At 1:00 p.m. a car leaves st. louis for chicago, traveling at a constant speed of 65 miles per hour. at 2:00 p.m. a truck leaves chicago for st. louis, traveling at a constant speed of 55 miles per hour. if it is a 305-mile drive between st. louis and chicago, at what time will the car and truck pass each other?

Answers

Answer 1

To find out when the car and truck will pass each other, set up an equation where the sum of the distances covered by each at their respective speeds equals 305 miles. After solving, it's determined they will pass each other at 4:00 p.m.

To determine at what time the car and truck will pass each other, we need to calculate how far each vehicle will have traveled before they meet. The car leaves St. Louis at 1:00 p.m., while the truck leaves Chicago at 2:00 p.m., one hour later. We assume they meet after the car has been traveling for t hours and the truck for t - 1 hours.

The distance the car travels is the product of its speed and time, which can be calculated as 65 miles per hour times t hours. The truck's distance is 55 miles per hour times (t - 1) hours. Since the total distance between St. Louis and Chicago is 305 miles, we combine these distances to form the equation:

65t + 55(t - 1) = 305

Solving this equation:

65t + 55t - 55 = 305120t - 55 = 305120t = 305 + 55120t = 360t = 360 / 120t = 3 hours

Since the car has been traveling for 3 hours after 1:00 p.m., the two vehicles will pass each other at 4:00 p.m.


Related Questions

For what values of x does f(x)= x^2 +9x +20 reach its minimum value?

Answers

Final answer:

The minimum value of the quadratic function f(x)= [tex]x^2[/tex] +9x +20 is achieved at x = -4.5, calculated using the vertex formula -b/2a.

Explanation:

The function f(x)= [tex]x^2[/tex] +9x +20 is a quadratic function. The minimum value of a quadratic function is achieved at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a, where a and b are coefficients of [tex]x^2[/tex] and x respectively in the standard form a[tex]x^2[/tex] + bx + c. Here, a=1 and b=9.

So, by applying the formula, the value of x will be -b/2a = -9/(2*1) = -4.5. Hence, the function achieves its minimum value when x = -4.5.

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What is the value of the 11th term of the sequence 1, -2, 4, -8, ...?
4,096
1,024
-2,048
-1,024

Answers

The pattern is that the next term is equal to the previous term multiplied by -2.
1
-2
4
-8
16
-32
64
-128
256
-512
1024
The answer is 1024

what divides an angle into two congruent angles

Answers

Bisector of a segment

A cubic centimeter of quartz, olivine, and gold weighs 2.5, 3.0, and 19.8 grams, respectively. this indicates that

Answers

it would indicate that quartz and olivine have similar densities but olivine is a little more dense. It also indicates that gold has a much greater density than either of the others

To solve the problem we must know about density.

The different weight shows that the solids have different density.

Given to us

A cubic centimeter of quartz, olivine, and gold weighs 2.5, 3.0, and 19.8 grams.

What are weight and mass?

We know that weight is the product of mass and acceleration due to gravity, also, mass is the product of density and volume.

[tex]\rm{ weight = mass \times acceleration\ due\ to\ gravity[/tex]

[tex]\rm{ w = m \times g[/tex]

[tex]\rm{ Mass = density \times volume[/tex]

[tex]m = \rho \times v[/tex]

What is the relationship between weight and mass?

In the three solids given, the acceleration due to gravity will be the same, also, it is already mentioned that the volume of the three materials is the same that is 1 cubic centimeter.

[tex]w = m \times g\\w = (\rho \times v) \times g\\\\w = \rho \times 1\ cm^3 \times 9.81[/tex]

Therefore, the only thing that can vary is the density of the solids. Hence, the different weight shows that the solids have different density, the more is the weight the more is the density of the solid.

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What can you conclude about the slope of the values in the table? Check all that apply.
The slope is 3.
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.

Answers

The conclusion that can be drawn from the slope of the values given in the table is:

3. Slope is undefined.

5. Graph is a vertical line.

First, let's determine the value of the slope by applying the slope formula using two points given from the table, say, (1000, 20) and (1000, 23):

Slope formula = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let,

[tex](1000, 20) = (x_1, y_1)\\\\(1000, 23) = (x_2, y_2)[/tex]

Substitute:

[tex]slope(m)=\frac{23 - 20}{1,000 - 1,000}\\\\slope (m) =\frac{3}{0}[/tex] (undefined)

Zero cannot divide 3 hence, the slope is undefined.

Slope that are vertical have rise but no run, thus, their slope is undefined.

(see attachment for image showing an example of how an undefined slope looks like on a graph.)

Therefore, the conclusion that can be drawn from the slope of values given in the table is:

3. Slope is undefined.

5. Graph is a vertical line.

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Question 2: Remember that there are 5 lead male roles and 4 lead female ones. If you must seat the male leads together and the female leads together, the three producers together and the director by himself, how many different ways can you seat 13 people around the circular table?

Answers

Answer: 103,680
----------------------------------------------

Explanation:

There are 13 people total. We can group up the male leads since they must sit together. Consider this group of five as one "person". Do the same for the female leads since they must sit together as well. The same applies to the producers.

Effectively we have these groups
* Male leads
* Female leads
* Producers
* Director

So we have 4 "people" in a sense sitting around the table giving (n-1)! = (4-1)! = 3! = 3*2*1 = 6 different ways to arrange these four groups.

Within the "male leads" group, there are 5! = 120 ways to permute the members.
Within the "female leads" group, there are 4! = 24 ways to permute the members.
Within the "producers" group, there are 3! = 6 ways to permute the members.
Within the "director" group, there's only one person so 1! = 1 way to arrange the members
So there are 120*24*6*1 = 17,280 different ways to arrange any one of the six permutations of the four groups.

Overall, there are 6*17,280 = 103,680 total permutations.

If f(x)=5x-2 and g(x)=2x+1, find(f-g)(x)

Answers

2x-3, just find the like terms in both of the equations and subtract them such as 5x and 2x and -2 and 1
5x-2x= 3x    -2-(+1)= -3

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?

Answers

Let "x" be the  longest side and "y" be each of remaining sides
If the triangle is аcute then:

y² + y² > x² 
2y² > 30²
2y² > 900
y² > 450
y > √450
y > 21.21 ← to the nearest hundredth

This means the length of each of the remaining sides is not less than 21.22 in  (to the nearest hundredth), so the smallest possible perimeter of the triangle =
30 + 21.22 + 21.22 = 72.44 in.


Find the first five terms of the sequence described by the following recursive formula: an = an – 1 + an – 2 where a1 = 1.2 and a2 = 2.3

1.2, , , ,


Find the first six terms of the sequence described by the following recursive formula:
an = an – 1 + an – 2
where a3 = -5 and a4 = 3


,
,
,
,
,

Answers

The first if a twisted version of a Fibonacci sequence :P

If a1=1.2 and a2=2.3 and a(n)=a(n-1)+a(n-2)

a3=3.5, a4=5.8, a5=9.3

So the first five terms are:  1.2, 2.3, 3.5, 5.8, 9.3

The second is another modified Fibonacci sequence...

If a3=-5 and a4=3 then:

3=-5+a2, a2=8

-5=8+a1, a1=-13

a5=-5+3=-2

a6=-2+3=1

So the first six terms are -13, 8, -5, 3, -2, 1
Final answer:

The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five or six terms, we substitute the given initial conditions into the formula and repeatedly apply it to find subsequent terms.

Explanation:

The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five terms, we begin with a1 = 1.2 and a2 = 2.3. Then we use the formula to find the next terms:

a3 = a2 + a1 = 2.3 + 1.2 = 3.5a4 = a3 + a2 = 3.5 + 2.3 = 5.8a5 = a4 + a3 = 5.8 + 3.5 = 9.3

So the first five terms of the sequence are 1.2, 2.3, 3.5, 5.8, and 9.3.

Similarly, to find the first six terms of the sequence with a3 = -5 and a4 = 3, we use the formula:

a5 = a4 + a3 = 3 + (-5) = -2a6 = a5 + a4 = -2 + 3 = 1

So the first six terms of this sequence are -5, 3, -2, 1, -1, and 0.

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The frequency table shows the results of a survey comparing weekly gasoline costs to the average number of miles a car can drive on a gallon of gasoline. Marcel converts the frequency table to a conditional relative frequency table by row. Which value should he use for Y? Round to the nearest hundredth. 0.19 0.45 0.82 0.90

Answers

When you round to the nearest tenth, and you only get a single decimal like .8 there is always a zero next to it but you can't see it. 

In this case if you divide 27 by 30 you will get 0.9. Round that and you will get 0.90  


Answer:

Its D on Ed2022

Step-by-step explanation:


How to write 0.000028 in scientific notation?

Answers

for Scientific notation you want to have the first non-zero digit before the decimal point. So count how many places you need to move the decimal point to the right and this will be your exponent.

2.8 x 10^-5

If you moved the decimal to the left the exponent would be positive.

Graph y = log8^x and its inverse

Answers

The answer is C...................

Answer:

Third one will be correct.

Step-by-step explanation:

Given  : y =[tex]log_{8}(x)[/tex].

To find : Graph  and its inverse.

Solution : We have given that

y =[tex]log_{8}(x)[/tex].

For x - intercept , y =0.

y = 0

0 =[tex]log_{8}(x)[/tex].

x = 1

(1,0)

Inverse of  y =[tex]log_{8}(x)[/tex].

Interchange the x and y.

x = [tex]log_{8}(y)[/tex].

Solving for y

y = [tex]8^{x}[/tex].

Then For x = 0

y =  [tex]8^{0}[/tex].

y = 1

For inverse ( 0 ,1)

Then we can see from given graphs Third one will be correct.

Therefore, Third one will be correct.

HELP ROUND 479065.389037 TO THE NEAREST THOUSAND

Answers

ROUND 479065.389037 TO THE NEAREST  THOUSAND = 479,000
479065.389037

if you want to round both sides to the nearest thousand, it will be

479000.389

if you just want a whole number it will be

479000

hope this helps :D

The formula is used to find the area of a parallelogram. if the base of a parallelogram is doubled and its height is doubled, how does this affect the area?

Answers

Formula for finding the area of a parallelogram: a equals bh
A equals two b × two h
A equals four bh

The area of a parallelogram would be quadrupled if the height and weight of it were doubled





(I had to write out certain words because my keyboard is not fully working)

Choose the correct simplification of the expression (7x − 3)(4x2 − 3x − 6).

28x3 − 33x2 − 33x − 18
28x3 + 33x2 − 33x + 18
28x3 − 51x2 − 33x + 18
28x3 − 33x2 − 33x + 18
a b c d

Answers

D. 28x^3-33x^2-33x+18 

Answer:

The expression (7x − 3) × (4x² − 3x − 6) is equivalent to  28x³ - 33x² - 33x + 18 .

Step-by-step explanation:

As given the expression in the question be as follow .

= (7x − 3) × (4x² − 3x − 6)

= 7x × (4x²- 3x - 6) - 3 × (4x² - 3x - 6)

Now open the bracket

= 7x × 4x² + 7x × -3x + 7x × -6 -3 × 4x² -3 × -3x - 3 × -6

= 28x³ -21x² -42x -12x² + 9x +18

= 28x³ -21x² - 12x² -42x + 9x + 18

= 28x³ - 33x² - 33x + 18

Therefore the expression (7x − 3) × (4x² − 3x − 6) is equivalent to  28x³ - 33x² - 33x + 18 .

Which one of the binomials is a factor of this trinomial?

x^2-13x+40

A. x-8
B. x+8
C. x-4
D. x+4

Answers

Factored form:
(x-8)(x-5)
Proof:
-8-5=-13
-8*-5=40

Final answer: A

True or False.
A binomial is also a polynomial.

Answers

True. A binomial is a polynomial that is the sum of two terms.

Write an equation for ab is congruent to segment bc

Answers

     ~
ab = bc

I believe...

Answer:

[tex]\overline {ab}\cong \overline {bc}[/tex]

Step-by-step explanation:

We are asked to write an equation for the given statement.

Statement:

Segment 'ab' is congruent to segment 'bc'.

We know that segment is written by a bar on name of segment as: [tex]\overline {ab}[/tex] and [tex]\overline {bc}[/tex].

Congruent sign is [tex]\cong[/tex]

Therefore, our required equation would be: [tex]\overline {ab}\cong \overline {bc}[/tex]

Find the sum of the following infinite geometric series, if it exists.
1.02 + 2.04 + 4.08 + 8.16 +…

20

Does not exist

22

24

Answers

We can see that for every increment, the number gets doubled positively. Since we are looking for the value when the repetition is made infinite, therefore the value at that point would also be infinite. Since infinite is imaginary, therefore the correct answer is:

Does not exist

A ball bearing is shaped like a sphere and has a diameter of 2.5 centimetres. What is the volume contained inside the ball bearing? Use 3.14 for pi. Round your answer to the nearest hundredth. 8.18 cubic centimeters 7.15 cubic centimeters 7.08 cubic centimeters 6.89 cubic centimeters

Answers

To solve:

The diameter is already given (2.5), and it can be divided by 2 to find the radius.

2.5/2=1.25

Plug 1.25 and Pi into the equation for a sphere to find the volume:

(4/3)(1.25^3)(3.14)=8.177

Answer: About 8.18 cm^3

Answer: 8.18 cubic centimeters

Step-by-step explanation:

Given : A ball bearing is shaped like a sphere .

The diameter of ball = 2.5 centimeters

Then , the radius of the ball =[tex]\dfrac{2.5}{2}=1.25\text{ cm}[/tex]

We know that the volume of a sphere is given by :-

[tex]\text{Volume}=\dfrac{4}{3}\pi r^3[/tex]

Then , the volume of ball is given by :-

[tex]\text{Volume}=\dfrac{4}{3}(3.14) (1.25)^3\\\\\Rightarrow\ \text{Volume}=8.17708333333\approx8.18\text{ cubic centimeters}[/tex]

Can someone help me!

Answers

If you have to simplify.

14 + 3i + 12 + 7i + 6 + 2i

Combine like terms.

12i + 32

32 + 12i
I got -12i-24 I really hope this hella i can explain more if you need me too

How is the graph of y = 8x^2 − 1 different from the graph of y = 8x^2?

Answers

Since a constant 1 is subtracted from the equation, the result is a graph shifted downward by one unit with respect to the original equation.

Answer:

1 up⊕⊕⊕⊕⊕⊕⊕⊕

Step-by-step explanation:

a restaurant offers 3 kinds of bread 4 kinds of meat and 3 kinds of cheese

Answers

3 x 4 x 3 = 12 x 3 = 36 different combinations

Answer:

36 combos

Step-by-step explanation:

Plz vote me for Brainilest

How many zeros are there at the end of 100!?

Answers

Well, at the END of 100, none excluding post decimal zeroes, including them there are infinite. If you meant how many zeroes inside 100, 2 then.

Final answer:

The number of zeros at the end of 100! is determined by counting the multiples of 5 in the factorization, including higher powers like 25. The result is a total of 24 zeros at the end of 100!.

Explanation:

To determine how many zeros are at the end of the factorial of 100 (100!), we need to know how many times the number 10 can be factored within that number. Since 10 is the product of 2 and 5, we should count the number of 2s and 5s in the prime factorization of 100!. The number of zeros at the end of 100! will equal the smaller of these two counts. However, because there are more 2s than 5s in the prime factorization, we only need to count the number of 5s as every 5 will have a corresponding 2 to form a 10.

For 100!, we count how many multiples of 5 there are within that range, including the multiples of 25 (since 25 includes an extra 5), and possibly higher powers of 5 if applicable. For example, 5 is counted once, 25 is counted twice (as 25 = 5×5), and so on.

Therefore, the number of zeros at the end of 100! equals the sum of the integer division of 100 by 5, plus the integer division of 100 by 25, and so on for any higher powers of 5. However, since 100 < 125, we do not need to consider any higher powers than 25.

We calculate:

100 ÷ 5 = 20,

100 ÷ 25 = 4.

Adding these together (20 + 4), we find that there are 24 zeros at the end of 100!.

Please Help!!!
which statement is true about the system x-3y = 5 and y = x - 7 ?

Answers

There is only one solution since they have different slopes.
Because they have different slopes (1/3 and 1), they will only have 1 solution

Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.

Answers

28.7251 =

 28 degrees

 then take the decimal and multiply by 60 to get the minutes

 so 0.7251 *60 = 43.506, use the whole number (43)

 so now you have 28 degrees, 43 minutes

 now take the remaining decimal ( 0.506) and multiply by 60

0.506*60= 30.36

 when you have a decimal left over for the seconds, keep that as is.

 so you now have 28 degrees, 43 minutes and 30.36 seconds

 use ' for minutes and " for seconds

28 degrees 43' 30.36"

rounded to the nearest second would be 28 degrees 43 minutes and 30 seconds

quotient of two more than a number and eight

Answers

Answer:  This would be expressed as:   " (x + 2) / 8 " .

You buy a commemorative coin for $110. Each year, t, the value V of the coin increases by 4%
Part a: Write a function that can be used to find the coin’s value after t years.
Part b: If the coin’s value continues to grow 4% per year, what will the approximate value be in 8 years? Round to two decimal places.

Answers

a. f(x)= 100*1.04^t
Exponential functions follow the form of y=ab^x, where a is the principal amount, b is the rate of growth or decay (1+0.04), and x is the time.

b. f(8)= 100*1.04^8
100*1.368569...
136.856

Final answer: $136.86

Answer:

$136.86

Step-by-step explanation:

A purse contains dimes and nickels. The total value of all the coins is, at most, $2.50, and there are at least three of each coin. Which of the following systems correctly shows the system that describes the possible number of nickels (n) and dimes (d) in the purse?

<= That means greater than or equal to or less than or equal to

1.n >= 3
d >= 3
0.05n+0.1d <= 2.50

2. n <= 3
d <= 3
0.05+0.1d <= 2.50

3. n <= 3
d<= 3
n + d >= 2.50

4. n>=3
d >= 3
n + d <=2.50

Answers

1 is the correct answer. d and n each have to be at least three, so the sign is correct. also, the sum of nickels and dimes is at most 2.50, so the sign is correct there, too.
The answer is 3. If it says "at most", that means that the total value of money has to be less than or equal to 2.50. Same thing with "at least." There would have to be more than 3 of each coin because 3 nickels and 3 dimes don't add up to 2.50. 

2. The value of a Plasma TV bought new for $3,700 decreases 25% each year. Identify the function for the value of the television. Does the function represent growth, or decay?
V(t) = 3700(1.25)t; growth
V(t) = 3700(0.75)t; decay
V(t) = 3700(1.25)t; decay
V(t) = 3700(0.75)t; growth

Answers

The value of a Plasma TV decreases by 25% each year So it's decay function which is
V(t) = 3700(1-r)^t
Where r is 25/100=0.25
V(t) = 3700(1-0.25)^t
V(t) = 3700(0.75)^t

So the answer is
V(t) = 3700(0.75)t; decay

Answer:      V(t) = 3700(0.75)t; decay

Step-by-step explanation:

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