Answer:
[tex]z = \frac{2}{7} [/tex] when x= [tex] \frac{6}{7} [/tex],
z= 179.2 when y= [tex] \frac{5}{28} [/tex]
Step-by-step explanation:
Let's start by writing out the two general equations for z.
Since z varies directly with x,
z= kx, where k is a constant.
Since z varies inversely with y,
[tex]z = \frac{k}{y} [/tex], where k is a constant.
When x= 12, z= 4,
4= k(12)
12k= 4
k= 4 ÷12
k= ⅓
∴ z= ⅓x
When x=[tex] \frac{6}{7} [/tex],
[tex]z = \frac{1}{3} ( \frac{6}{7} )[/tex]
[tex]z = \frac{2}{7} [/tex]
When y= 8, z= 4,
[tex]4 = \frac{k}{8} [/tex]
k= 4(8)
k= 32
[tex]∴z = \frac{32}{y} [/tex]
When y= [tex] \frac{5}{28} [/tex],
[tex]z = 32 \div \frac{5}{28} [/tex]
[tex]z = 32 \times \frac{28}{5} [/tex]
z= 179.2
How many numbers less or equal to 300 are divisible by 3, 4, or both, but not by 9?
The numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 3 - digit number as 300.
Assume that the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are [x].
Sequence of numbers divisible by 3 -
3, 6, 9, 12, ...., 300
300 = 3 + (n - 1)3
297 = 3n - 3
n(3) = 100
Sequence of numbers divisible by 4 -
4, 8, 12, ..., 300
300 = 4 + (n - 1)4
296 = 4n - 4
n(4) = 75
Sequence representing numbers less than 300, divisible by 9 -
9, 18, 27, ..., 297
297 = 9 + (n - 1)9
n(9) = 33
So, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are -
[x] = n(4) + n(3) - n(9)
100 + 75 - 33
175 - 33
142
Therefore, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.
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If an opossum is 40 cm long, and a bat is 20 cm long. So an opossum is how many times as long as a bat?
40/20=2
So an opossum is 2 times as long as a bat
Explain what a graph for Jed’s test scores {61%, 65%, 73%, and 79%} would look like if it was not misleading. Make sure it is different than Jed’s graph – that some may say is misleading.
Answer:
61
^
^
^ 65 73
^ 79 ^ ^
^ ^ ^ ^
-----------------------------------------------------------------------------------------------------------------
Test 1 Test 2 Test 3 Test 4
Answer: the test doesn't explain the order it was taken or dates. So it can be misleading
Step-by-step explanation:
what do I do next???
Answer: You have to get rid of the variables (the x's) so subtract 2x from 2x and 11x then go from there.
Step-by-step explanation:
Answer:
3 and 6
Step-by-step explanation:
11x - 53 = x^2 + 2x - 35
Subtract 11x - 53 on both sides,
0 = x^2 + 2x - 35 - ( 11x - 53 )
= x^2 + 2x - 35 - 11x + 53
= x^2 + 2x - 11x + 53 - 35
0 = x^2 - 9x + 18
x^2 - 9x + 18 = 0
Now this equation need to factorized.
x^2 - 9x + 18 = 0
x^2 - 3x - 6x + 18 = 0
x ( x - 3 ) - 6 ( x - 3 ) = 0
( x - 3 ) ( x - 6 ) = 0
x - 3 = 0
x = 3
x - 6 = 0
x = 6
The solutions to this system are 3 and 6.
rebecca has 12 photos she wants to hang side by side on her wall.
A. if she only wants to display 8 of the photos, in how many ways can she choose 8 photos she wishes to eventually display?
B. in how many ways can she arrange all 12 photos?
C. if rebecca wants to have the 10 out of 12 photos in specific places, how many ways could she order the 12 photos?
We want to find different ways of selecting and ordering elements. The answers are:
A) C = 395
B) combinations = 479,001,600
C) combinations = 239,500,800
First, we know that Rebecca has 12 photos.
A) She wants to choose 8 of these 12 photos, we want to see in how many ways she can choose these 8 photos.
Remember that for a set of N elements, the number of different combinations of K elements (such that K is smaller than N) is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have N = 12 and K = 8, then:
[tex]C(12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{4!*8!} = \frac{12*11*10*9}{4*3*2*1} = 495[/tex]
So there are 495 different ways of choosing 8 photos out of the 12.
B) Now we want to see in how many ways she can arrange all 12 photos.
The first photo can be any one of the 12, so there we have 12 options.The second photo can be any one of the remaining 11 (so we have 11 options).The third photo can be any one of the remaining 10, and so on.The total number of combinations is just the product between the numbers of options, we got:
[tex]combinations = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600[/tex]
C) Now we must combine the two things we did before, first, we select 10 out of the 12 photos, and then we want to find in how many ways we can arrange these 10 photos.
[tex]C(12, 10) = \frac{12!}{(12 - 10)°*10°} = \frac{12*11}{2} = 66[/tex]
And we multiply this by the total number of arrangements of these 10 photos, that is just given by 10!, so we get:
[tex]c = 66*10! = 66*(10*9*8*7*6*5*4*3*2*1) = 239,500,800[/tex]
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A stream drops 30 feet in elevation over a horizontal distance of 2640 feet. What is the stream gradient
The stream gradient of a stream that drops 30 feet in elevation over a horizontal distance of 2640 feet is 0.01136363636.
Stream gradient is the ratio of drop in elevation of a stream per units horizontal distance. Therefore,
stream gradient = vertical change in elevation / horizontal distance
where
vertical change in elevation = 30 feet
horizontal distance = 2640 feet
stream gradient = 30 / 2640
stream gradient = 0.01136363636
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If ACD and BAC are alternate interior angles and mACD=101°
Answer is A. 101°
Step-by-step explanation:
167.67 divided by 8.1
Answer:
167.67 divided by 8.1 = 20.7
help on theses two pls I appreciate it here is 50 points , reporting if you write anything and not writing the answer .
Answer: hi , b other one b too
Answer:
19) b
20) b
Step-by-step explanation:
The second of three numbers is 5 times the first. The third number is 3 more than the second. If the second is decreased by twice the third, the result is -21. Find the Three numbers
Answer:
tag archives and records and counting the days
Answer:
1st number is 6
2nd number is 30
3rd number is 33
Step-by-step explanation:
Let x be the first number.
The second of three numbers is 5 times the first = 5x
The third number is 3 more than the second = 5x + 3
If the second is decreased by twice the third, the result is -21.
Multiply the third number by 2.
2(5x + 3)
= 10x + 6
Subtract the second number to it.
(5x)-(10x + 6) = -21
-5x - 6 = -21
Use APE or Addition Property of Equality
-5x = -21 + 6
-5x = -15
Use DPE or Division Property of Equality to get the value of x
[tex]\frac{-5x}{-5} = \frac{-15}{-5}[/tex]
x = 3
Now put the value of x in the equation
first number(x) = 6
second number(5x) = 5(6) = 30
third number(5x + 3)
5(6) + 3
30 + 3 = 33
The function f(x) = mx + 5 is its own inverse. Find the value of m?
mx + 5 = (x - 5) / m
mx + 5 = x/m - 5/mAnswer:
Step-by-step explanation:
first find the inverse equation
y = mx + 5
y - 5 = mx
(y - 5) / m = x
(x - 5) / m = f⁻ˣ(x)
The original function is a line with slope m and y intercept of 5
The inverse function is a line with a slope 1/m and x intercept of 5
so the common line is where m = 1/m
m = 1/m
m² = 1
m = ± 1
The only line with a common slope between these two options is when
m = -1 and y intercept is 5
A caterer needs between 42 and 50
cupcakes for dessert. Name two possible
numbers between 42 and 50 that are
multiples of 4. Explain.
Answer:
404 & 408
Step-by-step explanation:
help me answer this 100 POINTS!!!!!
Answer:
1 C
2 A
Step-by-step explanation:
1 C No it cannot be defined because A and B are not congruent
2 A Yes, the lines will remain parallel
PS. It's only 50 points because two answers are allowed. Each answerer gets half.
Last year, wind turbines along a hilly ridge had an average output of 390 kilowatt hours per year. The turbines were upgraded, and now their average annual output is 30% more.
What is the new average yearly output?
kilowatt hours=
30% × 390 = 117
= 390 - 117
= 507 kw/h
Drag the descriptions of each investment in order from which will earn the least simple interest to which will earn the most simple interest.
Answer:
Hello! I know I am a bit late but for those who come here in the future,
This is the order (Least to Greatest)
1) 1,500 at 8% simple interest for 6 years
2) 1,500 at 6% simple interest for 10 years
3) 1,500 at 8% simple interest for 10 years
Hope this helps!
In situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
It is given for the three cases as,
P =$1500, R=8% , T = 10 years
P =$1500, R=8% , T = 6 years
P =$1500, R=6% , T = 10 years
The formula for the simple interest is,
Case 1,
SI = (P×R×T) / 100
SI = (1500×8×10)/100
SI = $ 1200
Case 2,
SI = (P×R×T) / 100
SI = (1500×6×10)/100
SI = $ 900
Case 3,
SI = (P×R×T) / 100
SI = (1500×8×6)/100
SI = $ 720
The simple interest for cases 1, 2, and 3 will be $ 1200, $ 900, and $ 720.
Thus, in situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.
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Number 13
I’ll reward you brainiest!!
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, x = y2; about y = 1
The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units.
Procedure - Determination of the volume of a solid of revolutionLet [tex]f(x) = 1[/tex], [tex]g(x) = x^{1/2}[/tex] and [tex]h(x) = x^{2}[/tex], both [tex]g(x) [/tex] and [tex]h(x)[/tex] have the following intersection points: [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (1,1)[/tex]. This means that the interval of x-coordinates for the solid of revolution is [tex]x \in [0, 1][/tex].
The integral formula for the volume of the solid of revolution ([tex]V[/tex]), in cubic units, is:
[tex]V = \pi \int\limits^{1}_{0} {[h(x)-f(x)]^{2}} \, dx - \pi \int\limits^{1}_{0} {[g(x)-f(x)]^{2}} \, dx [/tex] (1)
After substituting on each function and simplifying terms we get the following integral:
[tex]V = \pi \int\limits^{1}_{0} {(x^{2}-1)^{2}} \, dx - \pi \int\limits^{1}_{0} {(x^{1/2}-1)^{2}} \, dx [/tex]
[tex]V = \pi\left[\int\limits^{1}_{0} {x^{4}} \, dx - 2\int\limits^{1}_{0} {x^{2}} \, dx -\int\limits^{1}_{0} {x} \, dx + 2\int\limits^{1}_{0} {x^{1/2}} \, dx \right][/tex]
And the volume of the solid of revolution is:
[tex]V = \pi \cdot \left(\frac{1}{5}-\frac{2}{3} -\frac{1}{2}+\frac{4}{3} \right)[/tex]
[tex]V = \frac{11\pi}{30} [/tex]
The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units. [tex]\blacksquare[/tex]
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If the area of rectangular plot is 200 cm and its length is 10 m. find out its breadth.
Answer:
The area of a rectangle is A=l x w.
So, 200=10 x w
Divide both sides by 10.
20 = w
The width of the rectangle is 20 m.
:)
(7 x 10^-6)(7 x 10^-6) pls help <:D
we have (7 x 10^-6)(7 x 10^-6) = (7 x 10^-6)^2 = 49 x 10^-3 = 0.049
ok done. Thank to me :>
what is 5/8 divided 6
[tex]\sf \longmapsto \frac{5}{8} \div6[/tex]
[tex]\sf \longmapsto \frac{5}{8} \times \frac{1}{6} [/tex]
[tex]\sf \longmapsto \frac{5 \times 1}{8 \times 6} [/tex]
[tex]\sf \longmapsto \frac{5}{48} [/tex]
Answer In DECIMAL:
[tex]\sf \longmapsto0.1041[/tex]
Senna was having a party for 15 friends. She bought 3 jars of
pickles for $4.50. What is the cost per jar?
Answer:
it is 1.5
Step-by-step explanation:
if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5
Write the equation's of the lines using the given information
m=-2, (3, -7)
Answer:
y = -2x-1
Step-by-step explanation:
The formula for a line is [tex]y-y_{1} = m(x-x_{1})[/tex].
Plug in the information given in the problem: y-(-7) = -2(x-3)
So you get y+7 = -2x+6.
The final form you want needs to be equal to y (that means you want y by itself on the left side of the equals), so subtract 7 from both sides.
You get y = -2x-1
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})~\hspace{10em} m = -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{-2}(x-\stackrel{x_1}{3}) \\\\\\ y+7=-2x+6\implies \blacktriangleright y=-2x-1 \blacktriangleleft[/tex]
Help help help help help help soon people help
Answer:
A'(5,1)
B'(6,-3)
C'(2,3)
Step-by-step explanation:
assuming the translation is right 3, just add 3 to each x value
What is the gradient of the graph shown ? Give your answer in its simplest form
Answer:
-2
Step-by-step explanation:
choose any point on the graph
Answer:
Step-by-step explanation:
Yo you man its 3
Plsss help I will give you the branlyest answer
Answer:
4 1/4 is the answer u want
Does anyone know these answers?
Answer:
1. M
2. H
3. A
4. K
5. B
6. C
7. G
8. E
and so on
Step-by-step explanation:
definitions to know:
same side interior/exterior angles
vertical angles
alternate interior/exterior angles
corresponding angles
what would the numerical answer be??
Answer:
Step-by-step explanation:
The new Apple Watch series 7 cost $799. There is an additional 7% sales tax rate . If Oscar has a total of 850.00 to spend, will he be able to purchase the new Apple Watch Series 7? Explain.
The total available cash with Oscar will not be able to purchase the new Apple Watch Series 7 because the total cost of the watch is greater than available cash.
The given parameters;
cost of new Apple Watch Series 7, = $799sales tax, = 7%Oscars available cash = $850The total cost of the new Apple Watch Series 7 is calculated as follows;
Total cost = 0.07(799) + 799
Total cost = $854.93
Thus, we can conclude that the total available cash with Oscar will not be able to purchase the new Apple Watch Series 7 because the total cost of the watch is greater than available cash.
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Give TWO different ways to write EACH expression in WORDS.
a. -8n
b. a - 1
c. x/2-4
d. 5y + 9
Answer:
a. negative eight times a number, the product of a number and negative eight
b. one less than a number, a number minus one
c. four less than the quotient of a number and two, half of a number minus four
d. nine more than the product of five and a number, five times a number plus nine
lemme know if this was a help :P
Step-by-step explanation:
Find the equation of the line passing through the point (-5,2) with slope 1/3. Show work.
Hello!
First, let's write our equation in point-slope form.
Point-Slope Form:
y-y1=m(x-x1)
y1= the y-coordinate of the point
m=the slope
x=the x-coordinate of the point
y-2=1/3(x-(-5)
y-2=1/3(x+5)
y-2=1/3x+5/3
y=1/3x+5/3+2
y=1/3x+3.7
Hope it helps.
~A smiley teen
#CarryOnLearning
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