x is equal to 14.
To solve the equation X/111 = (5x - 28)/333 for x, we can cross-multiply to eliminate the denominators.
Multiplying both sides of the equation by 111 and 333, we get:
333 \(\times\) X = 111 \(\times\) (5x - 28)
Simplifying further:
333X = 555x - 3108
Next, we need to isolate the variable x. Let's subtract 555x from both sides of the equation:
333X - 555x = -3108
Combining like terms:
-222x = -3108
To solve for x, we can divide both sides of the equation by -222:
x = (-3108) / (-222)
Simplifying the division:
x = 14
Therefore, x is equal to 14.
Please note that it's important to double-check the calculations to ensure accuracy.
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sketch the graph of the function. f(x, y) = sin(x)
To sketch the graph of the function f(x, y) = sin(x), we can visualize it as a surface in a three-dimensional coordinate system. The graph of the function f(x, y) = sin(x) represents a surface in three-dimensional space. The graph depicts a series of sinusoidal waves as x varies.
To sketch the graph of the function f(x, y) = sin(x), we can visualize it as a surface in a three-dimensional coordinate system. In this case, the function depends only on the variable x, while y remains constant. As x changes, the value of sin(x) varies, resulting in a series of wave-like patterns along the x-axis.
When sketching the graph, we can plot various points on the surface by selecting different values for x and y, and evaluating sin(x) at those points. As x increases or decreases, the graph will display the familiar oscillating pattern of the sine function. The amplitude and frequency of the waves will depend on the range and step size chosen for x.
It is important to note that the graph of f(x, y) = sin(x) is a surface and not a curve in the traditional sense. It represents a continuous variation of the sine function along the x-axis, with the y-coordinate remaining constant.
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A high school science teacher has 78 students. of those students, 35 are in the band and 32 are on a sports team. there are 16 students who are not in the band or on a sports team. one student from the 78 students will be selected at random. let event b represent the event of selecting a student in the band, and let event s represent the event of selecting a student on a sports team. are b and s mutually exclusive events? responses no, because p(b∩s)=578. no, because the probability of, b intersection s, equals the fraction 5 over 78 . no, because p(b∩s)=4878. no, because the probability of, b intersection s, equals the fraction 48 over 78 . no, because p(b∩s)=6278. no, because the probability of, b intersection s, equals the fraction 62 over 78 . yes, because p(b∩s)=578. yes, because the probability of, b intersection s, equals the fraction 5 over 78 . yes, because p(b∩s)=6278.
It is deduced that b and s are not mutually exclusive events as A. No, because the probability of, b intersection s, equals the fraction 5 over 78
What is mutually exclusive?Two events are said to be mutually exclusive, if the two events cannot occur simultaneously, hence the intersection of such event defined as (BnS) will be 0.
We can obtain the probability of (BnS) as follows :
n(BnS) = number of students who are both in the band and in the sport team.
Let, this portion of students be represented as x :
(35-x) + (32-x) + x + 16 = 78
35 - x + 32 - x + x + 16 = 78
83 - x = 78
Collect like terms
83 - 78 = x
5 = x
Hence, n(BnS) = 5
Therefore, the probability of B and S will be :
n(BnS) / total number of students
P(BnS) = 5/78
Since, P(BnS) ≠ 0 ; then the events are not mutually exclusive
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oh please help me i need help with this problem!
Answer:
Its the first option
Step-by-step explanation:
Hope my answer helped :)
Determine the height of a picture when the total height of the picture with the frame is 38.5 cm.
A graph of the relationship modeled by the equation is shown in the image attached below.
If the graph continues, the point (28, 24) will not be on the graph.
The height of a picture when the total height of the picture with the frame is 38.5 cm would be 34.5 cm.
How to graph the relationship modeled by the equation?In this scenario, the total height of a picture in its frame (in centimeters) would be plotted on the y-axis of the graph while the height of the picture (in centimeters) would be plotted on the x-axis of the graph.
Based on the ordered pair (28, 24), we would determine if it lies on the graph of the equation:
y = x + 4
24 = 28 + 4
24 = 32 (False).
When the total height of the picture with the frame is 38.5 cm, the height of a picture can be calculated as follows;
y = x + 4
38.5 = x + 4
x = 38.5 - 4
x = 34.5 cm.
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Complete Question:
The equation y = x + 4 models the total height of a picture in its frame, y, in centimeters with respect to the height of the picture, x, in centimeters.
a. Graph the relationship modeled by the equation. Be sure to label the axes.
b. If the graph continues, will the point (28, 24) be on the graph?
c. Determine the height of a picture when the total height of the picture with the frame is 38.5 cm.
5. Use the digits 3, 4, 5, 6, 7 and 8 to complete the statement.
Answer:
Step-by-step explanation:
i don't see a statement but use 7 i guess
What signal word lets the reader know when Erica called Megan?
and
next
then
with
Answer:
next
Step-by-step explanation:
pls mark as brainliest
Answer:
Step-by-step explanation:B
a boat sails from port p to port q at a speed of 20 km/h along a straight course. once the boat reaches port q, it sails back to port p along the same course at a speed of 30 km/h. if the total time taken by the boat is 1 hour, find the distance between ports p and q.
Answer:
12
Step-by-step explanation:
Time=D/S
T1=PQ/20
T2=PQ/30
Total Time=T1+T2
1=PQ/20+PQ/30
PQ=12
draw any triangle on a paper a,b,c. measure sides with scale.write type of triangle.?
Answer:
Scalene Triangle
Step-by-step explanation:
Measure the side and if the none of the sides are equal then it will be a scalene triangle
169.2 is what percent of 128? Round to the nearest thousandth.
Answer:
169.2 is 132.1875% of 128
Step-by-step explanation:
PLS HELPPPPPPPPPPPPPP IM CRYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Answer:
1. 3.75 or 3/4
2. 5.3
3. 4.5
4. 3.4
Step-by-step explanation:
hope this helped i tried :/
1) 3.75
2) 5.33
3) 4.5
4) 3.42
Use Trigonometric substitution to eliminate the roots 1.1. 164+2 + 1 Use Trigonometric substitution to eliminate the roots 1.1. V64+2 + 1 1.2. V4z2 – 49
To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.
1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:
V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49
We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:
V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)
Here is a more detailed explanation of the substitution:
In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.
When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3
In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.
When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)
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when the base-$b$ number $11011 b$ is multiplied by $b-1$, then $1001 b$ is added, what is the result (written in base $b$)?
we express the result in base $b$: $b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)
To find the result when the base-$b$ number $11011_b$ is multiplied by $b-1$ and then $1001_b$ is added, we can follow these steps:
Step 1: Multiply $11011_b$ by $b-1$.
Step 2: Add $1001_b$ to the result from step 1.
Step 3: Express the final result in base $b$.
To perform the multiplication, we can expand $11011_b$ as $1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0$.
Now, we can distribute $b-1$ to each term:
$(1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0) \cdot (b-1)$
Expanding this expression, we get:
$(b^4 - b^3 + b^2 - b^1 + b^0) \cdot (b-1)$
Simplifying further, we get:
$b^5 - b^4 + b^3 - b^2 + b^1 - b^4 + b^3 - b^2 + b^1 - b^0$
Combining like terms, we have:
$b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0$
Now, we can add $1001_b$ to this result:
$(b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0) + (1 \cdot b^3 + 0 \cdot b^2 + 0 \cdot b^1 + 1 \cdot b^0)$
Simplifying further, we get:
$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$
Finally, we express the result in base $b$:
$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)
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intersecting lines r, s, and t are shown below. s t 23° r 106° x° what is the value of x ?
To find the value of x, we need to use the fact that when two lines intersect, the sum of the adjacent angles formed is equal to 180 degrees.
In this case, the angle formed between lines s and t is 23 degrees, and the angle formed between lines r and s is 106 degrees. Let's denote the angle between lines t and r as x.
Using the information given, we can set up the equation:
(106 degrees) + (23 degrees) + x = 180 degrees
Combine the known values:
129 degrees + x = 180 degrees
To isolate x, subtract 129 degrees from both sides of the equation:
x = 180 degrees - 129 degrees
x = 51 degrees
Therefore, the value of x is 51 degrees.
In conclusion, the value of x, the adjacent angles formed between intersecting lines t and r, is 51 degrees.
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Jayden had $8 last week. He now has $11. what is the percent of change?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
initial money = $8
final money = $11
percent of change = ?
Step 02:
percent of change
percent of change = ( final money - initial money ) / initial money * 100
= ( 11 - 8 ) / 8 * 100
= 3/8 * 100
= 0.375 * 100 = 37.5 %
The answer is:
The percent of change is 37.5 %
Can someone pretty pls help
Answer:
3÷4 = 0.75
Step-by-step explanation:
We are to find:
3÷ 4
3÷4 =
= 3 ÷ 4
= 3 × 1/4
= 3 × 0.25
= 0.75
Calculate the reliability of the following system:
0.90 0.90
0.90 0.90 0.85
0.85 0.85 0.92
The reliability of the given system is 0.4033.
To calculate the reliability of a system, we need to multiply the reliability values of all the components in the system. In this case, we have a system composed of three components with the following reliability values:
Component 1: 0.90
Component 2: 0.90 0.90 0.85
Component 3: 0.85 0.85 0.92
To find the overall system reliability, we multiply these values together:
System reliability = Component 1 reliability x Component 2 reliability x Component 3 reliability
System reliability = 0.90 x (0.90 x 0.90 x 0.85) x (0.85 x 0.85 *x 0.92)
System reliability ≈ 0.90 x 0.6831 x 0.6528 ≈ 0.4033
Therefore, the reliability of the given system is 0.4033.
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The number of minutes, m, that it takes to
print a batch of newspapers is inversely
proportional to the number of printers used,
n.
The equation of proportionality is m =
100
n
Calculate how long it will take to print a
batch of newspapers if 20 printers are
used.
If your answer is a decimal, give it to 1 d. p.
It will take 5 minutes to print a batch of newspapers if 20 printers are used.
What is proportionality?
Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.
We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:
m = k/n
where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:
m = 100/n
To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:
m = 100/20 = 5
So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.
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what is -4 {2 - y} + 3y = 3 {y - 4}
Complete the synthetic division problem below. -31 2 - 2 3 What is the quotient in polynomial form?
Answer:
the answer is // x^2 - x +1 (apex)
Step-by-step explanation:
If x = log, 4 and y = log, 3, find the value of log, 10 and lo9, (1.2) in terms of x and y.
The value of log 10 is 1 while the value of log 1.2 is y + x - 1.
What is Logarithm?A logarithm is a mathematical operation that determines how many times a certain number, called the base, is multiplied by itself to reach another number. Logarithms even describe how humans instinctively think about numbers.
The value of log 10 = 1 (this is a standard law), it cannot be further broken down
log 1.2 = log (12/10)
log 1.2 = log 12 - log 10
log 1.2 = log (3 x 4) - log 10
log 1.2 = log 3 + log 4 - log 10
but log 3 = y
log 4 = x
and log 10 = 1
Substituting the values
log 1.2 = log 3 + log 4 - log 10
log 1.2 = y + x - 1
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5.
12.8 ft
9 ft
9 ft
Answer:
what do we have to solve? surface area? volume?
Answer:
9 x 9 = 81
9 x 12.8 x 1/2 (basically just dividing by 2) = 57.6(area of 1 triangle), 57.6 x 4(there are 4 sides of triangles) = 230.4
Let's add all the given areas:
81 + 230.4 = 311.4 ft^2
Hi!! Can you please help with this question and explain how to solve it??
Find the height in centimeters of a square pyramid with a volume of 144 cm3 and a base edge length equal to the height. Give the approximate answer rounded to 2 decimal places.
9514 1404 393
Answer:
7.56 cm
Step-by-step explanation:
The volume is given by the formula ...
V = 1/3b²h . . . . where b is the base edge length, and h is the height.
Here we have V = 144 cm³, and b = h. Filling in these values and solving for h, we get ...
144 cm³ = 1/3h³
432 cm³ = h³
h = ∛432 cm ≈ 7.55953 cm
The height of the pyramid is about 7.56 cm.
Answer:
\(7.56cm\)
Step-by-step explanation:
Given that,
base length = Height
so,
\(volume = \frac{1}{3} {b}^{2} h \\ \)
We can also write this as( according to this question)
\(v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3} \)
let's solve
\(v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55\)
\(base = height = 7.55cm \\ \)
= 7.56cm
An angle measures 62.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answer: 55.9 degrees and 124.1 degrees
Step-by-step explanation:
What is geometric mean of 4 and 32???????
Answer: 18
Step-by-step explanation:
I just found the number in between
Answer:
8\(\sqrt{2}\)
Step-by-step explanation:
The geometric mean of 2 numbers a and b is \(\sqrt{ab}\) , then
\(\sqrt{4(32)}\)
= \(\sqrt{128}\)
= \(\sqrt{64(2)}\)
= \(\sqrt{64}\) × \(\sqrt{2}\)
= 8\(\sqrt{2}\)
13. 11 Consider the following function for maximization using simulated annealing: f(x) = Jx(1. 5 - x) in the range (0, 5). If the initial point is x(0) = 2. 0, generate a neighboring point using a uniformly distributed random number in the range (0, 1). If the temperature is 400, find the pbobability of accepting the neighboring point
The probability of accepting the neighboring point is 0.166.The probability of accepting the neighboring point ,
given the function f(x) = Jx(1.5 - x), the initial point x(0) = 2.0, and a uniformly distributed random number in the range (0, 1) is 0.166. Simulated annealing is a heuristic optimization method used to find the global maximum or minimum of a function.
In this case, we are trying to maximize the function f(x) = Jx(1.5 - x) in the range (0, 5) with an initial point x(0) = 2.0 and a uniform random number generator in the range (0, 1) to generate neighboring points.
The probability of accepting a neighboring point is determined by the Metropolis criterion, which takes into account the difference in function values between the current point and the neighboring point and the current temperature.
At a high temperature, the probability of accepting a worse point is higher, while at a low temperature, the probability of accepting a worse point is lower.
In this case, the temperature is given as 400. We first generate a neighboring point by adding a random number between (-1, 1) to the current point x(0) = 2.0.
Let's say the generated neighboring point is x(1) = 1.234. We then calculate the difference in function values between the current point and the neighboring point, which is Δf = f(x(1)) - f(x(0)) = Jx(1.5 - x(1)) - Jx(1.5 - x(0)).
If Δf is positive, the neighboring point is better than the current point and should be accepted. If Δf is negative, the neighboring point is worse than the current point and may still be accepted with a probability of exp(Δf/T), where T is the temperature.
In this case, exp(Δf/T) = exp(-(f(x(1)) - f(x(0)))/T) = exp(-(Jx(1.5 - x(1)) - Jx(1.5 - x(0)))/T) = exp(-(Jx(1.5 - 1.234) - Jx(1.5 - 2.0))/400) = 0.166. Therefore, the probability of accepting the neighboring point is 0.166.
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among all the pairs of numbers whose difference is 14 , find the pair with the smallest product. what is the product?
So, 15 and 1 is the pair of numbers whose difference is 14, with the smallest product as 15.
To find the pair of numbers with the smallest product whose difference is 14, we can start by taking the two numbers to be as close to each other as possible. This means we can take one number to be 14 less than the other. For example, we can take the numbers to be 15 and 1. The difference between these two numbers is 14, and their product is 15, which is the smallest product possible for a pair of numbers whose difference is 14.
So, 15 and 1 is the pair of numbers whose difference is 14, with the smallest product as 15.
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Question:
Cube A has a volume of 128 cm. If the edge lengths of cube B are half the size of the edge lengths of cube A, what is the volume of cube B?
cube A
cube B
V = 128 cm
V = ?
o 16 cm3
O 64 cm3
O 32 cm
Cannot be determined
Answer:
16 cm3
Step-by-step explanation:
4 x 4 x 8 = 128
2 x 2 x 4 = 16
Answer:16 cm
Step-by-step explanation:
4b+14=22
solve the equation
Answer:
B= 2
Step-by-step explanation:
4b+14=22
-14 -14
4b=8
/4 /4
b=2
The value of b in the expression is,
b = 2
We have to given that,
An expression to simplify,
4b + 14 = 22
Now, We can simplify it as,
4b + 14 = 22
Subtract 14 both side,
4b + 14 - 14 = 22 - 14
4b = 8
Divide by 4;
b = 8/4
b = 2
Therefore, The solution of expression is,
b = 2
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Subtract 8x10 from x² - 2x.
Answer:(4 x 103) x (2 x 107) = ( 4 x 2 ) x ( 103 + 7 ) = 8 x 10 10.
Step-by-step explanation:
The obtained expression after subtracting 8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Is given expression is, Subtract 8x¹⁰ from x² - 2x.
In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
=8x¹⁰-x²+2x
=8(x²)⁵-x²+2x
=x²(8x⁴-1)+2x
Thus, the obtained expression after subtracting 8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.
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Which integer represents 8ºC below 0?
8ºC below 0 is -8ºC (negative eight degrees celsius).
Below means subtract. 0 - 8 = -8.