Answer: 17
Hello,
Step-by-step explanation:
n is divisible by 4.
n +1 is divisible by 5
n + 2 is divisible by 6
n <1000
[tex]\left\{\begin{array}{ccc}n&=&4*k_1\\n+1&=&5*k_2\\n+2&=&6*k_3\\\end{array}\right.\\\\4*k_1+1=5k_2\Longrightarrow\ k_2=\dfrac{4k_1+1}{5} \Longrightarrow\ k_1=1+5*t\ , k_2=1+4*t\\\\4*k_1+2=6k_3\Longrightarrow\ k_3=\dfrac{4(1+5t)+2}{6} \Longrightarrow\ k_3=1+\dfrac{10*t}{3} \\\\\Longrightarrow\ t=3z\\k_3=1+10z\\n+2=6(1+10z)\\n=4+60z\\\\1000 < 4+60z \Longrightarrow\ z \leq 16\\[/tex]
There are 17: from 4+0*60=4 to 4+16*60=964.
Answer:
17
Step-by-step explanation:
these positive integers are :
4, 64, 124, 184 ... , 964
964 = 4 + (n-1) (60)
964 = 4 + 60n -60
964 = 60n -56
60n = 1020
n = 1020/60
n = 17
so, the number of special integers smaller than 1000 are = 17
-2z² + 4z + 2z² = ?
Can someone please explain how to do this?
Answer:
4z
Step-by-step explanation:
-2z² + 4z + 2z²
Combine like terms
-2z^2 + 2z^2 +4z
0z^2 +4z
4z
[tex]\\ \sf\longmapsto -2z^2+4z+2z^2[/tex]
Combine like. variables[tex]\\ \sf\longmapsto -2z^2+2z^2+4z[/tex]
[tex]\\ \sf\longmapsto (-2+2)z^2+4z[/tex]
[tex]\\ \sf\longmapsto 0z^2+4z[/tex]
[tex]\\ \sf\longmapsto 4z[/tex]
if 2x+1 is a factor of 2x³ +x²-kx-1, find the value of k
Answer:
k=2
Step-by-step explanation:
Find the zeros of the factor
2x+1=0
x=-½
Plug x=-½ into the function and equate to 0
2(-½)³+(-½)²-k(-½)-1=0
2(-1/8)+¼+½k-1=0
-¼-1+¼+½k=0
-1+½k=0
½k=1
k=2
Step-by-step explanation:
2x+1=0
x=-1/2
Now p(x)= 2x^3 + x^2 -kx-1
subtitute value of x:
p(-1/2)= 2(-1/2)^3 + (-1/2)^2 -k(-1/2)-1
p(-1/2)=2*-1/8+1/4+k/2-1
p(-1/2)=-1/4+1/4+k/2-1
p(-1/2)=k/2-1
2x+1 is the factor of p(x) so
k/2-1=0
k/2=1
k= 2
Evaluate the expression if a =
- 2, b = -3, c = 2, x = 2.1, y = 3, and z = - 4.2.
4a - |3b + 2cl
Answer:
-13
Step-by-step explanation:
expression =4a-|3b+2c|
subtitute all values in the expression:
=4(-2) -|3(-3)+2(2)|
=-8-|-9+4|
=-8-|-5|
=-8-(5)
=-8-5
=-13
Note:if you need to ask any question please let me know.
The value of the expression from the variables is -13
How to evaluate the expression from the variablesFrom the question, we have the following parameters that can be used in our computation:
4a - |3b + 2cl
Also, we have
a = - 2, b = -3, c = 2, x = 2.1, y = 3, and z = - 4.2.
substitute the known values in the above equation, so, we have the following representation
4a - |3b + 2cl = 4 * -2 - |3 * -3 + 2 * 2|
Evaluate
4a - |3b + 2cl = -13
Hence, the expression from the variables is -13
Read more about expressions at
https://brainly.com/question/30492964
#SPJ3
Tap A takes 6 minutes to fill a tank and tap b takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill the tank if the pipe is in use when both taps are turned on
Answer: approximately 4.7368 minutes
This decimal value is the result of computing 90/19
=====================================================
Explanation:
Let's find the LCM of 6, 9 and 15. First, list out the prime factorization of each value.
6 = 2*39 = 3*315 = 3*5The unique prime factors are 2, 3, and 5. We have 2 show up at most once, 3 show up at most twice, and 5 show up at most once. The LCM is 2^1*3^2*5^1 = 2*9*5 = 18*5 = 90.
We'll use this LCM value to set up an example below.
---------------
Consider the tank to be 90 gallons. If we only use tap A, keep tap B closed, and don't open pipe C, then tap A fills the tank at a rate of 90/6 = 15 gallons per minute since it needs 6 minutes to completely fill the tank.
If we have tap B do all the work (keep tap A and pipe C closed), then the rate is 90/9 = 10 gallons per minute for this tap.
Keeping pipe C closed, the two taps A and B work together to have a combined rate of 15+10 = 25 gallons per minute.
Now we consider pipe C being opened. This drains the tank and can do so in 15 minutes (assume the taps A and B aren't open). If we're dealing with a full 90 gallon tank, then its rate is 90/15 = 6 gallons per minute.
The net rate is 25-6 = 19 gallons per minute. We can think of it as a tug of war where the taps A and B ultimately win out despite the fact that pipe C is draining the water. The two taps fill the tank faster than the pipe can drain the tank.
In other words, the tank ultimately gets filled up rather than drained out over the long run. That net speed is at 19 gallons per minute.
The amount of time needed is approximately 90/19 = 4.7368 minutes.
Side note: you can start with any size tank. It doesn't have to be 90 gallons. I picked on this value because it works cleanly with the original given numbers 6, 9 and 15.
Answer:
[tex]x=\frac{90}{19}[/tex] = 4.73 minutes
[tex]\frac{1}{6}x +\frac{1}{9}x - \frac{1}{15} x = 1[/tex]
[tex]\frac{135}{810}x +\frac{90 }{810}x - \frac{54}{810} x = 1[/tex]
[tex]\frac{171}{810}x = 1[/tex]
x = 4.73 minutes
Step-by-step explanation:
(s-4)8=8(s-4) does this demonstrate Distributive property?
Answer:
no...
8s -32 is the distributive property
Step-by-step explanation:
the sum of three consecutive even integers is less than or equal to 42. find the largest set of these numbers
Answer:
13, 14, 15
Step-by-step explanation:
13 + 14 + 15 = 42
Better explanation:
n + (n+1) + (n+2) = 42
42 - 2 - 1 = 39
n + n + n = 39
3n = 39 divide by 3 to isolate n
n = 13
So it starts with 13 and goes up from there.
How do you write a number less than one and one-third in an algebraic expression?
Step-by-step explanation:
x<1
x<(1/3)
yes this is the answer
x^2-3x+8 is x=4 will choose brainly
Answer:
12Step-by-step explanation:
[tex] {x}^{2} - 3x + 8[/tex]
(Putting value of x = 4)
[tex] = {4}^{2} - 3 \times 4 + 8[/tex]
= 16 - 12 + 8
= 24 - 12
= 12 (Ans)
Answer:
It is 12
Step-by-step explanation:
[tex]f(x) = {x}^{2} - 3x + 8[/tex]
When x is 4, substitute x as 4:
[tex]f(4) = {(4)}^{2} - 3(4) + 8 \\f(4) = 16 - 12 + 8 \\ f(4)= 12[/tex]
Sports Co buys soccer balls from their supplier at $20 per bat. They sell these for $40.
What percentage mark-up have they applied to soccer balls?
Answer:
buy for $20 and sell for $40
is 100% mark-up
Step-by-step explanation:
A new car sales person, sold an average of $46,975 per day for the first two days she worked. The next one days she worked, she sold an average of $45,765. How much did she sell on average per day over the entire time she worked?
Answer:
$46,571.67
Step-by-step explanation:
if your description is right and complete, she sold cars on the first 2 days as average for $46975.
and on the third day for $45765
to calculate the total average we need to know the total amount of sales and then divide it by the observation period length (3 days).
how do we get the total sales ?
we know the average of the first 2 days. we don't need to find the exact value for every day, but we know the exact value for these first 2 days : 2×46975 = $93950
as the average of these 2 days = (day1 + day2)/2
46975 = (day1 + day2)/2
day1 + day2 = 2×46975 = 93950
it is not important what two (day) numbers created 93950. we know that this was the total sum of the first two days. and that is enough.
so, we have in total
$93950 on the first 2 days
$45765 in the third day
-------------
$139715 for all 3 days
the average per day is then
139715 / 3 = $46,571.67
In a shooting match , the probability that Sheila hits the target is 3/7 for every shoot . If she takes 21 shots , how many times would you expect Sheila to hit the target?
Answer:
9
Step-by-step explanation:
Probability is 3/7
that 7 represent all shots and 3 represents successful ones
so,
sarah shots 21 times that means 9 of them would hit the target.
A butterfly can fly mile in a minute. How long would it take the butterfly to
fly ſ mile?
O A + = 10 minute
O B. = minute
O c. x = minute
OD3 = minutes
SUBMIT
A company that makes barber scissors has found that the sales volume for barber scissors is directly proportional to the size of the sales force and inversely proportional to the price of the scissors. If 19440 pairs were sold in 2003, when there were 54 salespeople and the price was $20 a pair, what is the sales forecast for the upcoming year with 50 salespeople and a price of $18 a pair?
Answer:
20,000 pairs of barber scissors.
Step-by-step explanation:
The sales volume V for barber scissors is directly proportional to the size S of the sales force and inversely proportional to the price P of the scissors.
In other words, we can write that:
[tex]\displaystyle V = \frac{kS}{P}[/tex]
Where k is the constant of proportionality.
19,440 pairs were sold in 2013, when there was 54 salespeople and the price was $20 a pair. Hence, V = 19440 when S = 54 and P = 20. Substitute and determine the value of k:
[tex]\displaystyle \begin{aligned} (19440) &= \frac{k(54)}{(20)} \\ \\ 19440 &= \frac{27}{10}k \\ \\ k &=\frac{10}{27}(19440) = 7200 \end{aligned}[/tex]
Hence, our equation is:
[tex]\displaystyle V = \frac{7200S}{P}[/tex]
We want to determine the sales forecast with 50 salespeople and a price of $18 a pair. Hence, S = 50 and P = 18:
[tex]\displaystyle \begin{aligned} V&= \frac{7200(50)}{(18)} \\ \\ &= 20000\end{aligned}[/tex]
In conclusion, 20,000 pairs of barber scissors can be expected to be sold.
For the equation: – 36 – 4r = -2(-6 + 6r), what is the value of r?
Answer:
r = 6
Step-by-step explanation:
– 36 – 4r = -2(-6 + 6r)
+36 +36
----------------------------------
-4r = -12r + 48
+12r +12r
----------------------------------
8r = 48
/8 /8
----------------------------------
r = 6
Answer:
r = 6
Step-by-step explanation:
– 36 – 4r = -2(-6 + 6r)
-36 - 4r = 12 - 12r
-48 - 4r = -12r
-48 = -8r
r = 6
1 7/8y = 4 1/2
Seriously, math is going to kill me! Lol!
Answer:
y = 2 2/5
Step-by-step explanation:
1 7/8y = 4 1/2
Change to improper fractions
1 7/8 = (8*1+7)/8 = 15/8
4 1/2 = (2*4+1)/2 = 9/2
15/8 y = 9/2
Multiply each side by 8/15
8/15 * 15/8y = 9/2 * 8/15
y = 9/15 * 8/2
y = 3/5 *4
y = 12/5
Changing back to a mixed number
y = 2 2/5
Write an equation to tell this
story: We scored 9, 3, and 7
points. We need N points to
reach 35.
[tex]\frac{x+19}{-2} = 5[/tex]
Answer this question <3
Answer:
[tex] \frac{x + 19}{ - 2} = 5 \\ x + 19 = 5 \times ( - 2) \\ x + 19 = - 10 \\ x = - 19 - 10 \\ \boxed{x = - 29 }[/tex]
The value of x is -29.Guided Practice
The value of a car depreciates every year. Suppose you buy a new car for $17,000, and each year its value is only 90% of what it was the previous year. Write an equation that represents the value of the car, y, after x years.
A.
y=0.90 · 17,000xy equals 0.90 times 17,000 superscript x baseline
B.
y=17,000 · 0.90xy equals 17,000 times 0.90 superscript x baseline
C.
y=17,000 · 0.10xy equals 17,000 times 0.10 superscript x baseline
B.
y=17,000 · 0.90xy equals 17,000 times 0.90 superscript x baseline
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Since the car’s initial value was $17,000, a = 17,000. Since the car retains 90% of its value each year, b = 0.90.
Which equation represents a line which is parallel to the line y = -x + 5?
2x – 3y = 21
o
3x + 2y = -2
Submit Answer
2y - 3x = 2
2x + 3y = –21
PLS HELP ASAP
Answer:
2x + 3y = -21
Step-by-step explanation:
Parallel lines have same slope.
2x + 3y = -21
3y = - 2x - 21
y = [tex]y = \dfrac{-2}{3}x-\dfrac{21}{3}\\\\y=\dfrac{-2}{3}x-7[/tex]
Please help
Which of the following is in the solution set of the inequality -3 > -3t+ 6?
A. -1/3
B. 1/3
1مرايا C. 4
D. -4
Answer: C) 4
==========================================================
Explanation:
Let's isolate t
-3 > -3t + 6
-3+3t > 6
3t > 6+3
3t > 9
t > 9/3
t > 3
This means any value can replace t such that it's larger than 3.
Something like t = 1/3 = 0.33 won't work since it's not larger than 3.
But something like t = 4 would work because it makes t > 3 true.
That's why choice C is the final answer.
Find the inverse of each of the given functions. f(x) = 4x − 12 f−1(x) = x +
Find the inverse of each of the given functions. f(x) = 4x − 12 f−1(x) = x +
first one is 1/4
second one is 3
Answer:
first box is 1/4
second box is 3
for the next question on the page ( h(x) = (2x-4)/3 ) the answer is C (h^-1(x) = (3x+4)/2 )
Step-by-step explanation:
round off 19340 to 1 s f
Answer:
20000
Step-by-step explanation:
This is because when you round to the signifigant figure, you basically look at any digits at the start of the number, which isn't zero. In this case it would be in the ten thousand 19340. So you round 19340 to the nearest 10 thounsand, which, would be 20000
can someone help me please?
Answer:
[tex]2x - x + 25 - x = x \: terms \: togther \\ 2x - x - x + 25 \\ = 0x + 25 \\ = 25 \\ thank \: you[/tex]
Answer:
2×12-12+25-12
24-12+13
24+13-12
37-12
25
Find the area of this circle please.Use 3 for pi…Thank you
Answer:
27 ft^2
Step-by-step explanation:
r = 3 ft (that's the radius)
and pi = 3
A = pi r^2
or
3 * r^2
plug in r = 3
so 3 * 3^2 = 3 * 9 = 27 ft^2
(note: 3^2 = 3 * 3. Squaring means we multiply the number by itself)
yeah i suck at math
4. After tennis training, Andy collects twice as many balls as Roger and five more than Maria. If Roger collected r balls, in terms of r, how many balls did:
a) Andy collect?
b) Maria collect?
c) The total number of balls collected?
Answer:
It's b I'm pretty sure.
Step-by-step explanation:
[tex]2 \times 3 + 45 \div 2 - 6 + 9[/tex]
Answer according to BODMAS
Answer: 31.5
Step-by-step explanation:
Answer: 31.5
Concept:
When encounter questions that ask for operation on algebraic expressions, using BODMAS or PEMDAS method would be easier. Since this question asked for using BODMAS, then it is:
BracketOrderDivisionMultiplicationAdditionSubtractionSolve:
Given
2 × 3 + 45 ÷ 2 - 6 + 9
Simplify by division
=2 × 3 + 22.5 - 6 + 9
Simplify by multiplication
=6 + 22.5 - 6 + 9
Simplify by addition
=28.5 + 9 - 6
=37.5 - 6
Simplify by subtraction
=31.5
Hope this helps!! :)
Please let me know if you have any questions
In 2015, 120000 people voted. The number of viewers who voted in 2015 was 20% more than those in 2014. Calculate the numbers of viewers who voted in 2014
Answer:
Given;
120,000 people voted in 2015.
In 2015, 20% more people voted than 2014.
Therefore:
How many more people voted in 2015 = 20% of 120,000
= 24,000
Total number of people voted in 2014 = 120,000 - 24,000
= 96,000
Ans) 96,000 people voted in 2014.
What is the value of the expression 2 + 3/4 (1 1/2 + 3.8)
Answer:
5.975
Step-by-step explanation:
what happened to the speed of earth rotation from equator towards the poles answer in short
Answer:
Specifically, Earth rotates faster at the Equator than it does at the poles. Earth is wider at the Equator, so to make a rotation in one 24-hour period, equatorial regions race nearly 1,600 kilometers (1,000 miles) per hour. Near the poles, Earth rotates at a sluggish 0.00008 kilometers (0.00005 miles) per hour.
Step-by-step explanation:
I hope this will help you :-)