Answer: 40 mph
Step-by-step explanation: let s = speed in traffic
(s+17) = out of traffic
:
Write a time equation; time = dist/speed
traffic time + normal speed time = 4 hrs
46%2Fs + 80%2F%28%28s%2B17%29%29 = 4
multiply by s(s+17) to cancel the denominators
46(s+17) + 80s = 4s(s+17)
46s + 782 + 80s = 4s^2 + 68s
126s + 782 = 4s^2 + 68s
Arrange as a quadratic equation on the right
2s^2 - 29s - 391 = 0
Use the quadratic formula a=2; b=-29; c=-391
I got a positive solution of
s = 23 mph in traffic
:
:
:
Check this by finding the actual times. Normal speed: 23 + 17 = 40 mph
46/23 = 2 hrs in traffic
80/40 = 2 hrs at normal speed
----------------------------
total time 4 hrs
0 = 4s^2 + 68s - 126s - 782
4s^2 - 58s - 782 = 0
simplify, divide by 2
so the answer is 40mph
The sum of matrices A and B is C.
Answer:
Step-by-step explanation: -3
Mr. Oates has 3/4 pound of oatmeal he uses 2/3 of the oatmeal to big muffins how much oatmeal does Mr. Courts have left
Answer:
1/12
Step-by-step explanation:
3/4-2/3 = 9/12-8/12 = 1/12
which sentence is true
Simplify
4a + 5b – 3b + a
2 marks)
Answer:
5a+2b
Step-by-step explanation:
4a + 5b – 3b + a
Combine like terms
4a +a + 5b-3b
5a+2b
Is 3b-8=13;-7 a solution?
Answer:
See below
Step-by-step explanation:
[tex]3b-8=13 \implies 3b=21 \implies \boxed{b=7}[/tex]
[tex]-7 \text{ is not a solution for the equation}[/tex]
A study was conducted to analyze the amount of time spent sitting at a desk for employees over a work day. The time spent sitting was recorded for a large sample of employees and found to follow a bell-shaped distribution with a mean of about 280 minutes. The smallest amount of time was 100 minutes and the largest amount of time was 460 minutes. Unfortunately, the standard deviation was not reported in the summary. Which of the following represent the most appropriate value for that standard deviation?
A. Options 60 minutes
B. 90 minutes
C. 180 minutes
D. 360 minutes
The value of the the expression:
50 times the sum of 64 and 36?
3,236
2,354
4,104
5,000
Answer:
5000
Step-by-step explanation:
Let's start by evaluating what we are given. 50 times the sum of 64 and 36. Ok, so 50 times which is the way to write x (multiply) and the sum of 64 and 36 is another way to write 64 + 36.
Lets put this together now!
50 x ( 64 + 36 ) = 50 x ( 100 )
= 5000
Which of the following expression(s) are equivalent to 0.16? Select all that apply.
A)
16
100
B)
9
50
OD) 16%
.
Answer:a
Step-by-step explanation:
Can someone tell me why the answer for this absolute value equation is all real numbers?
Answer:
yo its not that hard it just means that it can be any number
what is 2 times 80+ 185-40+699-59
Answer:
945
Step-by-step explanation:
Answer:
1730 (2 times the whole expression) or 945 (2 times the addend of 80) [what is implied when 80+ 185-40+699-59 is not in parenthesis]
Step-by-step explanation:
2 times (80 + 185 - 40 + 699 - 59) →
2 (80 + 185 - 40 + 699 - 59)
2 ((((80 + 185) - 40) + 699) - 59)
2 ((265 - 40) + 699) - 59)
2 (225 + 699) - 59)
2 (924 - 59)
2 (865)
1730
_____________________
2 times 80 + 185 - 40 + 699 - 59 →
2(80) + 185 - 40 + 699 - 59
(((160 + 185) - 40) + 699) - 59
((345 - 40) + 699) - 59
(305 + 699) - 59
1004 - 59
945
what is 15 700 000 rounded to the nearest hundred thousandth
Which line is perpendicular to a line that has a slope of -1/3?
Answer:
Any line with slope -1/(-1/3)=3.
Step-by-step explanation:
If a line l has slope m, any line perpendicular to l will have slope equal to -1/m.
Answer: line EF
Step-by-step explanation:
Did it in edg
29023789236+8974937077834758371=
The probability that the parking lot of a mall is full on a holiday is 0.19. The probability that it is a holiday is 0.29. What is the probability that the parking lot is full given that today is a holiday?
66%
15%
5.51%
Answer:
66%
Step-by-step explanation:
Use conditional probability.
P(full | holiday) = P(full AND holiday) / P(holiday)
P(full | holiday) = 0.19 / 0.29
P(full | holiday) ≈ 0.66
Answer:
I'm sure the answer is 15%
Step-by-step explanation:
14 increased by 14 5/7
A square field has 3,844 sq. meters of land. What is the width of the field?
Answer:
The side length is 62 meters
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
3844 m^2 = s^2
Take the square root of each side
sqrt( 3844 m^2) = sqrt(s^2)
62 m= s
The side length is 62 meters
Use the rules of significant figures to simplify the following expression:
25.5 x 10.09
Answer here
5 times a number is 6 less than the square of that number
Answer:
5x = x^2 - 6
Step-by-step explanation:
a number can be represented by x,
5 times a number can be represented as the product of 5 and x, 6 less than the square of that number tells us that this is equal to a number squared minus 6. is tells us that these two expressions are equal.
If you want a working number, just solve by completing the square once this is in standard form. This is then converted to vertex form.
x^2-5x-6 = (x-5/2)^2-49/4 = (x^2-5x+25/4) -49/4 = x^2-5x-6.
(x-5/2)^2-49/4=0
(x-5/2)^2=49/4
(x-5/2) = ±√49/4
(x-5/2) = ±7/2
x=5/2±7/2
x=(5±7)/2
x=12/2,-2/2
x=6,-1
Thus, the number can either be 6 or -1.
During one waiter's shift, he delivered 13 appetizers, 17 entrees, and 10 desserts. What percentage of the dishes he delivered were:
A. desserts?
B. appetizers?
C. entrees?
Answer:
deserts are 32.5%
appetizers are 42.5%
deserts are 25%
Step-by-step explanation:
let me know if i helped
13. In a recent Barangay election, Mr. Reyes won as Barangay Chairman with 3,074
votes. If there are 5,800 voters in the barangay, what percentage voted for Mr.
Reyes?
A) 12%
B) 47%
C) 53%
D) 88%
Answer:
53%
Step-by-step explanation:
Total voters = 5,800
5,800= 100%
3,074=X
X=3,074*100/5,800= 53%
PLZ HELP FAST looks easy
Answer:
45
90
135
180
225
Step-by-step explanation:
It represents a function because each element in the domain is matched with exactly one element in the range.
Amanda is 25 years old. In 5 years time she will be twice as old as Simone.how old is Simone ?
Answer:
15 years old.
Step-by-step explanation:
Amanda is currently 25 years old.
In 5 years of time, she will be twice as old as Simone.
25+5=30.
30/2=15.
Thus, Simone is 15 years old.
Which of the following statements is true for all sets A,B and C? Give a proof
or a counter example.
(a) A ⊆ ((A∩B)∪C).
(b) (A∪B)∩C = (A∩B)∪C.
(c) (A\B)∩C = (A∩C) \ (B∩C).
Answer:
(a) and (b) are not true in general. Refer to the explanations below for counterexamples.
It can be shown that (c) is indeed true.
Step-by-step explanation:
This explanation will use a lot of empty sets [tex]\phi[/tex] just to keep the counterexamples simple.
(a)Note that [tex]A \cap B[/tex] can well be smaller than [tex]A[/tex]. It should be alarming that the question is claiming [tex]A\![/tex] to be a subset of something that can be smaller than [tex]\! A[/tex]. Here's a counterexample that dramatize this observation:
Consider:
[tex]A = \left\lbrace 1 \right\rbrace[/tex].[tex]B = \phi[/tex] (an empty set, same as [tex]\left\lbrace \right\rbrace[/tex].)[tex]C = \phi[/tex] (another empty set.)The intersection of an empty set with another set should still be an empty set:
[tex]A \cap B = \left\lbrace 1\right\rbrace \cap \left\lbrace\right\rbrace = \left\lbrace\right\rbrace[/tex].
The union of two empty sets should also be an empty set:
[tex]((A \cap B) \cup C) = \left\lbrace\right\rbrace \cup \left\lbrace\right\rbrace = \left\lbrace\right\rbrace[/tex].
Apparently, the one-element set [tex]A = \left\lbrace 1 \right\rbrace[/tex] isn't a subset of an empty set. [tex]A \not \subseteq ((A\cap B) \cup C)[/tex]. Contradiction.
(b)Consider the same counterexample
[tex]A = \left\lbrace 1 \right\rbrace[/tex].[tex]B = \phi[/tex] (an empty set, same as [tex]\left\lbrace \right\rbrace[/tex].)[tex]C = \left\lbrace 2 \right\rbrace[/tex] (another empty set.)Left-hand side:
[tex](A \cup B) \cap C = \left(\left\lbrace 1 \right\rbrace \cup \left\lbrace \right\rbrace\right) \cap \left\lbrace 2 \right\rbrace\right = \left\lbrace 1 \right\rbrace \cap \left\lbrace 2 \right\rbrace = \left\lbrace \right\rbrace[/tex].
Right-hand side:
[tex](A \cap B) \cup C = \left(\left\lbrace 1 \right\rbrace \cap \left\lbrace \right\rbrace\right) \cup \left\lbrace 2 \right\rbrace\right = \left\lbrace \right\rbrace \cup \left\lbrace 2 \right\rbrace = \left\lbrace 2 \right\rbrace[/tex].
Apparently, the empty set on the left-hand side [tex]\left\lbrace \right\rbrace[/tex] is not the same as the [tex]\left\lbrace 2 \right\rbrace[/tex] on the right-hand side. Contradiction.
(c)Part one: show that left-hand side is a subset of the right-hand side.
Let [tex]x[/tex] be a member of the set on the left-hand side.
[tex]x \in (A \backslash B) \cap C[/tex].
[tex]\implies x\in A \backslash B[/tex] and [tex]x \in C[/tex] (the right arrow here reads "implies".)
[tex]\implies x \in A[/tex] and [tex]x \not\in B[/tex] and [tex]x \in C[/tex].
[tex]\implies (x \in A\cap C)[/tex] and [tex]x \not\in B \cap C[/tex].
[tex]\implies x \in (A \cap C) \backslash (B \cap C)[/tex].
Note that [tex]x \in (A \backslash B) \cap C[/tex] (set on the left-hand side) implies that [tex]x \in (A \cap C) \backslash (B \cap C)[/tex] (set on the right-hand side.)
Therefore:
[tex](A \backslash B) \cap C \subseteq (A \cap C) \backslash (B \cap C)[/tex].
Part two: show that the right-hand side is a subset of the left-hand side. This part is slightly more involved than the first part.
Let [tex]x[/tex] be a member of the set on the right-hand side.
[tex]x \in (A \cap C) \backslash (B \cap C)[/tex].
[tex]\implies x \in A \cap C[/tex] and [tex]x \not\in B \cap C[/tex].
Note that [tex]x \not\in B \cap C[/tex] is equivalent to:
[tex]x \not \in B[/tex], OR[tex]x \not\in C[/tex], ORboth [tex]x \not\in B[/tex] AND [tex]x \not \in C[/tex].However, [tex]x \in A \cap C[/tex] implies that [tex]x \in A[/tex] AND [tex]x \in C[/tex].
The fact that [tex]x \in C[/tex] means that the only possibility that [tex]x \not\in B \cap C[/tex] is [tex]x \not \in B[/tex].
To reiterate: if [tex]x \not \in C[/tex], then the assumption that [tex]x \in A \cap C[/tex] would not be true any more. Therefore, the only possibility is that [tex]x \not \in B[/tex].
Therefore, [tex]x \in (A \backslash B)\cap C[/tex].
In other words, [tex]x \in (A \cap C) \backslash (B \cap C) \implies x \in (A \backslash B)\cap C[/tex].
[tex](A \cap C) \backslash (B \cap C) \subseteq (A \backslash B)\cap C[/tex].
Combine these two parts to obtain: [tex](A \backslash B) \cap C = (A \cap C) \backslash (B \cap C)[/tex].
Your $960 got an interest rate of 8.7% which was
compounded monthly for 3 years. What is your $960
worth after 3 years?
Answer:
D
Step-by-step explanation:
Stella has 215 coins and 89 of them are nickels. Two-thirds of the remaining coins are pennies. How many pennies does Stella have?
A. 38
B. 42
C. 66
D. 84
Answer: 84
Step-by-step explanation:
215 - 89 = 126
126 divided by 3 = 42
42 x 2 = 84
( this was how my teacher taught me to do these kind of problems)
Hope this helps! <3
Answer:
The answer is 84
Step-by-step explanation:
got it right on edge :D
how many many bricks can bob the dog use to make a wood chuck
Answer: none
Step-by-step explanation:
What are these questions, I want brainless btw
Answer:
Cats
Step-by-step explanation:
:)
if the mean of a negatively skewed distribution is 40 which of these values could be the median of the distribution
a.35
b.50
c.40
d.45
Answer:
c.40
plz mark brainliest if helpful
6. You earn 8% commission on sales. What is the commission if the sales
were as follows. 4 items at $1200,7 items at $650; 7 items at $600, and 6
items at $450? (no commas)*
Answer:
The total commission is=$1300
Step-by-step explanation:
The commission rate is a fixed number that applies to all the sales made by a salesperson. In our problem, the fixed commission rate is 8%, and the sales were as follows:
4 items at $1200 for a total of $4800. The commission is:
8% of 4800 = 0.08*4800 = $384
7 items at $650 for a total of $4550. The commission is:
8% of 4550 = 0.08*4550 = $364
7 items at $600 for a total of $4200. The commission is:
8% of 4200 = 0.08*4200 = $336
6 items at $450 for a total of $2700. The commission is:
8% of 2700 = 0.08*2700 = $216
The total commission is: $384+$364+$336+$216=$1300
The total commission is=$1300
A company earns $175 a week for 10 weeks. It then has a loss of $87 a week for 15 weeks. At the end of the 25 weeks what is the company's balance?
Judy’s Cake Shop makes fresh cakes to customer orders. After receiving the order by Judy’s assistant, which takes 2 minutes, Judy then takes 8 minutes to mix the ingredients for the cake and loads a cake pan for baking. Then the cake is put into the oven for 30 minutes. The oven can hold three cakes at one time. When the cake is taken out of the oven, it is cooled for 1 hour. The assistant then takes 2 minutes to pack the cake for pickup and bills the customer, which takes 3 minutes. a. What is the capacity of the process, and what is the bottleneck? b. What is the throughput time for a typical cake? c. If on average five orders are taken per hour, how many cakes are there in the process (on average)?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Time taken to receive order = 2 minutes
Ingredient mixing and cake loading = 8 minutes
Baking time = 30 minutes
Number of cakes oven can hold at a time = 3
Cooling time = 1 hour = 60 minutes
Cake packing = 2 minutes
Billing customer = 3 minutes
a. What is the capacity of the process, and what is the bottleneck?
The capacity of the process:
Within an hour : two bakings can be done =(30 minutes * 2) = 60 minutes
Also oven can hold 3 cakes, so, 3 cakes can be baked at a time.
Hence, 3 cakes in 30 minutes ;
6 cakes in an hour;
Hence, capacity of the process is 6cakes per hour.
The bottleneck is the oven, because if the number of ovens were to be increased, the process capacity will increase, similarly, if one of the oven gets faulty, then the process capacity reduces further.
b. What is the throughput time for a typical cake?
The throughput time, is the summation of all the time taken to fully complete an order :
Receipt of order + mixing + baking + cooling + packing + billing
2 + 8 + 30 + 60 + 2 + 3 = 105 minutes
c. If on average five orders are taken per hour, how many cakes are there in the process (on average)?
(Throughput time / 60) * average number of order
(105/60) * 5
= 1.75 * 5
= 8.75