regarding events A and
B below.
P(A or B) = 0.3
P(A and B) = 0.2
P(AB) =0.8
What is P(B)?
A) 0.1
B) 0.375
C) 0.25
D) 0.667
Answers
The calculated value of the probability of B is (c) 0.25
How to calculate the probability of BFrom the question, we have the following parameters that can be used in our computation:
P(A or B) = 0.3
P(A and B) = 0.2
P(A/B) =0.8
First, we have
P(A/B) = P(A and B)/P(B)
Substitute the known values in the above equation, so, we have the following representation
0.2/P(B) = 0.8
So, we have
P(B) = 0.2/0.8
Evaluate
P(B) = 0.25
Hence, the probability of B is 0.25
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i need help asap
than you!
Answers
The highest height for the daily rainfall were for 5 and 6 inches
How to Interpret Dot Plots?Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.
From the given dot plot, we see the number of times for each height of rainfall.
Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.
Thus, we conclude those were the highest heights for the daily rainfall.
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Philip has been experimenting with new recipes at his bakery for the past 8 months. This month, he tried a recipe for lavender vanilla muffins and gave samples to his customers. He asked them to rate the muffins on a scale of 1 to 10 stars. The median rating was 7 stars, and the interquartile range was 4 stars. ) What can you conclude from these data and statistics? Select all that apply. () No customer gave the muffins fewer than 8 stars. A typical rating for the muffins was 7 stars. The middle 50% of customer ratings had a range of 4 stars. Submit
Answers
- A typical rating for the muffins was 7 stars, since the median rating was 7 stars.
- The middle 50% of customer ratings had a range of 4 stars, since the interquartile range was 4 stars.
- We cannot conclude that no customer gave the muffins fewer than 8 stars, as the median is not necessarily equal to the mean, and it is possible that some customers rated the muffins below 8 stars. Therefore, this statement is not necessarily true.
which of the following figures have the smallest area?
Answers
The law firm of Dewey, Cheetham, and Howe handled 18 personal injury cases this past year. This was 9/7 of the cases handled by the rival firm of Gypsum-Goode. How many personal injury cases were handled by Gypsum-Goode this year?
Answers
Answer:
14 cases
Step-by-step explanation:
Let x be the number of personal injury cases this year by Gypsum Goode
x* 9/7 = 18
Multiply each side by 7/9
x * 9/7 *7/9 = 18 * 7/9
x = 14
Somebody please help pleaseeeee I’ll make brainlest please help anybody .
Answers
Answer:
C Is The Correct Answer
bella answered 33 questions on her math test. she earned a 92% on the test. how many questions did she answer correct
Answers
Answer: 30.36
Step-by-step explanation:
92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.
Leila is buying a dinosaur model. The price of the model is xxx dollars, and she also has to pay a 7\%7%7, percent tax.
Which of the following expressions could represent how much Leila pays in total for the model?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
\dfrac{107}{100}x
100
107
xstart fraction, 107, divided by, 100, end fraction, x
(Choice B)
B
0.7x+x0.7x+x0, point, 7, x, plus, x
(Choice C)
C
1.07x1.07x1, point, 07, x
(Choice D)
D
x+\dfrac{7}{10}xx+
10
7
xx, plus, start fraction, 7, divided by, 10, end fraction, x
(Choice E)
E
1.7x1.7x
Answers
The expressions that could represent how much Leila pays in total for the model
\dfrac{107}{100}x
100 107 Option A is correct.
This is further explained below.
Which of the following expressions could represent how much Leila pays in total for the model?The price of the model is x
Now we are given that she also has to pay a 7 tax.
Amount of tax =7 % x
\(=\frac{7}{100} x\)
the Total cost\(=x+\frac{7}{100} x\)
\(=\frac{107}{100} x\)
In conclusion, the statement might signify Leila's overall cost for the model. \(\frac{107}{100} x\)
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What is the first step you would take to solve the equation 1 1/2x 2 1/3
Answers
The first step would take to solve the equation 1 1/2x 2 1/3 is to convert the mixed fraction to improper fraction
What are fractions?Fractions are defined as the expressions that involves the part of a whole number or the part of a variable.
There are different types of fractions in mathematics. These fractions are namely;
Proper fractions.Improper fractionsComplex fractions.Simple fractions.Mixed fractions.Also, in converting mixed fractions to improper fractions, we have to multiply the denominator of the fraction by the whole number, then, add the value of the product to the numerator.
We have that;
1 1/2x 2 1/3
convert to improper fractions
3/2 × 7/3
Multiply
7/2
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PLEASE HELP
A bag hes 10 red marbles, 3 green marbles,
7 yelow marbles, and 5 blue merbles. What is
the probability of crowing a red marble and
then g, blue, marble without replacing the first?
Answers
Answer:
\(\frac{3}{5}\)
Step-by-step explanation:
Probability is the chance of an event happening. One finds the probability of an event by using the following general formula,
\(\frac{desired}{total}\)
In this case, the desired outcome is pulling whether a red or blue marble from the bag, the desired equals the sum of the number of red and blue marbles.
(red) + (blue)
= 10 + 5
= 15
The total number of marbles is the sum of all the number of marbles in the bag.
(red) + green) + (yellow) + (blue)
= 10 + 3 + 7 + 5
= 25
Now substitute these values into the formula to find the probability, then simplify,
\(\frac{15}{25}\)
Divide both the numerator and denominator by (5),
\(\frac{3}{5}\)
HELP PLEASE!
A local little league has a total of 80 players, of whom 20% are left-handed. How many
left-handed players are there?
Answers
Answer:
There are 16 left-handed players.
Step-by-step explanation:
Answer:
16
Step-by-step explanation: