Given:
z be inversely proportional to the cube root of y.
When y =0.064, then z =3.
To find:
a) The constant of proportionality k.
b) The value of z when y = 0.125.
Solution:
a) It is given that, z be inversely proportional to the cube root of y.
[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]
[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, z=3 when y=0.064. Putting these values in (i), we get
[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]
[tex]3=k\dfrac{1}{0.4}[/tex]
[tex]3\times 0.4=k[/tex]
[tex]1.2=k[/tex]
Therefore, the constant of proportionality is [tex]k=1.2[/tex].
b) From part (a), we have [tex]k=1.2[/tex].
Substituting [tex]k=1.2[/tex] in (i), we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]
We need to find the value of z when y = 0.125. Putting y=0.125, we get
[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]
[tex]z=\dfrac{1.2}{0.5}[/tex]
[tex]z=2.4[/tex]
Therefore, the value of z when y = 0.125 is 2.4.
Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n}[/tex]
or
[tex]n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For the given case, it is given that:
[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]
Let the constant of proportionality be k, then we have:
[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]
It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:
[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]
Thus, the constant of proportionality k is 1.2. And the relation between z and y is:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]
Putting value y = 0.0125, we get:
[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]
Thus, for the given relation between y and z, we have:
The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4Learn more about proportionality here:
https://brainly.com/question/13082482
Find an equation of the circle whose diameter has endpoints (6,4) and (2,-6)
Answer:
[tex](x-4)^2+(y+1)^2=29[/tex]
Step-by-step explanation:
We want to find a circle whose diameter has the endpoints (6, 4) and (2, -6).
Since this is the diameter, its midpoint will be the center of the circle. Find the midpoint:
[tex]\displaystyle M=\left(\frac{6+2}{2}, \frac{4+(-6)}2}\right)=(4, -1)[/tex]
So, the center of our circle is (4, -1).
Next, to find the radius, we can find the length of the diameter and divide it by half.
Using the distance formula, find the length of the diameter:
[tex]\begin{aligned} d&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\ &=\sqrt{(2-6)^2+(-6-4)^2}\\\\&=\sqrt{(4)^2+(-10)^2}\\\\&=\sqrt{116}\\\\&=2\sqrt{29}\end{aligned}[/tex]
So, the radius will be:
[tex]\displaystyle r=\frac{1}{2}d=\frac{1}{2}\left(2\sqrt{29}\right)=\sqrt{29}[/tex]
The equation for a circle is given by:
[tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex]
Substitute:
[tex](x-4)^2+(y+1)^2=29[/tex]
What is the length of leg s of the triangle below?
45
3
1072
90°
45
$
The length of the leg is 9.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
From the triangle,
S = length of the leg.
Now,
Applying the Pythagorean theorem.
√18² = 3² + s²
18 = 9 + s²
s² = 18 - 9
s² = 9
s = 9
Thus,
The length of the leg is 9.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ7
There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.
A - 7/2
B - 12/24
C - 1/12
D - 1/11
Can someone help me? It's urgent and thank you!
Answer:
-6 and -1
Step-by-step explanation:
The excluded values are the values of x that satisfy [tex]2x^{2} + 14x + 12 = 0[/tex]
Let us solve the equation [tex]2x^{2} + 14x + 12 = 0[/tex]
It's a quadratic equation
Thus, let us calculate the discriminant Δ
Δ [tex]= 14^{2} - 4 .2.12 = 100[/tex]
the discriminant is greater than 0, so the equation has two solutions
[tex]x = \frac{-14 - 10}{4} = \frac{-24}{4} = -6[/tex] or [tex]x = \frac{-14+10}{4} = \frac{-4}{4} = -1[/tex]
the excluded values are -6 and -1
Use the Pythagorean theorem to classify the triangle
formed by the three fences. Which is true about the
numbers 5, 12, and 13?
Answer:
they are equal
Step-by-step explanation:
The triangle with sides 5, 12, 13 is a right triangle because
a^2+b^2 = c^2
5^2+12^2 = 13^2
25+144 = 169
169 = 169
I'm using the pythagorean theorem converse.
3/4x × 12/11 ÷ 3x/22
Answer:
242/48
Step-by-step explanation:
7X^2+20x=24
X=?
Please answer to 2 d.p
Answer:
0.76
or
-0.76
hope this helps
Jeremy is conducting a survey about his coworkers’ in-office water consumption to encourage management to install more water dispensers at their location. He found that the population mean is 112.5 ounces with a standard deviation of 37.5. Jeremy has a sample size of 96. Complete the equation that Jeremy can use to find the interval in which he can be 99.7% sure that the sample mean will lie. 37.5 112.5 75 96 150 9.8
Using the z-distribution, as we have the standard deviation for the population, it is found that the 99.7% confidence interval is given by:
[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.99.7% confidence level, hence[tex]\alpha = 0.997[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.997}{2} = 0.9985[/tex], so [tex]z = 3[/tex].
The other parameters are:
[tex]\mu = 112.5, \sigma = 37.5, n = 96[/tex]
Hence, the interval is:
[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]
To learn more about the z-distribution, you can check https://brainly.com/question/25890103
i’ll give you what eva you like
Answer:
Number of additional inches= x
Number of additional topping= y
Total cost= 8+1.5(x)+0.75(y)
cost of pizza= 8+1.5x+0.75y-----------------------
hope it helps...
have a great day!!
+
(10x+2)
→
(9X+18) find the value of x
16
Step-by-step explanation:
10x+2=9x+18
-2 -2
10x=9x+16
-9x -9x
x=16
Hope this helps! :)
Answer:
x = 16°
Step-by-step explanation:
(10x + 2)° = (9x + 18)°
10x + 2 = 9x + 18
10x + 2 - 2 = 9x + 18 - 2
10x = 9x + 16
10x - 9x = 9x - 9x + 16
x = 16°
A rope is 9 1/2 meters long. How many pieces can be cut from the rope if
each piece is to be 1/4 meter?
assssssssssssssssssssssssssssssssss
Answer:
15, 9, 3n
Step-by-step explanation:
Just multiply the number of red balls by 3 to get total number, and divide the total number by three to get the number of red balls
Answer:
What math game is this?
Oh and this guy is correct.
Step-by-step explanation:
What is the explicit formula for the geometric sequence 2, 6, 18, 54, …?
Answer:
3x
Step-by-step explanation:
You multiply the pervious number with 3 to get the next number
For example 2 times 3 = 6
6 times 3 = 18
18 times 3 =54
54 times 3= 162
So on and so forth
The object below is made with six identical cubes. Each cube edge is 3 inches long.
As
3 in.
What is the surface area of the object in square inches?
Answer:
306 square inches.
Step-by-step explanation:
All surfaces of the cubes are exposed to the outside except 2 ( where 2 of the cubes join).
6 separate cubes have 6 * 6 faces exposed so this object has 36 - 2 = 34 surfaces exposed.
Each face of one cube = 3*3 = 9 in^2.
Therefore the surface area = 9 * 34 = 306 in^2.
what is the answer to this question
Answer:
[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]
279 students went on a field trip. Five buses were filled and 9 students traveled in cars. How many students were in each bus? PLEASEEEEE HELPPPPP ME you get 60 points i dont know if anyone cares but hey
Answer:
90 students.
Step-by-step explanation:
279-9=270, and 270 divided by 9 is 90.
A quadrilateral is a parallelogram if each____ divides a parallelogram into two____.
Answer:
diagonal, congruent triangles
Step-by-step explanation:
helpppp pleaseee its hard
Answer:
Ten thousands
Step-by-step explanation:
Replace all other digits with zero
This gives 40,000
Ten thousand (10,000) has the same amount of digits
which ratio is equivalent to the ratio 2:52
Answer:
1:26
Step-by-step explanation:
You can divide both sides by 2.
A silo in the shape of a cylinder is partially filled with corn to feed cows. The corn fills 25% of the height of the silo. What is the approximate volume of the part of the silo that is filled with corn if the silo is 12 feet in diameter and 60 feet high?
- PLEASE HELP im in the middle of an exam
Answer:
1695.6 cubic feet
Step-by-step explanation:
Given that,
The corn fills 25% of the height of the silo.
The diameter of silo, d = 12 feet
Radius, r = 6 feet
Height, h = 60 feet
The volume of the part of the silo that is filled with corn is given by :
[tex]V=25\%\ of\ \pi r^2 h\\\\=\dfrac{25}{100}\times 3.14\times 6^2\times 60\\\\V= $$1695.6\ feet^3[/tex]
So, the required volume is equal to 1695.6 cubic feet.
WILL MARK BRAINLIEST!!!!!find the length of AC
Answer:
20
Step-by-step explanation:
a²+b²=c²
25²-15²=b²
625-225=b²
400=b²
√400=√b²
20=b
If line a has a slope of -3 and is perpendicular to line b, what would is the slope of line b?
Answer:
Slope of line B: 1/3
Step-by-step explanation:
To find a slope perpendicular to another slope, you take its negative reciprocal.
Therefore, line B will have a slope of 1/3 because -3 -> -1/3 -> 1/3
is my dad abusive? today he grabbed my ears so hard and they turned so red and he put his arms around my face. then he kicked me really hard to the point where I peed, he also pushed me a lot and started slapping me. he did more which I can't remember but he also smashed my phone :) this all happened within 20 minutes and I could barely breathe after that lol. this may not seem so much but it is. this is too personal ig lol and I started self-harming again bc of him yay.
Answer:
Step-by-step explanation:
OMG! Don't do that! I am so sorry this is happening to you. Look I don't know how to comfort you. IF he keeps doing this tell your mom or litterally call 911. If he did it just on that day then try confronting him on it. And ask him why he did that! Don't self-harm you deserve so much more than that! You are awesome!
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars,of the item.Expression A: Expression B: Expression C: Expression D: Expression E: Which two expressions each represent the sale price of the item?AExpression A and Expression EBExpression B and Expression CCExpression B and Expression DDExpression C and Expression D
Answer:
Expression B: 0.8p
Expression D: p - 0.2p
Step-by-step explanation:
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.
Expression A: 0.2p
Expression B: 0.8p
Expression C:1 - 0.2p
Expression D: p - 0.2p
Expression E: p - 0.8p
Which two expressions each represent the sale price of the item?
Regular price of the item = $p
Sale price = 20% off regular price
Sale price = $p - 20% of p
= p - 20/100 * p
= p - 0.2 * p
= p - 0.2p
= p(1 - 0.2)
= p(0.8)
= 0.8p
The sale price is represented by the following expressions
Expression B: 0.8p
Expression D: p - 0.2p
The Chang family is on their way home from a cross-country road trip. During the trip, the function D(t)=3260−55t can be used to model their distance, in miles, from home after t hours of driving. find D(12) and interpret the meaning in the context of the problem.
Answer:
D(12) = 2,600 miles
It means a distance of 2,600 miles is already traveled from home after 12 hours
Step-by-step explanation:
To find D(12); all we have to do is to substitute the value of 12 for D
We have this as;
D(12) = 3260-55(12)
D(12) = 2,600
In the context of this problem, what this mean is that the distance away from home is 2,600 miles after traveling 12 hours
A rectangle measures 8/3 inches by 9/4 inches. What is its area?
Answer:
To find the area, you have to multiply the length times the width
Step-by-step explanation:
Answer:
The area of this rectangle is 6 square units.
Step-by-step explanation:
Multiply the width (8/3 inches) by the height (9/4 inches) to get the rectangle area:
8 9
----- * -----
3 4
8 * 9
This results in ---------- which itself reduces to 6.
4 * 3
The area of this rectangle is 6.
Macy's buys a coat from the manufacturer for $22.00. They markup the coat by 75%. Ms. Tonyes buys the coat and uses a 15% off coupon. How much does Ms. Tonyes pay for the coat before tax?
Answer:
Toney buys the coat for $ 14.8.
Step-by-step explanation:
Cost of coat =$ 22
Mark up by 75 %
discount = 10 %
Let toney pay $ R for the coat.
So, according to the question
R + 75 % R = 1.75 R
Now the cost is
1.75 R - 15 % of 1.75 R = 22
1.75 R - 0.2625 R = 22
R = 14.8
So, he buy the coat for $ 14.8.
hey again can u help me with this
Answer:
option C
Step-by-step explanation:
We will take 2 coordinates from the graph and Find the equation of the line.
Let the coordinates be : ( 0, 1) and (1, 3)
step 1 : find slope
[tex]slope , m = \frac{y_2 - y_ 1}{x_2 - x_1} = \frac{3-1}{1-0} = 2[/tex]
Step 2 : equation of the line :
[tex]( y - y_1) = m (x- x_1)[/tex]
[tex](y -1) = 2 ( x -0)\\y - 1 = 2x \\y = 2x + 1[/tex]
Therefore, y = 2x + 1 represent the equation of the line.
Answer:
C
Step-by-step explanation:
You need to solve for y = mx + b
You can solve for b right away. It is clear that the line crosses the y axis at (0,1) so you have
y = mx + 1 so far.
Normally you would need two clear points to solve for m, but since you know the y intercept, you need only 1 point.
The clearest point I can see is (-2,-3) which means that
x = -2
y = - 3
Put that into the equation and solve for m.
-3 = m(-2) + 1 Subtract 1 from both sides
-3-1 = m(-2) Combine
-4 = -2 m Divide both sides by - 2
-4/-2 = m
m = 2
Answer
only a and c are real choices. That's because m = 2 in both cases.
The equation we got is y = 2x + 1 which is c
A
B
С
D
If mZACD = 70°, then mZBCD = [? ]°
Answer:
35 is correct
Step-by-step explanation:
hope this helps.
Answer:
35°
Step-by-step explanation:
Angle ACD is 70°. The little tick marks on the angle mean both sides of the split are the same amount. This means if you divide the angle in half, you will find out what both of them are equal to.
What is the midpoint of the line segment graphed below?
A. (4,7/2)
B. (8,7/2)
c. (4,3/2)
D (8, 3/2)
Answer:
a) (4,7/2)
Step-by-step explanation:
Midpoint Formula:
[(-1+9)/2], [(2+5)/2]
(8/2, 7/2) = (4, 7/2)
