In 4 minutes, 1/15 hour, the robbers have a (96 mi/h)·(1/15 h) = 6.4 mile head start.
The cops must travel 65 miles in the time the robbers travel 48.6 miles. Hence their speed must be 65/48.6 times that of the robbers, or about
... 65/48.6×96 mi/h ≈ 128.4 mi/h
_____
The chase will be over after (55 mi)/(96 mi/h) = 34 minutes 22.5 seconds from the time of the robbery. The cops will have to cover the 65 miles in less than 30:22.5 minutes, or about 0.50625 hours.
The cops' speed then is 65 miles/(0.50625 hour) ≈ 128.39506... mi/h
he is right do not look down here to be sure so go with his answer
Can someone tell me X and Y?? I'm really bad at math
See the attached picture:
What's the length? Please help. Thanks.
I am attaching an image with explanation. I added in red labels like
(STEP NUMBER) <value in inches>
The STEP helps you follow the sequence of deductions, starting from dividing 24 by 4 to get "(1) 6 in" and so on from there. Lmk if there's something unclear.
The length is 9"
Simplify 5 to the fifth power over 5 to the eighth power.
(5^5) / (5^8)
1 / 5^3
The answer is 1 / (5^3)
An Uber fare in San Diego is $3.50 for the first ½ mile and additional mileage charged at a rate of $0.30 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $15? Please show or explain your calculations.
Answer:
3.6 miles
Step-by-step explanation:
For a trip of x miles, there are x-0.5 miles of it that are "additional", which makes (x-0.5)/0.1 additional tenths.
Then the charges (in dollars) are ...
... 3.50 + 0.30(x -0.5)/0.1
Adding a tip of $2 and requiring the total be less than $15 gives ...
... 3.50 + 0.30(x -0.5) + 2.00 ≤ 15.00
... 5.50 + 3(x - 0.5) ≤ 15.00 . . . . simplify a bit
... 4.00 +3x ≤ 15.00 . . . . . . . . . . simplify more
... 3x ≤ 11.00 . . . . . . subtract 4.00
... x ≤ 3.667 . . . . . . divide by 3
Miles are measured in tenths. We cannot go 3.7 miles on $15, but we can go 3.6 miles.
please show work
1. y = 2 x + 3
y = 3
2. y = 2 x - 5
y = x
3. y = 4x + 10
y = -6
(1)
substitute y = 3 into the other equation
3 = 2x + 3 ( subtract 3 from both sides )
0 = 2x → x = 0
solution : (x, y) → (0, 3 )
(2)
substitute y = x into the other equation
x = 2x - 5 ( subtract x and add 5 to both sides )
5 = x then y = x so y = 5
solution : (x, y) → (5, 5 )
(3)
substitute y = - 6 into the other equation
- 6 = 4x + 10 ( subtract 10 from both sides )
- 16 = 4x ( divide both sides by 4 )
x = - 4
solution : (x, y) = (- 4, - 6 )
Evaluate 1/x^-2 for x = 7.
A. -49
B. 1/49
C. 49
If the federal reserve sells 80000 in a treasury bond to a bank at 7% what is the immediate effect in the money supply
"It is decreased by $80,000" is the one among the following choices given in the question that would be an immediate effect on the money supply. The correct option among all the options that are given in the question is the first option or option "A". I hope that this is the answer that has actually come to your desired help.
mark brainliest plssss
help pls with math pls
slope = [tex]\frac{4}{3}[/tex] and equation of line is
y = [tex]\frac{3}{2}[/tex] x + 3
calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = 2, 7 ) and (x₂, y₂ ) = (- 1, 3 )
m = [tex]\frac{3-7}{-1-2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
calculate m using the gradient formula
with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (0, 3 )
m = [tex]\frac{3+3}{0+4}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]
the line crosses the y-axis at (0, 3 ) hence c = 3
y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line
Micheal's mean score for five tests was 82. if four of those tests were 83,75,93, and 67, what was the fifth score on his test?
Let T represent the fifth test score. The average is the sum of scores divided by their number.
... 82 = (83 +75 +93 +67 +T)/5
... 410 = 318 +T . . . . . . . multiply by 5
... 92 = T . . . . . . . . . . . . subtract 318
The fifth score was 92.
_____
One of the ways I like to work problems like these is to add the differences from the mean. Those are ...
1, -7, 11, -15
so their sum is -10.
The final score must be 10 above the mean in order for this total to be zero. 10 above the mean is 92.
Math problem please help!
and if you could explain how you got your answer that would be very helpful thanks!
-110 = 13 + 3(4h -6) . . . . . . given
-110 = 13 + 12h -18 . . . . . . . eliminate parentheses using the distributive property
-110 = 12h -5 . . . . . . . . . . . . collect terms
-105 = 12h . . . . . . . . . . . . . . add 5 to both sides of the equation
-105/12 = h = -8.75
______
There are many ways you can solve this. Another is to undo the operations done to h. The variable h is ...
multiplied by 4has -6 added to the producthas the sum multiplied by 3has 13 added to the productWhen you undo these, you do it in reverse order:
-110 -13 = 3(4h -6) . . . . subtract 13
-123/3 = 4h -6 . . . . . . . divide by 3
-41 +6 = 4h . . . . . . . . . .add 6
-35/4 = h . . . . . . . . . . . divide by 4
h = -8.75
Use the continuous change function A(t) = Pe^rt to answer the question.
You invest $2,500 in an account that grows 5% each year. What will be your investment amount after 6 years?
A.
$2,699.72
B.
$3,374.65
C.
$15,769.07
D.
$13,272.96
B
A(6) = 2500 × [tex]e^{(0.05(6))}[/tex] = 2500 × [tex]e^{0.3}[/tex] = $3, 374.65
My investment amount will be 3374.65 rupees after 6 years.
So, option B is the correct answer.
What is Euler's number ?
A(t) [tex] = p {e}^{rt} [/tex] is known as Euler's number.
A is the desired amount per account/price/population/etc. equal
P is the principal or amount you start with.
e is a particular irrational number that is approximately 2.718. Just as pi is a concrete irrational number, so is e. The Euler number is often used as a title for e. Just as pi is an infinite non-repeating decimal, so is e. And just as many people use 3.14 to approximate pi, some use 2.718 for e. However, using the special π button on the calculator gives a more accurate answer than 3.14, and using the e button on the calculator is more accurate than using 2.718.
r is a rate written as a decimal, not a percentage.
t is time.
Let's say you have a population of bacteria that is constantly growing at a rate of 15% per hour. If there were 40 bacteria at the beginning of the experiment, how many bacteria will there be after 8 hours?
A is the amount after 8 hours, it's unknown, so I'll just use the variable A.
P initially has 40 bacteria.
e I use the “e” button on my calculator.
r is the hourly rate of 15%, I write it as 0.15
t is time, in this case 8 hours.
A = 40•e^(0.15•8)
A = 132.8, you need to round down because you haven't reached the next whole number of bacteria.
132 bacteria after 8 hours.
Here given,invest amount is $2,500 and rate of interest is 5% and total time period is 6 years.
Here we need to use continuous function A(t)[tex] = p {e}^{rt} [/tex]
Where P is principal,r rate of interest is interest and t is time.
Now,
[tex]p = 2500 \\ r = 5\% = 0.05\\ t = 6 \: years[/tex]
So,after 6 years the amount become ,A(6)
= [tex]2500 \times {e}^{0.05 \times 6} \\ = 2500 \times {e}^{0.3} [/tex]
[tex] = 2500 \times 1.34986 \\ = 3374.65[/tex]
Therefore,my investment amount will be 3374.65 rupees after 6 years.
The continuous change function related one more question:
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Here are the numbers of times 14 people ate out last month. 7, 6, 5, 4, 3, 6, 5, 6, 5, 4, 4, 4, 6, 5 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."
the mode of the data is 4.
mode is the number repeats in the data set the most.
Answer:
6782
Step-by-step explanation:
Really easy seventh grade math can I get this problem answered? Thanks!!
x = 15
since the figures are similar then the ratios of corresponding sides are equal
[tex]\frac{x}{6}[/tex] = [tex]\frac{20}{8}[/tex] ( cross- multiply )
8x = 6 × 20 = 120 ( divide both sides by 8 )
x = 15
Calculate the quotient of 54256/45
A survey of 80 students found that 24 students both play in a band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table.
Determine what each letter in the table should be to complete this two-way table.
b =
d =
f =
g =
h =
Answer:
b = 24
d = 10
f = 32
g = 34
h = 46
Step-by-step explanation:
From the given table we find that students who are in band = 48
So 24 + b = 48
b = 48 - 24
b = 24
Total students who do not play sports = h
And h = students in band + students not in band
h = b + 22
h = 24 + 22 = 46
h = 46
Total students who play sports and who do not play sports = 80
g + h = 80
g + 46 = 80
g = 80 - 46 = 34
g = 34
Total students who are not in band and not in band = 80
48 + f = 80
f = 80 - 48
f = 32
Students who are not in Band but either play sports or do not play sports = f
d + 22 = f
d + 22 = 32
d = 32 - 22 = 10
d = 10
Using the change of subject, the values of the alphabet b, d, f g, h calculated from the table are 24, 10, 32, 34, and 46 respectively.
To find b :
24 + b = total
24 + b = 48
b = 48 - 24
b = 24
To find h :
b + 22 = total
b + 22 = h
24 + 22 = 46
h = 46
To find g :
g + h = 80
g + 46 = 80
g = 80 - 46
g = 34
To find d :
24 + d = g
24 + d = 34
d = 34 - 24
d = 10
To find f :
d + 22 = f
10 + 22 = f
f = 32
Therefore, the values of b, d, f g, h are 24, 10, 32, 34, and 46 respectively.
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Approximate square root of 5, 13, 21 and 38
[tex]\sqrt{5}=2.23607, \sqrt{13}=3.60555, \sqrt{21}=4.58258, \sqrt{38}=6.16441[/tex]
These are all approximate decimal versions of the given numbers' square roots. If you need help rounding the decimals to a certain number of digits, let me know.
I hope this helps :)
Please Help Soon!
(74)(72)=
A) 76
B) 78
C) 146
D)148
I believe that the answer is C, I don't know if it is addition or multiplication, but if is is addition, it would be 146, C
help me with this preblem
h(6) = 8
reading vertically from x = 6 , we get , horizontally that y = 8
A bag of marbles contains 7 red, 5 blue, 4 green, and 2 yellow marbles. Jon selects a marble, replaces it, then selects another marble. What is the probability that Jon selects a red marble and then a yellow marble?
Answer: about 0.0432 or 4.32%
Step-by-step explanation:
Given : A bag of marbles contains 7 red, 5 blue, 4 green, and 2 yellow marbles.
Total marbles = 7+5+4+2=18
Let R : Event of getting first marble as red .
Y= Event of getting second marble as yellow.
Jon selects a marble, replaces it, then selects another marble.
⇒Both events are independent .
Probability of getting first marble as red = [tex]P(R)=\dfrac{\text{Number of red marbles}}{\text{Total marbles}}[/tex]
[tex]\\\\=\dfrac{7}{18}[/tex]
Probability of getting second marble as yellow = [tex]P(Y)=\dfrac{\text{Number of yellow marbles}}{\text{Total marbles}}[/tex]
[tex]\\\\=\dfrac{2}{18}[/tex]
Now, the probability that Jon selects a red marble and then a yellow marble :
[tex]P(R)\times P(Y)=\dfrac{7}{18}\times\dfrac{2}{18}\approx0.0432=4.32\%[/tex] [ ∵ Event R and Y are independent .]
Hence, the probability that Jon selects a red marble and then a yellow marble is about 0.0432 or 4.32%.
Subtract.
7 1/5 − (−3/5)
This would just be 7 1/5 + 3/5 since the negative sign gets distributed and makes (-3/5) into a positive number.
From there you have basic math and you get 7 4/5.
The subtraction of the given expression will be [tex]7\dfrac{4}{5}[/tex].
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The subtraction will be calculated as:-
[tex]=7\dfrac{1}{5}-(-\dfrac{3}{5})[/tex]
[tex]= \dfrac{36}{5}+\dfrac{3}{5}\\\\\\= \dfrac{39}{5}\\\\\\= 7\dfrac{4}{5}[/tex]
Therefore subtraction of the given expression will be [tex]7\dfrac{4}{5}[/tex].
To know more about Expression follow
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Find the missing number of each unit rate. 18/3= ?/1 and 12/2= ?/1
the answer is 6/1 and 6/1 simply divide and put the answer over one
find the area of the regular decagon if the apothem is 5 inches and a side is 3.2 inches. Round to the nearest whole number
When you are given the side length and apothem of a regular polygon and asked for area, you are expected to use the formula
... A = (1/2)Pa
where P is the perimeter of the polygon, "a" is the apothem, and A is the area.
The only additional information you need is that a decagon has 10 sides, so its perimeter is 10×3.2 inches = 32 inches.
The area is ...
... A = (1/2)(32 in)(5 in)
... A = 80 in²
_____
Sometimes the dimensions of a problem like this don't quite add up. The geometry of a regular polygon means that the apothem can be found from the side length and vice versa. In this case, the side length of 3.2 inches means the apothem is about 4.92 inches; or the apothem of 5 inches means the side length is about 3.25 inches. Either way, the area is slightly different from that computed using the given numbers.
This is why I say you're expected to use the above formula. (You're not expected to think about it too much.)
Enter the solution (x,y) to the system of equations shown. y=5 , y=2x+16
2x + 16 = 5
2x = -11
x = -5.5
y = 5
(-5.5,5)
Final answer:
The solution to the system of equations y=5 and y=2x+16 is found using substitution, yielding the solution (-5.5, 5).
Explanation:
To solve the system of equations y=5 and y=2x+16, we can use the method of substitution. Since the first equation directly gives us the value of y, we can substitute y = 5 into the second equation to find the corresponding value of x. Doing so, we have 5 = 2x + 16. To solve for x, we subtract 16 from both sides to get -11 = 2x, and then divide both sides by 2 to find that x = -5.5. Thus, the solution to the system is (-5.5, 5).
Celine observed that 80% of patrons at the local library liked reading sci-fi novels. If 35 patrons did not like reading sci-fi novels, how many patrons did enjoy sci-fi novels?
Part A: Write an equation in one variable that can be used to find the total number of patrons at the library? Define the variable used in the equation.
Part B: How many patrons enjoy reading sci-fi novels? Show your work.
Part A. Let the total number of patrons be x. Then the number of patrons that liked reading sci-fi novels is x-35. Now
x-35 is 80%
35 is 100%-80%=20%.
Mathematically, you can write a proportion:
[tex]\dfrac{x-35}{80}=\dfrac{35}{20},\\ \\x-35=\dfrac{35\cdot 80}{20},\\\\x-35=140,\\\\x=175.[/tex]
Part B. The total nuber of patrons is 175, 35 did not like the sci-fi novels, then 140 liked.
Final answer:
To find the total number of library patrons, set up an equation using the given information. Then, solve the equation to determine the number of patrons who enjoy reading sci-fi novels.
Explanation:
Part A: Let's represent the total number of patrons at the library as 'x'. Since Celine observed that 80% of the patrons liked reading sci-fi novels, we can say that 80% of 'x' patrons enjoy reading sci-fi novels.
Therefore, the equation to find the total number of patrons can be written as: 0.8x = x - 35.
Part B: To find the number of patrons who enjoy reading sci-fi novels, we can solve the equation from Part A. First, let's simplify the equation: 0.8x = x - 35.
Then, we'll subtract 'x' from both sides of the equation: 0.8x - x = -35.
Combining like terms, we have: -0.2x = -35.
Finally, we'll divide both sides of the equation by -0.2 to solve for 'x': x = (-35)/(-0.2).
Plugging in the values, we get: x = 175. Therefore, there are 175 patrons who enjoy reading sci-fi novels.
!! GEOMETRY HELP PLEASE !!
x = 10
[tex]\frac{x-2}{4}[/tex] = 2 ( multiply both sides by 4 to eliminate fraction )
x - 2 = 4 × 2 = 8 ( add 2 to both sides )
x - 2 + 2 = 8 + 2
x = 10
solve the inequality:-3x-4/7 >5
x < - [tex]\frac{13}{7}[/tex]
add [tex]\frac{4}{7}[/tex] to both sides
- 3x > [tex]\frac{4}{7}[/tex] + [tex]\frac{35}{7}[/tex]
- 3x > [tex]\frac{39}{7}[/tex] ( divide both sides by - 3 )
note that when we divide/ multiply by a negative quantity we must reverse the inequality symbol
x < - [tex]\frac{13}{7}[/tex]
I need a little help! Can someone check my work? It's a written response with linear systems.
Task 1: You are given a linear system of two equations in two unknowns. Before solving, describe how can you mentally check whether the system is independent and consistent? In which order would you do your check? Why?
My thoughts are that you'd check to see if they are different or not, because if they are equal then they won't be consistent or independent, they'll be inconsistent or dependent. I'm not sure which order I would check them though. I'm actually not sure if my logic is even correct :/
Answer:
I'd say you need to be more specific.
Step-by-step explanation:
"Different" doesn't tell you much.
Consider the equations ...
y = 2x + 14x - 2y = -2These equations are "different", but they are dependent.
_____
I'd mentally (or actually) put the equations in the same form and compare the coefficients of x and y. If they have different ratios, the system is independent and consistent.
If they have the same ratio, the system will not have a single solution. Whether there is no solution or an infinite number of solutions depends on the constant, which I would examine next.
The system above can be put in the form
2x -y = -14x -2y = -2In both cases, the ratio of the x coefficient to the y coefficient is 2/-1 = 4/-2 = -2. This means the lines are at least parallel, if not identical. The numbers in the second equation are all 2 times the numbers in the first equation, so the equations are dependent, and there are an infinite number of solutions. (Both describe the same line.)
If the second equation were 4x -2y = 1, then the two equations would be describing parallel lines, so they would be called inconsistent.
what is (2 x10^-3) x (4x10^4)?
top left choice is correct. 0.002 g is 10^(-3) time the approximate number of seed in the jar 4*10^4 (40000) = 10
Separate the equation like this:
(4x2) (10^-3 x 10^4)
Then multiply the first and add the powers:
Final Answer: 8 x 10^1
hope that helps :)
(f ∘ g)(x) so if g(4) = 8 and f(8) = 22, then (f ∘ g)(4) =
Final answer:
To evaluate (f ∘ g)(4), we substitute the value of g(4) into f(x) which gives us 22.
Explanation:
To find (f ∘ g)(4), we need to first evaluate g(4) and then plug that value into f(x). Given that g(4) = 8 and f(8) = 22, we can substitute 8 into f(x) as follows:
(f ∘ g)(4) = f(g(4))
(f ∘ g)(4) = f(8)
(f ∘ g)(4) = 22
What values of x and y satisfy `-(13)/(3)x −2y = 7` and `3x + (2)/(5) y = 5` simultaneously?
A. x = 3 and y = −10
B. x = −3 and y = −3
C. x = 1 and y = 5
D. x = 3 and y = 10
A graph quickly shows the solution to be ...
... A. x=3 and y=-10
_____
There are a couple of different strategies you can employ to eliminate possibilities.
1. Since the equations involve fractions, you can look only at answers that deal well with the fractions. That is, look for x-values that are multiples of 3 and y-values that are multiples of 5. Right away, this suggests you are not interested in choices B and C.
2. You can look at the general nature of the equations to see where the lines lie on a graph. It can be handy to know that intercept form is ...
... x/a + y/b = 1
where a and b are the x- and y-intercepts, respectively. That is, you can divide by the constant on the right (or just pay attention to its sign) to check the signs of the intercepts. For the first equation, the intercepts are both negative. Hence there cannot be any 1st-quadrant solutions. (That line never goes through the first quadrant—eliminating choices C and D.)
Likewise, the intercepts for the second equation are both positive, so it will never go through the third quadrant—eliminating choice B.