Given:
x is directly proportional to y and inversely proportional to z.
x= 15 when y = 10 and z= 4.
To find:
The equation that connecting x, y and z.
Solution:
It is given that, x is directly proportional to y and inversely proportional to z.
[tex]x\propto \dfrac{y}{z}[/tex]
[tex]x=\dfrac{ky}{z}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, x= 15 when y = 10 and z= 4.
[tex]15=\dfrac{k(10)}{4}[/tex]
[tex]15\times 4=10k[/tex]
[tex]60=10k[/tex]
Divide both sides by 10.
[tex]\dfrac{60}{10}=k[/tex]
[tex]6=k[/tex]
Putting k=6 in (i), we get
[tex]x=\dfrac{6y}{z}[/tex]
Therefore, the required equation is [tex]x=\dfrac{6y}{z}[/tex].
HELP! THE ANSWER IS NOT C!
Answer:
The answer is B
Step-by-step explanation:
if correct plz mark brainliest and tell me if its wrong
Simplify: (8 2/3) ^ 4
Answer:
the answer is 558175
may it help you
Please someone help me i have been waiting for someone to help me
Answer: z=29 so Now: Cary is 38 years old while Dan is 29 years old.
In 5 years: Cary is 43 years old while Dan is 34 years old.
Step-by-step explanation: z=29 because 29+9=38 and 38+29=67 so 38+5=43 and 29+5=34.
plz mark me brainliest
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The university has decided that for the following year lecture costs will increase by 20% workshop costs by 10% and examination costs will stay the same .For level 2 the current hourly costs are 10,24,and 60 respectively. how much would the level 2 course cost in the following year
Answer:
$98.4.
Step-by-step explanation:
Since the university has decided that for the following year lecture costs will increase by 20%, workshop costs by 10%, and examination costs will stay the same, and that for level 2 the current hourly costs are 10, 24, and 60 respectively To determine how much the level 2 course cost in the following year, the following calculation must be performed:
10 x 1.2 + 24 x 1.1 + 60 = X
12 + 26.4 + 60 = X
98.4 = X
Thus, the level 2 course will cost $ 98.4 next year.
I need help please in my homework 100 point question
Answer:
5,000? what does it want me to find
Step-by-step explanation:
Can you help me please here is the image
Answer:
its c
i think
Step-by-step explanation:
By how much is 11/3 and 11/5 less than 7
Answer:
Step-by-step explanation:
11/3 + (7 - 11/5)
LCM of 3 and 5 is 15 so we have
55/15 + (105/15 - 33/15)
= 160/15 - 33/15
= 127/15.
Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service?
A. (0.17 – 0.27) + 1.65, 0.27 0.17 V 200
B. (0.17 – 0.27) 1.96 V (0.17)(0.83)+(0.27)(0.73) 400
C. (0.17 – 0.27) + 1.657 (0.17)(0.83)+(0.27)(0.73) 400
D. (0.17 – 0.27) + 1.96V (0.17)(0.83)+(0.27)(0.73) 200
E. (0.17 – 0.27) + 1.657 (0.17)(0.83)+0.27)(0.73) 200
Answer:
[tex]CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}[/tex]
Step-by-step explanation:
Given
[tex]n = 200[/tex]
[tex]x_1 = 34[/tex] -- City C
[tex]x_2 = 54[/tex] --- City K
Required
Determine the 90% confidence interval
This is calculated using:
[tex]CI = \bar x \± z\frac{\sigma}{\sqrt n}[/tex]
Calculating [tex]\bar x[/tex]
[tex]\bar x = \bar x_1 - \bar x_2[/tex]
[tex]\bar x = \frac{x_1}{n} - \frac{x_2}{n}[/tex]
[tex]\bar x = \frac{34}{200} - \frac{54}{200}[/tex]
[tex]\bar x = 0.17 - 0.27[/tex]
For a 90% confidence level, the z-score is 1.65. So:
[tex]z = 1.65[/tex]
Calculating the standard deviation [tex]\sigma[/tex]
[tex]\sigma = \sqrt{(\bar x_1)*(1 - \bar x_1) + (\bar x_2)*(1 - \bar x_2) }[/tex]
So:
[tex]\sigma = \sqrt{(0.17)*(1 - 0.17) + (0.27)*(1 - 0.27) }[/tex]
[tex]\sigma = \sqrt{(0.17)*(0.83) + (0.27)*(0.73)}[/tex]
So:
[tex]CI = (0.17 - 0.27)\± 1.65\frac{\sqrt{(0.17)*(0.83) + (0.27)*(0.73)}}{\sqrt {200}}[/tex]
[tex]CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}[/tex]
the aos of x=2?????????
what is the answer 4/5 + 1/2
Answer:
1.3
Step-by-step explanation:
the internet said it was 1.3
A tank is draining at a constant rate of 5 gallons of water in 4 hours how many gallons will drain in 15 hours.
For what value of k are the graphs of y = 3x + 4 and 2y = kx + 9 parallel?
2 -7
-9
5
Given A=
and B-
6
1
-1
If X-A=B, what is X?
-2
O
7
0
-11
12
-2
-5
-7 -12
5
0
11-12
Answer:
it is b furqufhrfhquh quf hqhf
Step-by-step explanation:bfygefy eyfeyfyewfyefwef eqf
\fn qf7f
The value of the matrix X is X = [tex]\left[\begin{array}{ccc}-7&-2\\7&0\\\end{array}\right][/tex].
What are Matrices?Matrices are a set of numbers arranged in such a way that the numbers are arranged in rows and columns.
Each number is called element in a matrix.
Given are two matrices.
A = [tex]\left[\begin{array}{ccc}2&-7\\6&1\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}-9&5\\1&-1\\\end{array}\right][/tex]
We have given that, a matrix X exists such that,
X - A = B
We can rearrange this as,
X = A + B
Adding the two matrices,
The entries will be,
2 - 9 = -7
-7 + 5 = -2
6 + 1 = 7
1 - 1 = 0
X = [tex]\left[\begin{array}{ccc}-7&-2\\7&0\\\end{array}\right][/tex]
Hence the X is option A.
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write sin 81 degrees in terms of cosine
Answer:
Sine, cosine and tangent formulas are used in RIGHT triangles. So you have one 90 degree angle and two acute angles that add up to 90 degrees (they are complimentary). So the cosine of one angle would be the same as the sine of the compliment to that angle... and vice versa. To answer this question, sin 81 = cos 9, since 81 and 9 are the two acute angles of the triangle and they both add up to 90 degrees. "Cos 9" is the answer when you wish to write "sin 81" in terms of "cosine."
Please give me brainiest
sine 81 degrees in terms of cosine is cos 9°
sin 81°
Trigonometric function:The angle is less than 90 degrees.it is an acute angle. Therefore, its in the first quadrant. The first quadrant, sine, cosine and tangent are positive.
sin 81° is less than 90 degree. Therefore, let's express them in terms of a cofunction.
Therefore,
sin x = cos(90 - x)
sin 81 = cos(90 - 81)
Therefore,
sin 81° = cos 9°
learn more on sine here: https://brainly.com/question/11962279
nine more than the quotient of 2 and a number of x
Answer: 9 + 2/x - x = -19
21p+35q
please help me!
Answer:
Simplifying
21p + 35q = 0
Solving
21p + 35q = 0
Solving for variable 'p'.
Move all terms containing p to the left, all other terms to the right.
Add '-35q' to each side of the equation.
21p + 35q + -35q = 0 + -35q
Combine like terms: 35q + -35q = 0
21p + 0 = 0 + -35q
21p = 0 + -35q
Remove the zero:
21p = -35q
Divide each side by '21'.
p = -1.666666667q
Simplifying
p = -1.666666667q
How long will it take for an investment of $9000 to double at 4% Interest compounded continuously? Round to the nearest tenth of a year.
Hassan sells fruits and vegetables at the marketThe mass of fruit and vegetables are in the ratio.
Fruit: vegetables = 5:7
If Hassan sells 1.33 tones of vegetables
then how many kilograms of fruits did he sell?
Answer:
950 kilograms
Step-by-step explanation:
Fruit: vegetables = 5:7
Fruit = 5
Vegetable = 7
Total ratio = 5 + 7 = 12
If Hassan sells 1.33 tones of vegetables
1 tonne = 1000 kilograms
1.33 tonnes of vegetables = 1330 Kilograms of vegetables
how many kilograms of fruits did he sell?
Let kilograms of fruits sold = x
Fruit: vegetables = 5:7
Fruit: vegetables = x : 1330
5 : 7 = x : 1330
5/7 = x/1330
Cross product
5 * 1330 = 7 * x
6,650 = 7x
x = 6,650/7
x = 950 kilograms
kilograms of fruits sold = 950 kilograms
Plz help ASAP 20 points 5. In circle A, the length of arc BC is 20π units.
What is the length of the radius of circle A?
A. 24 units
B. 48π units
C. 10 units
D. 4v3 units
Answer: i think the answer is B or C sorry
Step-by-step explanation:
have a nice day
The length of the radius of circle A is 24 units. The correct answer would be an option (A).
What is an arc?The arc is a portion of the circumference of a circle. The circumference of a circle is the distance or perimeter around a circle.
As per the question, we have
Arc length BC = 20π units and θ = 150°
The formula for calculating the arc states that:
Arc length = 2πr (θ/360)
Where r = the radius of the circle,
π = pi = 3.14
θ = the angle (in degrees) subtended by an arc at the center of the circle.
Substitute the known values, and we get
20π = 2πr (150/360)
10 = r (5/12)
r = 120/5
r = 24
Thus, the length of the radius of circle A is 24 units.
Learn more about the arc of the circle here:
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Factories the following question
Answer:
[tex]k(3a-2b)[/tex]
Step-by-step explanation:
In the equation [tex]3ak-2bk[/tex], 'k' is the only common term.
Factor out 'k':
[tex]3ak-2bk\\\\\boxed{k(3a-2b)}[/tex]
Hope this helps.
find the value of x and y in the following figure where ABCD is a parallelogram
Answer:
x = 3
y = 2
Step-by-step explanation:
Diagonals of a parallelogram bisect each other into two equal segments. Therefore:
3x - 1 = 2(x + 1)
Solve for x
3x - 1 = 2x + 2
Collect like terms
3x - 2x = 1 + 2
x = 3
Also:
5y + 1 = 6y - 1
Collect like terms
5y - 6y = -1 - 1
-y = -2
Divide both sides by -1
y = -2/-1
y = 2
After completing this activity, what is your initial explanation of how the populations of predators and prey are related? plz help
Answer:
prey and predators depends in each other .in the absence of one another is useless or meaning less. predators is responsible for population of prey.if less predators more prey and more predators means less prey.
Answer:
A predator-prey relationship tends to keep the populations of both species in balance. ... As the prey population increases, there is more food for predators. So, after a slight lag, the predator population increases as well. As the number of predators increases, more prey are captured.
Step-by-step explanation:
WILL IVE BRAINLEIST FOR FIRST AWNSER For Emma's birthday party, her dad bought a piñata to fill with small toys. The table shows the relationship between the weight of toys he adds, w, and the total weight of the piñata, p.
Weight of toys added, in pounds (w) 1 2 3 4
Total weight of piñata, in pounds (p) 4 5 6 7
Which of the variables is independent and which is dependent?
Complete the sentence.
The dependent variable is always
the independent variable.
The dependent is the one your mesuaring and that is the Total Weight. Independent is the one you change (I remember it as the is a I in independent which 'I' change) and that would be the toy weight
Solve for X:
3+X=9
16X= 32
54 - X + 2 = 78
Division:
9/3=
5⟌225
55 X 102 =
Answer: 1. 6
2. 2
3. -22
4. 3
5. 45
6. 5,610
Step-by-step explanation: #1: ok so for #1 we have to make this a subtraction problem by making the 9 as the first number and the 3 as the second but putting a minus symbol between them so we have to subtract 9 by 3 so 9-3=6 so 3+6=9 or X=6.
#2: ok so for #2 we have another inverse expression so instead of multiplication so we have to use division and make 32 the first number and 16 the second number and put a division symbol in between them so we have to divide 32 by 16 so 32 divided by 16=2 so 16(2)=32 also, the x next to 16 means multiplication so we have to put parentheses so we know its multiplication.
#3: this one is VERY confusing but what we have to do is add the 2 to 54 so 2+54=56 next we have to rearrange the numbers and had a negative symbol before the x and make 56 go to the second number and make the minus symbol a plus symbol so we made the expression -x+56=78 now we have to subtract 56 from both sides and so the expression is now -x+56-56=78-56 and now we subtract the numbers so now the expression is -x=78-56 and do it again so 78-56=22 so -x=22 and now we have to divide both sides of the expression so we have to make -x=22 -x/-1=22/-1 now we have to remove the symbols of the right side so the expression is now x=22/-1 and divide 22 by -1 so 22 divided by -1 is -22 so X=-22 or 54-(-22)+2=78.
#4: now for #4 we have to divide 9 by 3 so 9 divided by 3=3 or we can use multiplication by making 9 the answer and 3 the first number and solve so 3x(X)=9 so 3x3=9 so the answer is 9.
#5: now we have to divide 225 by 5 so we have to divide 22 by 5 and put our 4 on top op the 2 in the 10's column and multiply 4 by 5 which is 20 the subtract 22 by 20 so 22-20=2 and bring down the 5 making 25 and multiply 5 by 5 so 5x5=25 so now we have to subtract 25 by 25 which is 0 so the answer is 45.
#6: for this we have to multiply 55 by 102 so 55 times 102 is 5,610
Solve the following inequalities and give the solutions in both set and interval notations.
-2x + 5 < -x + 25
4y + 3 > 23 subtract 3 from both sides
4y > 20 divide both sides by 4
y > 5
-2y > -2 divide both sides by -2 (the order changes)
y < 1
(-oo, 1) ∪ (5, oo)
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SO SORRY IF THESE IS WRONG:(( JUST SAY IT TO ME NOT TO BULLY ME
Please help me I guve brainliest
Answer:
The base of the triangle is 32.5in.
The height of the triangle is 16.5in.
Step-by-step explanation:
I hope im right! Sorry if im wrong! Have a good day!
The square below represents one whole.
What percent is represented by the shaded area?
%
Answer:
70%
Step-by-step explanation:
Each blue line represents 10%. Since there are 7 blue lines, we just multiply 10% by 7 and we get 70%
Answer:
70%
Step-by-step explanation:
7 out of 10 rectangles were filled so that's 7/10. 7/10 also equals 70/100. Therefore it's 70 out of 100 or 70%.
The table shows values for the equations of a system:
What x-values are a solution to the system?
Select each correct answer
x=-3
x=-2
x=-1
x=0
x=1
x=2
x=3
According to the table, the solutions to the system of equations are x = 0 and x = 1.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
[tex]y_1 = 0.25^x[/tex]
[tex]y_2 = -0.75x + 1[/tex]
The solutions are the values of x for which:
[tex]y_1 = y_2[/tex]
Looking at the table, the solutions to the system of equations are x = 0 and x = 1.
More can be learned about a system of equations at https://brainly.com/question/24342899
Which group contains triangles that are similar. im having a hard time
Answer:
1st group contains triangles that are similar
Step-by-step explanation:
since its opposite corresponding angle are equal.
Carrie is seven years older than dan in three years the sum of their ages will be 83 find the age of each man now.
Cary is ___years old while dan is ____ years old.
Does anyone know this please