Answer:
Train P : [tex]t_{P} =\frac{330}{55}=6\ \text{hours}[/tex]
Train Q : [tex]t_{Q} =\frac{330}{55}+\frac{1}{2}=6\ \text{hours}\ 30\ \text{minutes}[/tex]
Step-by-step explanation:
The formula to compute the distance traveled by a train is:
[tex]d=s\times t[/tex]
Here,
d = distance traveled
s = speed of the train
t = time taken
From the provided information:
Train P :
d = 330 km
s = x km/h
Then time taken is:
[tex]t=\frac{d}{s}=\frac{330}{x}[/tex]
Train Q :
d = 330 km
s = (x - 5) km/h
[tex]t=\frac{330}{x}+\frac{1}{2}[/tex]
Both the trains traveled the same distance.
[tex]x\times \frac{330}{x}=(x-5)\times [\frac{330}{x}+\frac{1}{2}]\\\\330=\frac{330(x-5)}{x}+\frac{x-5}{2}\\\\330\times 2x=[660(x-5)+x(x-5)]\\\\660x=660x-3300+x^{2}-5x\\\\x^{2}-5x-3300=0\\\\x^{2}+60x-55x-3300=0\\\\x(x+60)-55(x+60)=0\\\\(x-55)(x+60)=0\\\\x=55[/tex]
Compute the time taken by the two trains as follows:
Train P : [tex]t_{P} =\frac{330}{55}=6\ \text{hours}[/tex]
Train Q : [tex]t_{Q} =\frac{330}{55}+\frac{1}{2}=6\ \text{hours}\ 30\ \text{minutes}[/tex]
Which table can be created using the equation below? –2 + 4x = y
Answer:
A
Step-by-step explanation:
x y
-5 -22
0 -2
3 10
Question (8 points)
Kirsten went to Champs and brought a pair of KD's for $99.99 and a shirt to match for $17.99. If Kirsten gave the
cashier $120, how much change will she get back
700,000,000+10,000,000+1,000,000+100,000+40,000+2,000+200+7 write the standard form above
Answer:
712,402,207
Step-by-step explanation:
;)
Answer: 711,142,207
Step-by-step explanation:
please help me with this question
Answer:
422 cm²
Step-by-step explanation:
Surface area of the composite figure = (surface area of the upper cuboid + surface area of lower cuboid) - 2(base area of the lower cuboid)
Surface area of composite figure = [tex] (2(lw + lh + hw)) + (2(lw + lh + hw)) - 2(l*w) [/tex]
Upper cuboid has the following dimensions:
[tex] l = 4, w = 3, h = 8 [/tex]
Lower cuboid has the following dimensions:
[tex] l = 10, w = 7, h = 5 [/tex]
Plug these values into the formula
Surface area of composite figure
[tex] = (2(4*3 + 4*8 + 8*3)) + (2(10*7 + 10*5 + 5*7)) - 2(4*3) [/tex]
[tex] = (2(12 + 32 + 24)) + (2(70 + 50 + 35)) - 2(12) [/tex]
[tex] = (136 + 310) - 24 [/tex]
[tex] = 446 - 24 = 422 [/tex]
Surface area of composite figure = 422 cm²
How is inductive reasoning used to recognize mathematical relationships?
Answer:
A general way of explaining this is
Suppose that we have a given property (or a pattern if we are working with a series of numbers):
Now, if that property is true, for example, for the numbers 1, 2, 3... etc. Then we can suppose that the property is also true for an unknown number N.
Now, if using the hypothesis that the property is true for N, we can prove that the property is also true for N + 1, then we actually proved that the property is true for all the set.
We actually can use any set, not only the natural numbers.
For example, we can use the set of the even numbers {2, 4, 6, 8....}, suppose that the property is true for a random number N, that is even, and then see if using that hypothesis we can prove that the property is also true for the next number in the set; N + 2.
if the bacteria population is doubling every hour, can you estimate the bacteria population at the time of 10 hours?
Answer:
Bacterial population at the time of 10 hours = 1040000
Step-by-step explanation:
Let the function that defines the bacterial population after 'x' hours is,
p(x) = a(b)ˣ
Where a = Initial population
And 'x' = Duration or time
Since bacterial population is getting doubled every hour,
2a = a(b)¹
b = 2
Therefore, function will be,
p(x) = a(2)ˣ
From the graph attached,
Point (5, 32500) lies on the graph of the function.
32500 = a(2)⁵
a = [tex]\frac{32500}{32}=1015.625[/tex]
Therefore, the function will be,
p(x) = 1015.625(2)ˣ
For x = 10 hours,
p(10) = 1015.625(2)¹⁰
= 1040000 bacteria
Rayne sold 3 desks at the local trade show. He paid $4.00 to rent the booth. He gave half of his revenue to the carpenter and was left with $185.50. At what price did Rayne sell each desk?
Rayne sell each desk at the price of $125.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given the following information;
The Number of desks sold = 3
The Amount of rent paid = $4
The Amount paid to carpenter = 1/2 of revenue
The Amount left = $185.50
If Rayee gave half of his revenue to the carpenter and then had $185.50 left.
The his revenue before paying the carpenter will be twice what he has left will be;
($185.50 * 2) = $371
Hence, the total revenue from the sale of 3 desk = ($371 + rent)
= (371 + 4)
= $375
Then each desk cost :
$375 / 3 = 125
Hence, Rayne sell each desk at the price of $125.
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The addition is one of the four fundamental mathematical operations. The selling price of each desk is $122.33.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
Revenue generated = Revenue left with Rayne + Revenue with carpenter
Since Rayne gave half of his revenue to the carpenter, therefore, both of them will have the same revenue will them
Revenue generated = Revenue left with Rayne + Revenue left with Rayne
Revenue generated = 2(Revenue left with Rayne)
Revenue generated = 2($185.50)
Revenue generated = $371
Also, Rayne paid a booth rent of $4. Therefore, the total revenue generated will be,
Total revenue generated = Revenue generated + $4
= $371 + $4
= $367
Since Rayne sell 3 desks, therefore, the selling price of each desk will be,
Selling price = $367 / 3
= $122.33
Hence, the selling price of each desk is $122.33.
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Find the property for
9 • (-1 • x) = 9 • (-x)
A teacher wanted to know how well the gifted students in here class perform relative to her other classes. She administers a standardized test with a mean of 50 and a standard deviation of 10. A student scores of 55, what percent of students have a higher score than hers
Answer: 30.85%.
Step-by-step explanation:
Let X denotes the score of random student.
Given: [tex]\mu = 50[/tex] and [tex]\sigma=10[/tex]
We assume that scores are normally distributed.
Then , the probability that a a student score higher than 55:
[tex]P(X>55)=P(\dfrac{X-\mu}{\sigma}>\dfrac{55-50}{10})\\\\=P(Z>0.5) \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.5)\\\\=1-0.6915\ [\text{By p-value table for z}]\\\\= 0.3085[/tex]
Hence, the percent of students have a higher score than hers is 30.85%.
Use the tables below to find (p − q)(2). A 2-column table has 3 rows. The first column is labeled x with entries 4, 2, negative 3. The second column is labeled p (x) with entries negative 1, 3, 2. A 2-column table has 3 rows. The first column is labeled x with entries 4, 2, negative 3. The second column is labeled q (x) with entries 1, negative 2, 5. (p – q)(2) =
Composite functions are multiple functions combined to form another function.
The value of the composite function (p - q)(2) is 5
To find (p - q)(2), we make use of the following composite function formula:
[tex](p - q)(x) = p(x) - q(x)[/tex]
Substitute 2 for x in the above formula
[tex](p - q)(2) = p(2) - q(2)[/tex]
From the table entries, we have:
[tex]p(2) =3[/tex]
[tex]q(2) = -2[/tex]
So, the equation becomes
[tex](p - q)(2) = 3 -- 2[/tex]
Rewrite the above equation as:
[tex](p - q)(2) = 3 + 2[/tex]
Take the sum of 3 and 2
[tex](p - q)(2) = 5[/tex]
Hence, the value of (p - q)(2) is 5
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Which of the following functions describes the sequence 4, –2, 1, –12, 14, . . .?
Answer:
D. f(1) = 4, f(n) = –1/2f(n – 1) for n > 1
Step-by-step explanation:
We assume your sequence is supposed to be ...
4, -2, 1, -1/2, 1/4, ...
This has no common difference, but it has a common ratio of -1/2. That is, the first term is 4, and each successive term is -1/2 times the previous one. The function is described by the recursive formula ...
f(1) = 4;
f(n) = -1/2·f(n-1)
-6x^3 -7x^2 +qx - 12 is divisible by 3x-4. There is no remainder. Find the value of q.
If [tex]3x-4[/tex] is a factor of [tex]p(x)=-6x^3-7x^2+qx-12[/tex], then [tex]x=\frac43[/tex] is a root of [tex]p(x)[/tex] so that [tex]p\left(\frac43\right)=0[/tex]:
[tex]-6\left(\dfrac43\right)^3-7\left(\dfrac43\right)^2+q\left(\dfrac43\right)-12=0[/tex]
[tex]\dfrac{4q-116}3=0[/tex]
[tex]4q-116=0[/tex]
[tex]4(q-29)=0[/tex]
[tex]\implies\boxed{q=29}[/tex]
Please help!! What is 6(4 - y) = 5 + 3?
Answer:
[tex] \boxed{ \boxed{ \bold{ \sf{2.6}}}}[/tex]Step-by-step explanation:
[tex] \sf{6(4 - y) = 5 + 3}[/tex]
Distribute 6 through the parentheses
[tex] \sf{24 - 6y = 5 + 3}[/tex]
Add the numbers
[tex] \sf{24 - 6y = 8}[/tex]
Move constant to right hand side and change it's sign
[tex] \sf{ - 6y = 8 - 24}[/tex]
Calculate
[tex] \sf{ - 6y = - 16}[/tex]
Divide both sides of the equation by -6
[tex] \sf{ \frac{ - 6y}{ - 6} = \frac{ - 16}{ - 6} }[/tex]
Calculate
[tex] \sf{y = 2.6}[/tex]
Hope I helped!
Best regards!!
Answer: Hi!
First, we need to distribute 6 to the terms inside of the parentheses, 4 and -y.
6 * 4 = 24
6 * (-y) = -6y
Our equation now looks like this:
24 - 6y = 5 + 3
We can now combine like terms.
24 - 6y = 5 + 3
5 + 3 = 8
Our equation now looks like this:
24 - 6y = 8
We can now use inverse operations to get rid of 24. Remember, our goal is to isolate the x. The inverse operation for addition (24 is positive) is subtraction, so we subtract 24 on both sides:
24 - 6y = 8
- 24 - 24
Our equation now looks like this:
-6y = -16
Last step! We now use inverse operations to get rid of -6. The inverse operation for multiplication is division (-6 is being multiplied by y); so we divide -6 on both sides.
-6y/-6 = y
-16/-6 = 8/3 = 2 2/3
Our equation now looks like this:
y = 2 2/3
Therefore, your solution is 2 2/3.
Hope this helps!
Tamara earns $15 an hour at her job working 25 hourse per week. If 21% of her paycheck goeas to taxes, what is Tamara's monthly cash inflow? (Assume this is her only source of income and that there are 4 pays per month.)
What is the greatest integer a, such that a^2 + 3b is less than (2b)^2, assuming that b is 5? Please answer and have a nice day!
===================================================
Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
------------------
Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get [tex]a \le 9[/tex]
So the greatest integer possible for 'a' is a = 9.
------------------
Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work
Answer:
9
Step-by-step explanation:
I just did the question on AOPS, please see the attachment down below.
Hope this helped! :)
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units? (x – 3)2 + (y – 5)2 = 6 (x – 3)2 + (y – 5)2 = 36 (x + 3)2 + (y + 5)2 = 6 (x + 3)2 + (y + 5)2 = 36
Answer:
D. is the answer
The equation that represents a circle with a center at (–3, –5) and a radius of 6 units is given by:
[tex](x + 3)^2 + (y + 5)^2 = 36[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, we have that:
The center has [tex]x_0 = -3, y_0 = -5[/tex].The radius is r = 6.Hence:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x + 3)^2 + (y + 5)^2 = 36[/tex]
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The length of a rectangle is 2 inches less than twice it’s width. If the perimeter of the rectangle is 74 inches, what is the area of the rectangle?
Answer:
341.25in²
Step-by-step explanation:
Width=x
Length=x+2
X+x+x+2+x+2=74
4x+4=74
4x=70
x=17.5
width=x=17.5
length=x+2=19.5
A=LW
A=17.5*19.5
A=341.25in²
Given, f(x) = 2x + 7
Find f(3)
f(3) = 13
Step-by-step explanation:f(x) = 2x + 7
replace x with 3
f(3) = 2×3 + 7
= 6 + 7
= 13
Solve for all values of x in simplest form
Answer:
x = -16/5 or
x = 6/5
Step-by-step explanation:
[tex]-\left|5+5x\right|-9=-20\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-\left|5+5x\right|-9+9=-20+9\\\\Simplify\\-\left|5+5x\right|=-11\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-\left|5+5x\right|}{-1}=\frac{-11}{-1}\\\\\left|5+5x\right|=11\\\\\mathrm{Apply\:absolute\:rule}:\\\\\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\5+5x=-11\quad \mathrm{or}\quad \:5+5x=11\\\\5+5x=-11\quad :\quad x=-\frac{16}{5}\\\\5+5x=11\quad :\quad x=\frac{6}{5}\\[/tex]
[tex]x=-\frac{16}{5}\quad \mathrm{or}\quad \:x=\frac{6}{5}\\[/tex]
The value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x = -16/5 or x = 6/5.
What do you mean by algebraic expressions ?
Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.
The algebraic expression given is -|5 + 5x| - 9 = -20
We know that a modulus sign is a representation of ran absolute value which has two values either a positive or negative value.\
After solving the expression we get :
-|5 + 5x| - 9 = -20
So , after removing the modulus sign we will get two expressions :
-(-(5 + 5x) - 9 = -20
5 + 5x = -11
or
-(5 + 5x) - 9 = -20
-(5 + 5x) = -11
Solving the two expressions we get the value of x as :
x = -16/5
or
x = 6/5
Therefore , the value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x = -16/5 or x = 6/5.
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What is the conjugate of 7-8i?
Answer:
7 + 8i
Step-by-step explanation:
Conjugate of 7 - 8i is 7 + 8i
Answer:
Step-by-step explanation:
7+8i
The base of a parallelogram is (2x + 3) units and the corresponding height is (3x – 2) units. Find the area of the parallelogram in terms of x. What will be the area of parallelogram if x = 30 units?please explain how you got the answer
Answer:
S = 6x² + 5x - 6
5544 sq. units
Step-by-step explanation:
Area of parallelogram is:
S = bhGiven:
b = 2x+3h = 3x -2Then:
S = (2x + 3)(3x - 2) = 6x² - 4x + 9x - 6 = 6x² + 5x - 6S = 6x² + 5x - 6
If x = 30, then plug it in the equation:
S = 6*30² + 5*30 - 6 = 5544 sq. unitsx is an irrational number between 7 and 10. find a value for x
Answer:
[tex]\boxed{ x = \sqrt{8.5} }[/tex]
Step-by-step explanation:
Hey there!
Irrational numbers are numbers that cannot be expressed as fractions.
[tex]\sqrt{8.5}[/tex]
=2.915475947422650235437076438772791538260699167442985977225003372433905030998356313832620163226517699278394811037677455675906936808085403142951613039412223590832527179885119634084324188271634828210865
The shown decimal goes on for 200 digits.
And it cannot be put into fraction form, meaning it is irrational.
Hope this help :)
Literally, irrational numbers are numbers that cannot be expressed as simple fractions. Some irrational numbers between 7 and 10 are 7.4833,7.9372,8.3666,8.4852,9.4868.
Given that
[tex]Min = 7[/tex]
[tex]Max = 10[/tex]
There are several ways to generate the irrational numbers between the given range.
One of the ways is as follows:
First, we list the pairs of relatively prime integers between the given range.
They are:
[tex]x = \{(7,8),(7,9),(7,10),(8,9),(9,10)\}[/tex]
Calculate the product
[tex]x = \{56,63,70,72,90\}[/tex]
Take the positive square root of the numbers to generate some irrational integers
[tex]x = \{\sqrt{56},\sqrt{63},\sqrt{70},\sqrt{72},\sqrt{90}\}[/tex]
[tex]x = \{7.4833...,7.9372....,8.3666...,8.4852....,9.4868....\}[/tex]
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Select all of the following statements that are true. All real numbers are natural numbers. All whole numbers are integers. All integers are whole numbers. All natural numbers are rational numbers. All irrational numbers are dense.
Answer:
All whole numbers are integers. AND All natural numbers are rational numbers.
Step-by-step explanation:
Answer:
The answer is D and E
Step-by-step explanation:
A particle travels 16.5 km in 30 minutes. What will be the speed of the particle in km / h ?
s=d/t
Step-by-step explanation:
s=16.5/0.5
s=33
33 km/h since 30 min is half an hour
Answer:
[tex] \boxed{ \huge{ \boxed{ \sf{ \bold{33 \: km/h}}}}}[/tex]Step-by-step explanation:
Distance ( d ) = 16.5 km
Time ( t ) = 30 minutes
( To convert minutes to hour , divide the minutes by 60)
Time ( t ) = [tex] \sf{ \frac{30}{60} }[/tex] = [tex] \sf{0.5}[/tex] hours
Now, let's find the speed
Speed = [tex] \sf{ \frac{distance \: travelled \: ( \: in \: km)}{time \: taken \: ( \: in \: hrs)} }[/tex]
plug the values
⇒[tex] \sf{ \frac{16.5}{0.5} }[/tex]
Calculate
⇒[tex] \sf{33 \: km/h}[/tex]
Hope I helped !
Best regards!!
does anyone know how to find square root quickly?
Answer: The quick way is to square the half of it.
Step-by-step explanation: You divide your main number by 2 and figure out that half. If it is still too big, divide by 2 again. If you need to keep repeating that is fine. Thank you multiply your answer by however many times you divided by 2.
Answer:
Step-by-step explanation: Make a perfect square list
This is one that goes to 15
[tex]\sqrt{1} \sqrt{4} \sqrt{9} \sqrt{16} \sqrt{25} \sqrt{36} \sqrt{49} \sqrt{64} \sqrt{81} \sqrt{100} \sqrt{121} \sqrt{144} \sqrt{169} \sqrt{196} \sqrt{225}[/tex]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The numbers on top are the square root and the numbers under are the answer or squared numbers. There is also a way to solve them if the number is between a number in the list like 18 but i don't feel like explaining that this is just the basic squares.
One of the factors of 12 is chosen what’s the probability the chosen factor is 4?
Answer:
1/6
Step-by-step explanation:
There are six factors of 12: 1, 2, 3, 4, 6, and 12.
So the probability that the chosen factor is 4 is 1/6.
In the library, there are 12x English books, 5x Chinese books and 4x Malay
books. If there are 15 fewer Indian books than Malay books, find the to
number of books in the library in terms of x.
Answer:
25x - 15
Step-by-step explanation:
Indian books = malay books - 15
=4x -15
Total books =
English books + chinese books + malay + indian
= 12x + 5x + 4x + 4x -15
= 25x - 15
Answer:
Step-by-step explanation:
Indian books = 4x - 15
Total books = 12x + 5x + 4x + 4x - 15 {add like terms}
= 25x - 15
0.4r = 1.6 pls answer ASAP and pls show how to correct
Answer:
r = 4.
Step-by-step explanation:
0.4r = 1.6
4r = 16
2r = 8
r = 4.
0.4(4) = 1.6
1.6 = 1.6
Hope this helps!
match each account of events with the type of chronology it illustrates. helppp !!
Convert 7s seconds to hours Idk which numbers go where for how my teacher does it he cross multiplies and divides and idk which numbers go where please help
Answer:
0.0208333...
Step-by-step explanation:
You would just divide 7 seconds by 3600 seconds (1 hr) and that would be ur answer so in this case it would be 0.0208333...
Answer:
1/48 or 0.02083 hours
Step-by-step explanation:
75s×1 min/60s×1 hour/60 mins so the seconds and minutes cancel out and you are left with 75/3600=1/48 hours