Answer:
See Explanation
Step-by-step explanation:
To do this, we will make use of the following rules:
Direct Variation: [tex]a\ \alpha\ b[/tex] => [tex]a = kb[/tex]
Inverse Variation: [tex]a\ \alpha\ \frac{1}{b}[/tex] ==> [tex]a = k/b[/tex]
Joint Variation: [tex]a\ \alpha\ bc[/tex] ==> [tex]a= kbc[/tex]
Direct, then inverse variation: [tex]a\ \alpha\ b\ \alpha\ \frac{1}{c}[/tex] ==> [tex]a= kb/c[/tex]
Having highlighted the rules, the solution is as follows:
1. m varies directly to a
[tex]m\ \alpha\ a[/tex]
[tex]m =ka[/tex]
2. p varies inversely as q.
[tex]p\ \alpha\ \frac{1}{q}[/tex]
[tex]p\ = k\frac{1}{q}[/tex]
3. [tex]r\ varies[/tex] directly as s and inversely as t.
[tex]r\ \alpha\ s\ \alpha\ \frac{1}{t}[/tex]
[tex]r = k\frac{s}{t}[/tex]
4. z varies jointly as [tex]e\ and\ f.[/tex]
[tex]z\ \alpha \ ef[/tex]
[tex]z = kef[/tex]
5. F varies directly as the [tex]square\ of\ t.[/tex]
[tex]F\ \alpha\ t^2[/tex]
[tex]F = kt^2[/tex]
6. d varies jointly r and t
[tex]d\ \alpha\ rt[/tex]
[tex]d = krt[/tex]
7. P is inversely proportional to h.
[tex]P\ \alpha\ \frac{1}{h}[/tex]
[tex]P= \frac{k}{h}[/tex]
8. P varies directly as V
[tex]P\ \alpha\ V[/tex]
[tex]P=kV[/tex]
9. d varies directly as the square of t
[tex]d\ \alpha\ t^2[/tex]
[tex]d = kt^2[/tex]
10. s varies jointly as b and d and inversely as the square L
[tex]s\ \alpha\ bd\ \alpha\ \frac{1}{L^2}[/tex]
[tex]s = k\frac{bd}{L^2}[/tex]
The translation of each statement to an equation using k as the constant of variation is
1. m varies directly to a.
m = k × a
m = ka
2. p varies inversely as q
p = k / q
3. r varies directly as s and inversely as t
r = (k × s) / t
r = ks / t
4. z varies jointly as e and f.
z = k × e × f
z = kef
5. F varies directly as the square of t.
F = k × t²
F = kt²
6. The distance (d) traveled by a car varies jointly as the rate (r) and the time (t) of travel.
d = k × r × t
d = krt
7. The air pressure (P) in inversely proportional to the altitude (h).
P = k / h
8. The amount of water pressure (P) in a closed container varies directly as the volume (V) of the
water.
P = k × V
P = kV
9. The distance (d) of a falling body varies directly as the square of the time (t) traveled.
d = k × t²
d = kt²
10. The stiffness (s) of a beam varies jointly as its breadth (b) and depth (d) and inversely as the
square of its length (L).
s = (k × b × d) / L²
s = kbd / L²
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help on geometry plzzzz find b
Answer:
5.5 cm
Step-by-step explanation:
s
Se necesitan cortar 3 cintas de 40 cm, 50 cm y 60 cm, en trozos igua-
les de manera que todas sean iguales y con la mayor longitud posible.
¿Cuántos trozos se cortarán?
Answer:
Se cortarán en 15 trozos.
Step-by-step explanation:
Para determinar la longitud de cada trozo tal que todos los trozos tengan la misma longitud, se descompone factorialmente cada número:
[tex]40 = 2\times 2 \times 2 \times 5[/tex]
[tex]50 = 2\times 5\times 5[/tex]
[tex]60 = 2\times 2\times 3\times 5[/tex]
Ahora, determinamos el factor común de los tres números. Se puede encontrar que los tres números comparten un 2 y un 5. Entonces, el factor común es:
[tex]r = 2\times 5 = 10[/tex]
Este factor común representa la longitud de cada segmento. La cantidad de elementos se obtiene al dividir la suma de longitudes de las cintas por el factor común:
[tex]x = \frac{40\,cm+50\,cm+60\,cm}{10\,cm}[/tex]
[tex]x = \frac{150\,cm}{10\,cm}[/tex]
[tex]x = 15[/tex]
Se cortarán en 15 trozos.
In a MBS first year class, there are three sections each including 20 students. In the first section, there are 10 boys and 10 girls, in the second section there are 15 boys and 5 girls, and in the third section, there are 12 boys and 8 girls. Five students are selected at random from each group to form committee of 15 students. What is the probability that all the 15 students selected are girls?
Answer:
[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls
Step-by-step explanation:
The selection is from a sample without replacement, so we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
All girls from the first group:
20 students, so [tex]N = 20[/tex]
10 girls, so [tex]k = 10[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_1 = P(X = 5) = h(5,20,5,10) = \frac{C_{10,5}*C_{10,5}}{C_{20,5}} = 0.0163[/tex]
All girls from the second group:
20 students, so [tex]N = 20[/tex]
5 girls, so [tex]k = 5[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_2 = P(X = 5) = h(5,20,5,5) = \frac{C_{5,5}*C_{15,5}}{C_{20,5}} = 0.00006[/tex]
All girls from the third group:
20 students, so [tex]N = 20[/tex]
8 girls, so [tex]k = 8[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_3 = P(X = 5) = h(5,20,5,8) = \frac{C_{8,5}*C_{12,5}}{C_{20,5}} = 0.0036[/tex]
All 15 students are girls:
Groups are independent, so we multiply the probabilities:
[tex]P = P_1*P_2*P_3 = 0.0163*0.00006*0.0036 = 3.52 \times 10^{-9}[/tex]
[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls
help its pre algebra
Answer:
$9 and $12
Step-by-step explanation:
Let "s" be small boxes and "L" be large boxes.
12*s + 6*L = $180
3*s + 2*L = $51
From the first equation:
L = ($180 - 12*s) / 6 = $30 - 2*s
Plug that into 2nd equation:
3*s + 2*($30 - 2*s) = 3*s + $60 - 4*s = $51
s = $9
L = $30 - 2*s = $30 - $18
L = $12
https://www.savvasrealize.com/community/classes/48717a31a64245798f610490cc796fd1/assignments/013ff67a0f7c4637b86efc678cf9a30b?ticket=ST-9550747-UqbA9WpbcG6durdKfUjH-prod-cas-caschart-5f5996dc76-78nbm
Answer:
17 to that answer
Step-by-step explanation:
nwwansws s rgjkl rf sghands
Find the value of x. Round to the nearest tenth. x=
27 , 34 , 11 ,
Answer:
x = 13.5
Step-by-step explanation:
x = 11 · (sin 34°) / sin 27°
Answer:
120
Step-by-step explanation:
180-27-34=119
119 round up to nearest 10 = 120
You look up at 1 but you are not soposed to answer the question by looking at 1, if you have nearest 10 to round then always look at the units.
Always look at the second digit of the nearest number that you would round up.
Example:
round 560 to the nearest 100.
The answer would be 600 because 0-4 goes down and 5-9 goes up,
and in this number 5 goes up so the answer would be rounded up.
If the question said round 560 to the nearest 10 then the answer would be the same because the second digit is 0 and 0 goes down so it does not make any difference. If the second digit goes down then you do not need to change your answer the answer would be the same as the question number.
A bag contains 6 cherry, 3 orange, and 4 lemon candies. You reach in and take 4 pieces of candy at random. Find the
probability that you have all orange candies.
Answer:
total 13 candies
denominator: 13C2
= 78
one possible way to get all orange
ANSWER: 1/78
A certain forest covers an area of 3500 km² suppose that each year this area decreases by 6.75% what will the area be after 15 years?
Answer:
Sure na bayan napo bayan
What is the volume of the figure below, in cubic centimeters?
2 rectangular prisms. One prism has a length of 12 centimeters, width of 9 centimeters, and height of 2 centimeters. The other prism has a length of 10 centimeters, width of 9 centimeters, and height of 8 centimeters.
756
936
1,008
1,080
The volume of the rectangular prism is V = 936 cm³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
To find the volume of the figure, we need to calculate the volumes of the two rectangular prisms separately and then add them together.
The volume of a rectangular prism is given by the formula:
Volume = length x width x height
For the first prism:
Length = 12 centimeters
Width = 9 centimeters
Height = 2 centimeters
Volume of first prism = 12 cm x 9 cm x 2 cm = 216 centimeters³
For the second prism:
Length = 10 centimeters
Width = 9 centimeters
Height = 8 centimeters
Volume of second prism = 10 cm x 9 cm x 8 cm = 720 centimeters³
Now, we add the volumes of the two prisms together to get the total volume of the figure:
216 cubic centimeters + 720 cubic centimeters = 936 centimeters³
Hence , the rectangular prism has volume of 936 cm³
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What does tan^2(x) mean
Answer:
Step-by-step explanation:
When the exponent is attached to the trig function like that, its essentially the same thing as taking the entire function to that power.
tan^2(x) = (tanx)^2
HELP ASAP PLEASE
Write an equivalent expression for 7 + 5 k minus 2 minus 3 k + n. Which statements are true about the steps for writing the equivalent expression? Check all that apply.
Combine the constant terms by adding 7 and –2.
The equivalent expression is 9 + 3 k.
n, 5 k, and negative 3 k are like variable terms.
Combine the like variable terms by adding the coefficients.
5 k and negative 3 k are like variable terms.
The constants 7 and –2 are like terms.
The equivalent expression is 5 + 2 k + n.
Combine the constant terms by adding 7 and 2.
Answer:
Combine the constant terms by adding 7 and –2.
Combine the like variable terms by adding the coefficients.
5 k and negative 3 k are like variable terms.
The constants 7 and –2 are like terms.
The equivalent expression is 5 + 2 k + n.
Step-by-step explanation:
Given
[tex]7 + 5k - 2 - 3k + n[/tex]
Required
Select right steps
True: The constants 7 and –2 are like terms.
True: Combine the constant terms by adding 7 and –2.
[tex]7 + 5k - 2 - 3k + n[/tex]
[tex]- 2+7 + 5k - 3k + n[/tex]
[tex]5 + 5k - 3k + n[/tex]
True: Combine the like variable terms by adding the coefficients.
[tex]5 + 5k - 3k + n[/tex]
[tex]5 + 2k + n[/tex]
True: The equivalent expression is 5 + 2 k + n.
The population of a certain city increased by 18,000 people.
Write a signed number to represent this population change.
Answer:
[tex]+18000[/tex]
Step-by-step explanation:
Given
Increment = 18000
Required
Represent as a signed number
If the initial population is x.
The new population (y) will be:
[tex]y = x + 18000[/tex]
It is "+" because the population of the city increases.
Hence, the signed number is [tex]+18000[/tex]
Help Me Please! I will give 40 points!!
Who is correct?
4^m x 4^5/ 4^n
Cung Pi simplifies to: 4^(m-n+5)
Thuy le simplifies it to: 4^m(n-5)
A. Cung Pi is correct
B. Thuy Le is correct
C. Both of them have equivalent expressions
D. Neither of them are correct
A. Cung Pi is correct. I hope this helps!
Triangle ABC is a right triangle with legs AB and AC. Points X and Y lie on legs AB and AC, respectively, so that AX:XB=AY:YC=1:2. If BY=16 units and CX=28 units, what is the length of the hypotenuse BC? Express your answer in simplest radical form.
Answer:
i don't get it
Step-by-step explanation:
Please help asap!
The graphs of linear functions f and g are shown.
Enter the solution to the equation f(x) = g(x).
9514 1404 393
Answer:
x = -3
Step-by-step explanation:
The solution to the equation ...
f(x) = g(x)
is the x-value where the functions have equal values. That is the x-coordinate of the point where the graphs intersect. The intersection point is (-3, 5), so the solution to the equation is x = -3.
Math help!!! Answers??
Answer:
5 = B, 13
and 6 = D, 18.4
Step-by-step explanation:
Hope it helps...
The price of an item has risen to $216 today. Yesterday it was $135. Find the percentage Increase.
Whats the question mark?
50/2000 = 6/?
pls help fastest get brainliest
Answer:
[tex]?=240[/tex]
Step-by-step explanation:
We can let the [tex]?[/tex] be [tex]x[/tex]. Rewriting the proportion, we get:
[tex]\frac{50}{2000}=\frac{6}{x}[/tex]
Solving for [tex]x[/tex], we get:
[tex]\frac{50}{2000}=\frac{6}{x}[/tex]
[tex]50*x=2000*6[/tex] (Cross-Products Property)
[tex]50x=12000[/tex] (Simplify)
[tex]\frac{50x}{50}=\frac{12000}{50}[/tex] (Divide both sides of the equation by [tex]50[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=240[/tex] (Simplify)
Since [tex]?=x[/tex], we know that [tex]?=240[/tex]. Hope this helps!
5x - 7y - 5x +6 +3y
Pls step by step. Or just answer!
what unfortunate mistake did the champion ice skater make with his gold medal
Answer:
He Had It Bronzed
Step-by-step explanation:
Hope this help pls mark as brainlest!!
6 AM: −5°
4 PM: 27°
What is the change in temperature from 6 AM to 4 PM?
-5 to 0 is 5 degrees
0 to 27 is 27 degrees
Total change = 5 + 27 = 32 degrees.
The area of a rectangle is 14 square units. It has side lengths x and y. Given each value for x, find y.
a: x = 2 1/3 units, y
b: x = 4 1/5 units, y
x = 7/6 units, y
Answer:
28
Step-by-step explanation: im not sure this type of work is not my best but i gave it a try
Please can someone help me thank you :)
Answer:
u funkin this is ur test idiot
Answer: 42
Step-by-step explanation:
Lwh equals volume
6*3*2 equals 36
2*3*1 equals 6
36 + 6 equals 42
Which is the graph of x - y = 1?
Ty
Ty
5
4
4
3
3
3
2
+
2
1
-5-4-3-2-1
6
4
tar
X
-1
1 2 3
1 2 3 4 5
5 -5-4-3-2-1,
22
2
3
2
3
4
3
4
15
4
3
Save and Exit
Next
Submit
Mark this and return
Answer:
Step-by-step explanation:
The graph of x - y = 1 is plotted below
Plotting linear graphsThe given equation is:
x - y = 1
The equation can be rewritten as:
y = x - 1
This is of the form y = mx + 1
where m is the slope
c is the y-intercept
Compare the equation y = mx + 1 with y = x - 1
The slope, m = 1
The y-intercept, c = -1
The graph of the equation y = x - 1 is plotted below
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Alex has x number of baseball cards Danny has 10 more baseball cards than Alex how many baseball cards does Danny have:write your expression here
Answer:
x+10
Danny has 10 + x baseball cards
19/20-3/10
Simplify if needed
For brainliest
Answer:
Answer is 0.65
Step-by-step explanation:
Answer: 13/20
Step-by-step explanation:
Add. Express the sum as a fraction in simplest form. −1/3+1/2 The sum is
Answer:
1/6
Step-by-step explanation:
92 divided by the sum of 49 and 36?
Answer:
92/85
Step-by-step explanation:
how do i graph x+4y=8
Answer:
x = 8 y = 2
(8,2)
Step-by-step explanation:
You have to find the value of both x and y
x + 4y = 8
to find x you have to cancel out y so,
x + 4(0) = 8
x = 8
to find y you have to cancel out x
0 + 4y = 8
4y = 8
divide both sides by 4
y = 2
Hope this Helps!!!
By changing the equation to slope intercept form we draw the graph and graph is given in attachment.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Let us convert the equation of line x+4y=8 to slope intercept form.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
x+4y=8
4y=8-x
Divide both sides by 4
y=-x+2
Now let us find few point to draw the graph.
If x=0
y=2
If x=1
y=1
If x=2
then y=0
if x=3
then y=-1
Now plot (0, 2), (1, 1) and (3, -1) and draw the graph
Hence, by plotting the points (0, 2), (1, 1) and (3, -1) we draw the graph and the graph is in attachment.
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Solve the following equation.
4x - 2 = 22-8x
Answer:
x = 2
Step-by-step explanation:
4x - 2 = 22 - 8x
Move all variables to a single side by adding 8x to both sides of the equation.
4x + 8x - 2 = 22 - 8x + 8x
12x - 2 = 22
Add 2 to both sides to move the constants to one side.
12x - 2 + 2 = 22 + 2
12x = 24
Divide both sides by 12 to isolate the x.
12x / 12 = 24 / 12
x = 2
Answer:
x = 2
Step-by-step explanation:
Add 2 to both sides.
4x - 2 +2 = 22 - 8x + 2
Simplify.
4x=-8+24
Add 8x to both sides.
4x+8x= -8x + 24 + 8x
Simplify.
12x = 24
Divide both sides by 12.
12x/12 = 24/12
Simplfy.
x = 2
hope this helps! :)