Answer:
the answer is 1/5 because y/x gives you k
The constant of proportionality [tex]k[/tex] is [tex]\frac{1}{5}[/tex].
What is constant of proportionality.
The constant of proportionality is the constant value of the ratio between two proportional quantities.
[tex]$k=\frac{y}{x}$[/tex]
Where [tex]k[/tex] is the constant of proportionality.
It is given that the table which shows the relationship [tex]y=kx[/tex] is,
x y
60 12
45 9
30 6
15 3
We have to find the value of [tex]k[/tex].
According to the formula of constant of proportionality,
Let,
[tex]${{k}_{1}}=\frac{{{y}_{1}}}{{{x}_{1}}}$[/tex]
[tex]${{k}_{1}}=\frac{12}{60}[/tex]
[tex]$\therefore {{k}_{1}}=\frac{1}{5}$[/tex]
Now,
Let,
[tex]${{k}_{2}}=\frac{{{y}_{2}}}{{{x}_{2}}}$[/tex]
[tex]${{k}_{2}}=\frac{9}{45}[/tex]
[tex]$\therefore {{k}_{2}}=\frac{1}{5}$[/tex]
The third is,
[tex]${{k}_{3}}=\frac{6}{30}[/tex]
[tex]$\therefore {{k}_{3}}=\frac{1}{5}$[/tex]
and
[tex]${{k}_{4}}=\frac{3}{15}[/tex]
[tex]$\therefore {{k}_{4}}=\frac{1}{5}$[/tex]
Hence, the Option [tex]$C$[/tex] is correct answer.
Learn more about constant of proportionality:
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Evaluate the surface integraliintegral.gifSF � dSfor the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.F(x, y, z) = xy i + yz j + zx kS is the part of the paraboloidz = 2 ? x2 ? y2 that lies above the square 0 ? x ? 1, 0 ? y ? 1,and has upward orientation
Looks like the paraboloid has equation
[tex]z=2-x^2-y^2[/tex]
and [tex]S[/tex] is the part of this surface with [tex]0\le x\le1[/tex] and [tex]0\le y\le1[/tex]. Parameterize [tex]S[/tex] by
[tex]\vec s(u,v)=u\,\vec\imath+v\,\vec\jmath+(2-u^2-v^2)\,\vec k[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Take the normal vector to [tex]S[/tex] to be
[tex]\vec s_u\times\vec s_v=2u\,\vec\imath+2v\,\vec\jmath+\vec k[/tex]
Then the flux of [tex]\vec F[/tex] across [tex]S[/tex] is
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S[/tex]
[tex]\displaystyle=\int_0^1\int_0^1(uv\,\vec\imath+v(2-u^2-v^2)\,\vec\jmath+u(2-u^2-v^2)\,\vec k)\cdot(2u\,\vec\imath+2v\,\vec\jmath+\vec k)\,\mathrm du\,\mathrm dv[/tex]
[tex]\displaystyle=\int_0^1\int_0^1(2u^2v+(2v+1)u(2-u^2-v^2))\,\mathrm du\,\mathrm dv=\boxed{\frac{293}{180}}[/tex]
Please help me with this. Thank you!
Answer:
First choice listed
Step-by-step explanation:
Pick 2 points from the table and find the slope between them. I chose (30,12) and (20,8). Apply the slope formula to find the cost per CD:
[tex]\frac{Cost}{CD}= \frac{30-20}{12-8}=\frac{5}{2}[/tex]
The function then is C = 5/2d. or C = 2.5d, first choice
C = 2.5d. Plugging in for d and C we get the same solution on each side
!PLEASE HELP! WILL GIVE BRAINLIEST!!
A projectile launched straight up into the air with an initial velocity of 20 meters per second from a height of 10 meters. How long will it take for the projectile to hit the ground?
please solve and show your work!!
What is the solution to the inequality below? 12x > 6(x - 2)
Answer:
x > -2
Step-by-step explanation:
12x > 6 (x - 2)
12x > 6x - 12
6x > - 12
x > - 2
Yannick and Jean are playing a guessing game with integers. Yannick wrote these clues to help Jean guess the unknown integer. n+6 greater than or equal to 15 and n+5<15 What is the value of the unknown integer, n?
Answer:
9
Step-by-step explanation:
The solution to ...
n +6 ≥ 15
is found by subtracting 6:
n ≥ 9
__
The solution to ...
n +5 < 15
is found by subtracting 5:
n < 10
__
The only integer that is at least 9 and less than 10 is 9.
The value of the unknown integer, n, is 9.
The expression (3x2 + 5x – 12) – 2(x2 + 4x +9) is equivalent to which of the following:
A. x2 – 3x – 30
B. x2 + 13x + 6
C. 5x2 + x – 18
D. x2 + 3x – 21
Show Your Work
Answer:
A. x² -3x -30
Step-by-step explanation:
Using the distributive property to eliminate parentheses, we get ...
3x² +5x -12 -2x² -8x -18
Then, collecting terms gives ...
= (3-2)x² +(5-8)x +(-12-18)
= x² -3x -30 . . . . . . . . . . . . . matches selection A
A crane lifts 50 Newtons 2 meters. How much work is done?
50 Nm
100 Nm
200 ft-lbs
2 Nm
Answer:
Step-by-step explanation:
2 meter is like 6.4 yards
so i would say B is the answer
Final answer:
The work done by the crane in lifting 50 Newtons over a distance of 2 meters is 100 Nm.
Explanation:
The work done by a crane can be calculated by multiplying the force applied by the distance over which the force is applied. In this case, the crane is lifting 50 Newtons over a distance of 2 meters. Therefore, the work done is:
Work = Force x Distance
Work = 50 N x 2 m = 100 Nm
So, the correct answer is 100 Nm.
Which figures demonstrate a single reflection?
Select each correct answer.
Answer:
Please see the attached image below, to find more information about the graph
The figures that are obtained by a single reflection are shown in the image inside a red rectangle.
The axis of reflection is shown with a black line.
- The figure from the left shows horizontal reflection
- The figure from the right shows vertical reflection
which is equivalent to "12 chars for every 3 tables"?
Is it 12 chairs per three tables? I might be wrong..
Answer: 12 chairs per 3 tables
Step-by-step explanation:
WRITE THE EQUATION OF THE PARABOLA with a directrix of y=1 and a focus of (0,-1).
Answer:
-4y = x², or y = - x²/4, or y = -(1/4)x²
Step-by-step explanation:
Because the focus is beneath the directrix, this vertical parabola opens down. The general formula is 4py = x².
Because the distance between focus and directrix is 2 units, p = -1 here. The negative sign shows that the parabola opens down.
4py = x² becomes 4(-1)y = x², or -4y = x², or y = - x²/4
The ratio of the radio of sphere A and sphere B is Ra\Rb =2/5. The volume of sphere b is 64 pied cu ft. What is the volume of sphere A
The volume of a sphere with radius [tex]r[/tex] is [tex]V=\dfrac43\pi r^3[/tex]. Sphere B has a volume of [tex]64\pi[/tex], so
[tex]V_B=\dfrac43\pi{r_B}^3\implies r_B=\sqrt[3]{\dfrac{64\pi}{\frac43\pi}}=\sqrt[3]{48}[/tex]
Now,
[tex]\dfrac{r_A}{r_B}=\dfrac25\implies r_A=\dfrac{2r_B}5[/tex]
so sphere A has volume
[tex]V_A=\dfrac43\pi\left(\dfrac{2r_B}5\right)^3=\dfrac{512}{125}\pi[/tex]
Which is the correct answer a,b,c, or d. Need to now ASAP!
Answer:
I think C
Step-by-step explanation:
Taylor took 6 hours to drive home from college for Thanksgiving break, a total distance of 290 miles. She was able to average 50 miles per hour for part of the trip but had to slow down to 45 miles per hour for the rest of the time due to poor weather. How many hours did she drive each speed.
PLEASE SHOW WORK/HOW TO SOLVE IT :)
Answer:
50 mph: 4 h45 mph: 2 hStep-by-step explanation:
Let t represent the time driving at 50 mi/h. Then her total distance driven (in miles) is ...
distance = speed · time
290 = 50t + 45(6-t)
20 = 5t . . . . . . . . . . . subtract 270, collect terms
4 = t . . . . . . divide by the coefficient of t
Taylor drove 4 hours at 50 miles per hour, then 2 hours at 45 miles per hour.
What is 144 in exponential form? A) 212 B) 27 C) 43 D) 122
Answer:
D
12²
Step-by-step explanation:
Given in the question, an integer = 144
To find the exponential form 144 we will do factorisation
The prime factorisation of 144 is
2 × 2 × 2 × 2 × 3 × 3
So the exponential form is 2[tex]^{4}[/tex] × 3²
The other way is
√144 = 12
which means
12² = 144
Answer: 12^2=144
Step-by-step explanation:
Which means (12)(12)=144
can someone please help me with this problem
Answer:
294.5 sq meters
Step-by-step explanation:
I found the area of the circle, subtracted away the area of the sector, then had to add back in the area of the triangle. The areas for each is as follows:
[tex]A_{c}=\pi (11.1)^2[/tex]
A = 387.0756 sq m
[tex]A_{s}=\frac{130}{360}*\pi (11.1)^2[/tex]
A = 139.7773
[tex]A_{t}=\frac{1}{2}(11.1)(11.1)sin(130)[/tex]
A = 47.1922
Now taking the area of the circle - area of sector + area of triangle:
387.0756 - 139.7773 + 47.1922 = 294.5 sq m
Answer:
294.5
Step-by-step explanation:
Kendra surveyed a random sample of 100 members of a local gym. She found that 40% of the gym members surveyed had taken a yoga class. Kendra wanted to know if it is plausible that 50% of the entire population of gym members had taken a yoga class. Kendra performed 100 trials of a simulation. Each trial simulated a sample of 100 gym members under the assumption that 50% of the population had taken a yoga class. The dot plot shows the results of the simulations. What is the best conclusion for Kendra to make based on the data?
A. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
B. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is likely.
C. It is plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
D. It is plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is likely.
Answer: A, it is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
Answer:
Option A is correct.
Step-by-step explanation:
Kendra surveyed a random sample of 100 members of a local gym. She found that 40% of the gym members surveyed had taken a yoga class.
Kendra performed 100 trials of a simulation. Each trial simulated a sample of 100 gym members under the assumption that 50% of the population had taken a yoga class.
The best conclusion based on the plot is - A. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
math question, help. I got two different answers for this and I don’t know which one is correct. please include steps
Answer:
16/(3(x+1))
Step-by-step explanation:
We can factor the denominator of the second term, which lets us see how to combine terms:
[tex]\displaystyle\frac{7}{x+1}-\frac{5}{3x+3}=\frac{7}{x+1}-\frac{5}{3(x+1)}\\\\=\frac{3\cdot 7}{3(x+1)}-\frac{5}{3x+3}=\frac{21-5}{3(x+1)}=\frac{16}{3(x+1)}[/tex]
Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation
4.5x+3y=2:
A(...,1/3)
B(2/3,...)
Answer:
A(2/9, 1/3)
B(2/3, -1/3)
slope = -1.5
Step-by-step explanation:
A graph can show the coordinates of interest: A(2/9, 1/3); B(2/3, -1/3).
Rearranging the equation to slope-intercept form, we have ...
3y = -4.5x +2
y = -1.5x +2/3
The slope is -1.5.
Final answer:
After solving for the missing coordinates, point A is (2/9, 1/3), and point B is (2/3, -1/3). Calculating the slope using these two points gives us a slope (m) of -3/2 for the line.
Explanation:
To find the missing coordinates for point A, we plug y=1/3 into the equation 4.5x+3y=2 and solve for x. Here is how:
4.5x + 3(1/3) = 2
4.5x + 1 = 2
4.5x = 1
x = 1 / 4.5
x = 2/9
Therefore, A(2/9, 1/3)
To find the missing coordinate for point B, we plug x=2/3 into the equation 4.5x+3y=2 and solve for y. Here is how:
4.5(2/3) + 3y = 2
3 + 3y = 2
3y = -1
y = -1/3
Therefore, B(2/3, -1/3)
To find the slope of the line, we use the two points A(2/9, 1/3) and B(2/3, -1/3). The slope formula is (y2 - y1) / (x2 - x1), which gives:
m = (-1/3 - 1/3) / (2/3 - 2/9)
m = (-2/3) / (4/9)
m = (-2/3) * (9/4)
m = -3/2, which is the slope of the line.
What is the area of the base of the cone below? Round the answer to the nearest tenth if necessary.
Answer:
19.5
Step-by-step explanation:
Answer:
Area of the base is 19.5 unit square.
Step-by-step explanation:
The volume of the cone is given as = 52 cubic inches
Height or h = 8 inches
Volume of the cone is given as : [tex]\pi r^{2} \frac{h}{3}[/tex]
[tex]52=3.14\times r^{2} \times\frac{8}{3}[/tex]
[tex]52= r^{2} \times 8.37[/tex]
[tex]r^{2} =6.212[/tex]
r = 2.492 inches
Now, area of the base is given as [tex]\pi r^{2}[/tex] because it is a circle.
Area = [tex]3.14\times2.492\times2.492[/tex]
= 19.499 ≈ 19.5 unit square.
which fraction is closer to 1/2 than to 0 or 1
A fraction is closer to 1/2 than to 0 or 1 if its numerator is more than half of 0 and less than half of the denominator. For instance, 3/5 is closer to 1/2 than to 0 or 1 because its numerator is more than half of 0 and less than half of 5.
Explanation:To determine which fraction is closer to 1/2 than to 0 or 1, consider the numerical value of the fractions in relation to 1/2. As a rule of thumb, if a fraction has a numerator that is half the denominator, it equals 1/2. When the numerator is less than half the denominator, the value is less than 1/2; when the numerator is over half the denominator, the value is greater than 1/2.
For example, if we take 1/3, it is clear that this value is less than 1/2 because the numerator, 1, is less than half of the denominator, 3. Comparatively, the fraction 2/3 is closer to 1 than to 1/2 since the numerator, 2, is greater than half of the denominator, 3.
Another example would be comparing 3/5 and 4/5 to 1/2. The fraction 3/5 has a numerator that is more than half of the denominator, making it closer to 1/2 than to 0 or 1, while 4/5 is closer to 1. Therefore, 3/5 is the fraction that is closer to 1/2 than to 0 or 1.
A fraction closer to 1/2 than to 0 or 1 falls in the range (> 1/3 but < 2/3); 5/8 is an example of such a fraction. An intuitive understanding and the use of a common denominator can aid in identifying and comparing these fractions.
Explanation:Determining which fraction is closer to 1/2 than to 0 or 1 involves understanding the number line and how fractions fall on it.
To identify such a fraction, it should be evident that any fraction greater than 1/2 will naturally be closer to 1, while any fraction less than 1/2 is closer to 0.
Therefore, we look for a fraction in the range (> 1/3 but < 2/3) to ensure it is closer to 1/2.
By using the intuitive sense of fractions, which is like having an understanding of fractions through visualization or practical examples, we can gauge the closeness to 1/2.
For instance, we know that 1/3 is less than 1/2, and similarly, 2/3 is more than 1/2.
Following this line of reasoning, the addition of fractions (1/3 + 1/6 = 1/2) indicates that 1/6 is the gap needed to reach from 1/3 to 1/2.
A fraction such as 5/8 would be a good example of a fraction closer to 1/2.
This fraction is more than 1/2 (4/8) but less than 3/4 (6/8), placing it comfortably closer to 1/2 on the number line.
Employing the common denominator strategy also helps to compare fractions effectively, by aligning them to a unifying reference point.
whast is the value of -3/4-(-3/8)?
Answer:
- 3/8
Step-by-step explanation:
- 3/4 - (-3/8)
= -3/4 + 3/8
= -6/8 + 3/8
= - 3/8
surface area is measured in cubic units or units3? true or false
Answer:
FALSE
Step-by-step explanation:
Area is a two-dimensional measure, so is measured in linear units that have a power of 2 (not 3).
_____
Please note that the exponent applies to linear units, such as meters or inches. Area can also be measured in area units with no exponent, such as barns or acres. (A "barn" is equal to 10^-28 m^2. It is used in nuclear physics to measure cross sectional areas of atomic particles. I think of it as one of the jokes built into modern physics, having its origins in the saying "can't hit the broad side of a barn.")
Final answer:
The statement that surface area is measured in cubic units is false. Surface area is measured in square units, whereas cubic units are used for volume. For example, the surface area of a cube is calculated as 6 times the area of one face, whereas volume is the cube of the side length.
Explanation:
The statement that surface area is measured in cubic units or units³ is false. Surface area is actually measured in square units (units²), not cubic units. Cubic units are used to measure volume, not surface area.
For example, the surface area of a cube that has a side length of 4 units would be 6(4x4) = 96 units², because a cube has 6 sides and each side would be a square with an area of 4x4.
On the other hand, the volume of the same cube would be 43 = 64 units³, because volume is calculated by multiplying length by width by height.
For example, if you take a large cube with a side length of 3 units, its total surface area would be 3 x 3 x 6 = 54 units² and the volume would be 33 = 27 units³.
However, if this cube is replaced with 27 small cubes, each with a side length of 1 unit, the combined surface area becomes much larger at 162 units², while the total volume remains the same at 27 units³.
The vertices of a triangle are A(−6, −3), B(0, 3), and C(−6, 0). Draw its image after a dilation with respect to the origin using a scale factor of 1/3. All I need to know is the points of the new triangle.
Thanks!
Answer:
A'(-2, -1), B'(0, 1), C'(-2, 0)
Step-by-step explanation:
When dilation is about the origin, the scale factor multiplies each individual coordinate.
A' = (1/3)A = (-6/3, -3/3) = (-2, -1) . . . . for example
The rest is mental arithmetic, since all given coordinate values are divisible by 3.
coefficient of x^2 in expansion of the binomial theorem (2x-1)^4 show your work
Answer:
24
Step-by-step explanation:
If you use Pascal's triangle, which I did, you will look at the 5th row of the triangle which contains the numbers 1, 4, 6, 4, 1
If we expand using a = 2x and b = -1, then the expansion looks like this:
[tex]1(2x)^4(-1)^0+4(2x)^3(-1)^1+6(2x)^2(-1)^2+4(2x)^1(-1)^3+1(2x)^0(-1)^4[/tex]
If you simplify all that down by multiplying, you'll get
[tex]16x^4-32x^3+24x^2-8x+1[/tex]
If you don't know how to use Pascal's triangle, you need to learn. It's so very cool!
number 7 and 8 and explain pls
Answer:
7. x=8
8. x=7
Step-by-step explanation:
7. The segment marked 30 is bisected by the segment marked x. So, you have a right triangle with legs x and 15 and hypotenuse 17. The Pythagorean theorem applies:
x^2 + 15^2 = 17^2
x^2 = 289 -225 = 64
x = √64 = 8
__
8. The arc subtended by the chord x is 360° -230° -65° = 65°. Since this is the same measure as the arc subtended by the chord of length 7, x will also be of length 7.
___
In fact, this geometry is impossible. The combination of circle radius, arc measure, and chord length cannot be obtained all in the same circle. The answer you get will depend on how you work the problem.
A traffic light near a museum is green for 30 seconds, yellow for 5 seconds, and red for 15 seconds. If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is .
Answer:
about 0.254
Step-by-step explanation:
The light is red for 0.3 of the period, so that is the probability one car is stopped. Probability 3 cars are stopped and 5 are not is 0.3^3·0.7^5, about 0.004538. In the group of 8 cars, there are 56 different ways 3 of the cars can be stopped, so your overall probability could be 56·0.004538 ≈ 0.254.
_____
Comment on the question
Many factors go into a driver's decision to stop at a light. Many factors go into the distribution of arrival times at a light. Here, the problem is only tractable if we assume that cars arrive at the light individually and at random times with respect to the light's fixed 50-second cycle. (This is possibly the case only early in the morning hours when traffic is at its lightest (not associated with bar closings or night shift changes).)
Please help asap
Inverse of a Function
Answer:
[tex]f^{-1} (x)=-\frac{1}{6}x+1[/tex]
Step-by-step explanation:
To find the inverse of a function in equation form, first I recommend changing the f(x) to a y:
y = -6x + 6
Next step is to switch the x and y:
x = -6y + 6
Now solve for the new y:
x - 6 = -6y and
[tex]-\frac{1}{6}x + 1=y[/tex]
You can put the inverse notation back in for y like I did in the answer section above.
simply
[tex]\sqrt[4 ]{162 {b}^{8} } [/tex]
Answer:
see below
Step-by-step explanation:
[tex]\sqrt[4]{162b^8}=\sqrt[4]{2\cdot 3^4b^8}=\sqrt[4]{2(3b^2)^4}\\\\=3b^2\sqrt[4]{2}[/tex]
the radius of a circle with an area of a circle with an area of 60 square centimeters is represented by the expression sqrt 60/x centimeters. what is another way of expressing the radius?
Answer:
[tex]\dfrac{2\sqrt{15\pi}}{\pi}[/tex]
Step-by-step explanation:
[tex]\displaystyle\sqrt{\frac{60}{\pi}}=\sqrt{\frac{4\cdot 15\pi}{\pi^2}}=\frac{2}{\pi}\sqrt{15\pi}[/tex]
Can someone please just make some equations for me? I would be so grateful. Look at the graph.
3) For Zach, if his heart beats 15 times in 10 seconds, his heart beats 1.5 times in 1 second. Multiply this by 25 to get the number of times his heart will beat in 25 seconds → 1.5 * 25 = 27.5 times per 25 seconds. 1.5 * 60 = 90 times per minute. 1.5 * 120 = 180 times per two minutes. Do the same for your heart beats. 14 beats per 10 seconds is 1.4 beats per second. 1.4 * 25 = 35 times per 25 seconds. 1.4 * 60 = 84 times a minute. 1.4 * 120 = 168 times per two minutes.
4) Zach's equation would be H = 1.5n and yours would be H = 1.4n
5) Your heat beats just a little bit slower than Zachs. Everyone is different and there are many different things that can affect heart rate. Maybe he walked a little more than you did or maybe he was stressing about something which made his heart beat a little faster.
I hope this helps you!