The distance traveled by car has to travel to catch up to the train is 240 miles.
Given that,
A train travels due north at 40 mph.
A car travels toward the train from the same starting point leaving 2 hours later than the train.
If the car is traveling at 60 mph.
We have to determine,
How many miles will the car have to travel to catch up to the train?
According to the question,
The distance will the car have to travel to catch up to the train is determined by using the following formula;
[tex]\rm Speed = \dfrac{Distance}{Time}[/tex]
Let the distance will the car have to travel to catch up to the train be x.
Then,
The distance traveled by car in times t is,
[tex]\rm Speed = \dfrac{Distance}{Time}\\\\Distance = Speed \times Time\\\\ x = 40 \times t\\\\x = 60t[/tex]
And car travels toward the train from the same starting point leaving 2 hours later than the train.
Then,
The distance traveled by train in time (t+2) is,
[tex]\rm Speed = \dfrac{Distance}{Time}\\\\Distance = Speed \times Time\\\\ x = 40 \times( t+2)\\\\x = 40(t+2)[/tex]
Substitute the value of x in equation 2 from equation 1,
[tex]\rm x = 40(t+2)\\\\60t=40t+80\\\\60t-40t=80\\\\20t=80\\\\t = \dfrac{80}{20}\\\\t = 4[/tex]
Therefore,
The distance traveled by car has to travel to catch up to the train is,
[tex]\rm x = 60t\\\\x = 60\times 4\\\\x = 240 \ miles[/tex]
Hence, The distance traveled by car has to travel to catch up to the train is 240 miles.
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What is the value of z in the equation 3z − 7 = 14? (4 points)
Answer:
7
Step-by-step explanation:
Write the sum in sigma notation. 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50
Please mark brainliest
The sum in sigma notation for the sequence as follows:
From
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50
first term=5
common difference=5
number of terms=10
n=nth term
therefore the total will be:
(i=2 to 10)∑(5(n-1)+5
Find the product. 4(−12)(−3) A) −144 B) −96 C) 144 D) 72
The temperature has been going down at a constant rate. In 3 hours it went down 15 degrees. Which expression best shows the temperature change each hour? A.−15⋅−3 B. 15⋅3 C. −15÷3 D.15÷3
Lines b and c are parallel. What is the measure of <6?
m<6 = 45
m<6 = 54
m<6 = 117
m<6 = 126
Answer:
m<6 = 54
St,ep-by-step explanation:
Lines b and c are parallel.
13x +9 and 5x+9 are consecutive exterior angles.
Consecutive exterior angles are supplementary.
[tex]13x+9+5x+9= 180[/tex]
Now we solve for x. combine like terms
[tex]18x+18= 180[/tex]
Subtract 18 from both sides
[tex]18x=162[/tex]
Divide both sides by 18
x=9
So the value of x=9
angle 6 and 5x+9 are vertical opposite angles . they are equal
m<6= 5x+9
Plug in 9 for x
m<6= 5(9)+9=54
m<6 = 54
Answer:
m<6 = 54
Step-by-step explanation:
Write the prime factorization of 18. Use exponents when appropriate and order the factors from least to greatest (for example,
2
2
3
5
).
Submit
The prime factorization of 18 is 2 x 3², dividing 18 first by 2 and then by 3 twice.
Explanation:The prime factorization of a number represents that number written as the product of its prime factors. Let's take 18 as an example. First, we will find the smallest prime number that can divide 18, which is 2. When 18 is divided by 2, the quotient is 9. Then, we continue to divide 9 by the smallest possible prime number, which is 3. We can divide 9 by 3 two more times. Therefore, the prime factorization of 18 is 2 x 3², where 2 and 3 are the prime factors and ² is an exponent indicating that 3 is a factor twice.
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helpppp! pls! 10 points
What is the sum of the geometric sequence -4,24,-144...if there are 8 term? A.-959,781 B. 29,637 C. 26,661 D. 959,780 PLEASE HELP
Answer:
The sum of 8 terms of series is 959,780
D is correct
Step-by-step explanation:
Given: -4, 24, -144, ......
There are 8 terms.
We need to find the sum of 8 terms.
First term, a=-4
Common ratio, r=-6
[tex]a_n=-4\cdot(-6)^{n-1}[/tex]
Sum of 8 term
[tex]Sum=a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8[/tex]
[tex]Sum=\sum_{n=1}^{8}a_n[/tex]
[tex]Sum=-4+24-144+864-5184+31104-186624+1119744[/tex]
[tex]Sum=959,780[/tex]
Hence, The sum of 8 terms of series is 959,780
What is the length of segment CE if AE = 15 inches and ED = 5 inches and EB = 3 inches?
A. 45 inches
B. 9 inches
C. 15 inches
D. 14 inches
We have to determine the length of segment CE if AE = 15 inches and ED = 5 inches and EB = 3 inches.
Since ,we can observe that AB and CD are chords intersecting at point E.
Therefore, by intersecting chord theorem which states:
" When two chords intersect each other inside a circle, the products of their segments are equal"
So, [tex] AE \times EB= CE \times ED [/tex]
[tex] 15 \times 3= CE \times 5 [/tex]
[tex] 45= CE \times 5 [/tex]
[tex] CE = \frac{45}{5} [/tex]
CE = 9 inches.
So, the measure of segment CE is 9 inches.
So, Option B is the correct answer.
A radio tower casts a shadow of 8.2 ft long and a 36-inches and a fourth-grader walking home cast a shadow of 1.5 inches. How tall is the radio tower?
Answer: 196.8
Step-by-step explanation:
Start off by reading the problem.
A radio tower casts a shadow of 8.2 ft long and a 36-inches and a fourth-grader walking home cast a shadow of 1.5 inches. How tall is the radio tower?
Then take what you know from the problem and put it in a fraction looking thing:
like this:
1.5 8.2
__ = __
36 x
So after you've done this you will want to:
Multiply 36 x 8.2 = 295.2
take 295.2 then Divide by 1.5
=196.8
Answer:
196.8
Step-by-step explanation:
Simplify the radical expression.
square root of 20
A. 2√10
B. 5√2
C. 2√5
D. 2
if anyone has the answers to the unit test let me know :)
four-barrel of colored marbles you randomly select three blue to Yellow 7 red eight green and two purple marbles. find the experimental probability of randomly selecting either green or purple marble
Standard number cube is rolled 180 times. Predict how many times 3 or 5 will be the result
The movie open the other day. So far 500,000 people have seen it. the producers of the movie needed to know if the people liked it. a random sample of 8000 people were asked as they were leaving the theater if they like the movie. of those interviewed 4,200 enjoyed the movie. predict the total number of people who have enjoyed the movie.
Jamestown Builders has a development of new homes. there are 6 different floor plans 7 exterior color than an option of either one car or two car garage . How many choices are there for one home?
if no digit may be used more than once how many 5 digits can be formed using only three digits. 8 1 2 5 and7?
The answer provides the experimental probability of selecting green or purple marbles, predicts the occurrences of rolling 3 or 5 on a number cube, and estimates the total number of people who enjoyed the movie.
Experimental Probability Calculation: In the given scenario, there are 8 green marbles and 2 purple marbles, making a total of 10 marbles. The probability of selecting a green or purple marble is the sum of the individual probabilities, which is (8/10) + (2/10) = 0.8.
Expected Outcome of Rolling a Number Cube: Since a standard number cube has numbers 1 to 6, each number has an equal probability of 1/6. Predicting how many times 3 or 5 will be rolled out of 180 rolls can be calculated by (1/6 + 1/6) x 180 = 60 times each for 3 and 5.
Total Number of People Who Enjoyed the Movie: Based on the sample data, 4,200 out of 8,000 people enjoyed the movie. Extrapolating this to the total viewers, the predicted number of people who enjoyed the movie would be: (4,200/8,000) x 500,000 = 262,500 people.
Rewrite in simplest radical form x56x16
A man weighs 180 lb. He jogs a mile in 8 minutes. How many calories has he used up?
A man weighing 180 lb has burned approximately 100 calories by jogging one mile, based on the average estimate that jogging one mile burns almost 100 calories.
The question relates to the calculation of calories burned during exercise, specifically jogging. Based on the information provided that running or jogging one mile burns almost 100 calories, we can calculate the energy expenditure for a man weighing 180 lb who jogs a mile in 8 minutes.
Since the provided calories burned per mile is an average, the actual number might vary slightly based on individual metabolism and effort level, but it serves as a useful approximation.
To determine how many calories the man has used up, we can use the given information:
Running or jogging one mile burns almost 100 calories.The man jogs a mile, which means he has burned approximately 100 calories for that activity.Therefore, the man has burned approximately 100 calories during his 8-minute mile jog.
the rational roots of a polynomial function F(x) can be written in the form p/q,
where p is a factor of the constant term of the polynomial, and q is a factor of the leading coefficient
TRUE OR FALSE??
ANSWER
True
EXPLANATION
According to the Rational Roots Theorem,the rational roots of a polynomial function F(x) can be written in the form
[tex] \frac{p}{q} [/tex]
,
where p is a factor of the constant term of the polynomial, and q is a factor of the leading coefficient.
The polynomial must be written in standard form.
This means the polynomial must be written in descending powers of x.
The leading term is the first term of a polynomial written in standard form.
The constant term is the term independent of x.
PROBABILITY PROBLEM! NEED HELP AND EXPLAIN/SHOW WORK
HHHEEELLLPPP PLEASE
1] Amanda’s gross annual salary is $62,112.
What is the maximum amount of rent she can afford to pay?
Round your answer to the nearest dollar.
A $2588
B $1866
C $1449
D $1236
2] Jonathan is signing a lease for an apartment that rents for $1240/month.
How much will he pay to move in if he must pay the first and last months’ rent and a security deposit equal to 80% of his monthly rent?
A $2976
B $3472
C $3542
D $3720
Answer:
first one would be c
Step-by-step explanation:
The probability of picking two black marbles from a box at random without replacement is 1091 . The probability of drawing a black marble first is 514 . What is the probability of picking a second black marble, given that the first marble picked was black?
Final answer:
The probability of picking a second black marble, given that the first marble picked was black, is 1.
Explanation:
To find the probability of picking a second black marble, given that the first marble picked was black, we can use the formula for conditional probability: P(A|B) = P(A and B)/P(B).
In this case, A represents the event of picking a black marble on the second draw, and B represents the event of picking a black marble on the first draw.
We are given that P(B) = 514, and the probability of picking two black marbles without replacement is 1091. Therefore, P(A and B) = P(A|B) * P(B) = (1091/514) * (514/1091) = 1.
So, the probability of picking a second black marble, given that the first marble picked was black, is 1.
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. at the end of the 6th year, the tree was \frac{1}{5} taller than it was at the end of the 4th year. by how many feet did the height of the tree increase each year?
A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area of the washer?
use the distance formula and the pythagorean theorem to find the distance, to the nearest tenth, from T (4,-2) to (-2,3).
Rewrite the radicand as two factors, one of which is a perfect cube.
3/250
Find the surface area of the equilateral triangular pyramid.
Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below. x – y = 7 3x – 2y = 8 Step 1: x = y + 7 Step 2: 3(y + 7) – 2y = 8 Step 3: 3y + 7 – 2y = 8 Step 4: y + 7 = 8 Step 5: y = 1
Which of the following sets shows all the numbers from the set {2, 3, 4, 5} that are part of the solution to the inequality 4n + 6 > 22?
Answer:
the answer is
{2, 3, 4}
Step-by-step explanation:
if 5 is the only one that works and it has to be inequality so
{2, 3, 4} can be the only answer
What is the volume of a cylinder with a diameter of 12 in. and a height of 7 in.?
Answer
Find out the volume of a cylinder .
To prove
Formula
[tex]Volume\ of\ cylinder = \pi r^{2}h[/tex]
Where r is the radius and h is the height.
As given
Diameter of 12 in. and a height of 7 in.
[tex]Radius = \frac{Diameter}{2}[/tex]
[tex]Radius = \frac{12}{2}[/tex]
Radius = 6 in
[tex]\pi = 3.14[/tex]
put all the values in the formula
[tex]Volume\ of\ cylinder = 3.14\times 6\times 6\times 7[/tex]
= 791.28 in³
Therefore the volume of the cylinder is 791 .28 in³ .
Find the distance d from (6.1, 5.9) to (-5.9, -4.1) .
A.
6.63
B.
15.62
C.
22.00
D.
244.00
Answer:
your answer is B
Step-by-step explanation:
Question 4 :)))))))$$$))))$$
Johnny flips a coin three times. what is the probability he lands on heads every time
[tex] |\Omega|=2^3=8\\
|A|=1\\\\
P(A)=\dfrac{1}{8}=12.5\% [/tex]
Write an inequality for the given statement: The sum of –18 and a number is more than 22. A. 18 – n < 22 B. 18 – n > 22 C. –18 + n < 22 D. –18 + n > 22