Answer:
y = 0.5x + 4, or y = 1/2x + 4 (if you prefer fractions)
Step-by-step explanation:
y = mx + b (slope intercept form / standard form) ; m = 0.5 or 1/2, b = 4.
m = linear coefficient/slope(denoted by a in a 1 degree binomial)
b = constant coefficient / y-intercept (denoted by b in a 1 degree binomial)
to convert this equation into a standard form equation. You need to isolate y and leave the coefficients on the other side.
0.5x = y - 4
0.5x (+4) = y - 4 (+4)
0.5x + 4 = y
y = 0.5x + 4
Answer:
y=0.5x+4
Step-by-step explanation:
0.5x= y-4
add 4 on both sides
and then you get:
y=0.5x+4
Complete the ordered pair to m x+y=7 (4.)
The completed ordered pair is (4, 7 - 4m).
Given: The equation m x + y = 7. To complete the ordered pair, we need one of the variables (m, x, y) and the other one must be known. Let's assume that the value of x is 4 and we need to find the value of y. Then the ordered pair is (4, y).Putting the value of x in the equation we have,=> m x + y = 7=> m(4) + y = 7=> 4m + y = 7 => y = 7 - 4m.
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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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Help please. I need this to be explained in order for brainliest.
The value of the angle cos(L)° will be 0.42.
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental area of study in mathematics, with applications in a wide range of fields such as physics, engineering, navigation, architecture, and more.
Given that in a triangle JKL the side KL is 15 and the side JK is 36. The value of cos(L)° is the ratio of the side JK and KL.
cos(L)° = JK / KL
cos(L)° = 15/36
cos(L)° = 0.42
Therefore, the value of the angle cos(L)° will be 0.42.
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i don't know how to do this
Step-by-step explanation:
the slope-intercept form of a line (= linear function) is
y = ax + b
"a" is the slope of the line and represents the ratio "y coordinate change / x coordinate change" when going from one point to another on the line.
"b" is the y-intercept (the y value when x = 0; in other words, the y value where the line intercepts the y axis).
so, for the slope, let's compare 2 points. and let's pick just the first 2.
(1, 8) to (2, 11).
x changes by +1 (from 1 to 2).
y changes by +3 (from 8 to 11).
so, the slope is +3/+1 = 3/1 = 3
and our equation looks like
y = 3x + b
to get b, we use one point. I pick the first one for the smallest numbers :
8 = 3×1 + b = 3 + b
5 = b
the full line equation is therefore
y = 3x + 5
The residents of a city voted on whether to raise property taxes the ratio of a yes votes to no votes was 5 to 4 if there were 4923 total votes how many yes votes were there ?
Answer:
2,735 yes votes
Step-by-step explanation:
First we have too determine the ratio of yes votes to the total number of votes.
We can rationalize thus
If there are 5 yes votes and 4 no votes, the total number of votes = 5+ 4 = 9
So 5/9th of the total votes are yes votes
If the total number of votes = 4923 , number of yes votes = 5/9 x 4923
= 2,735 yes votes ANSWER
We can check to see if our reasoning is correct:
Total number of no votes = 4923 - 2735 = 2188
Yes votes to Nay votes = 2735 : 2188
As a fraction:
2735 / 2188 = 1.25
1.25 = 1 1/4 = 5/4 which is the ratio of yes to no votes and tallies with the question data
what is the explicit formula for this sequence? -7,-3,1,5,…
Answer:
\(a_n=4n-11\)
Step-by-step explanation:
The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:
\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)
Explain in words the difference between alb and a (b) (i) Explain the meaning of a div b and a mod b. (ii) Prove or disprove that if a, b and d are integers with d > 0, then (a + b) div da div d+ b div d. (2 marks) (2 marks) (2 marks)
The difference between `a/b` and `(a/b): `The difference between `a/b` and `(a/b)` is that `a/b` denotes a fraction while `(a/b)` means the floor function of a/b.
The floor function of a number is the largest integer less than or equal to that number. Thus, `(a/b)` denotes the greatest integer that does not exceed a/b.
(i) The meaning of `a div b` and `a mod b`:
The quotient of `a` and `b` is denoted by `a div b`.
The remainder when `a` is divided by `b` is denoted by `a mod b`.
In other words, when `a` is divided by `b`, `a` leaves a remainder of `r` if `r` is between `0` and `b-1`.
Thus, `a = bq + r` where `0 ≤ r ≤ b-1`.
ii. Prove or disprove that if a, b, and d are integers with d > 0, then (a + b) div d ≤ a div d + b div d.Proof:
Let `a, b, d` be integers such that `d > 0`.
Then, `(a+b) = [(a+b) div d]d + (a+b) mod d`...(1)
`a = [a div d]d + a mod d`...(2)
`b = [b div d]d + b mod d`...(3)
Adding equations `(2)` and `(3)`, we get `a+b = [(a+b) div d]d + a mod d + b mod d`
Since `a mod d` and `b mod d` are less than `d`, it follows that `a mod d + b mod d < d`.
Therefore, `[(a+b) div d] = floor[(a+b)/d] ≤ (a+b)/d`We can substitute the above inequality in equation `(1)` and simplify to get:(a+b) div d ≤ a div d + b div d + 1This shows that `(a+b) div d ≤ a div d + b div d` is true in general.
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without using dividing powers of 10 to write three division expressions that are each equivalent to 35.78 / 6
Answer:
Step-by-step explanation:
find the volume of a composite figure.
6ft, by 4ft, by 4ft, by 6ft, by 12ft equals
The Volume of the given composite shape is: 432 ft³
What is the Volume of the composite figure?The formula for the volume of a triangular prism is:
Volume = base area * height
The volume of a cuboid is:
Volume = Length * Width * Height
Thus:
Volume of composite shape = (6 * 12 * 4) + (6 * 6 * 4)
= 432 ft³
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1/2
3/4
b
5/6
7/8
Lines a and b are parallel What is the measure of <8 if ~1 measures 110°?
A)
35
B)
55
a
70°
D)
110
Answer:
i think it's B, I'm not 100% sure
Which of the following correlation coefficients represents the strongest relationship between two variables? -.75 +.60 .00 +.30
The correlation coefficient that represents the strongest relationship between two variables is -0.75.
In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.
The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.
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If f(x)=2x+6. And f(x)=12. What does x=__
Answer:
x=3
Step-by-step explanation:
f(x)=2x+6
f(x)=12
Hence:
2x+6=12
2x+6-6=12-6
2x=6
x=6/2
x=3
25 cents:R4have a good night
Answer:
“It is hard enough to remember my opinions, without also remembering my reasons for them!”
- Friedrich Nietzsche
Step-by-step explanation:
Good Night ig-Answer:
Goog nigh
Ig byeeeeeeeeeee
A cylinder is sliced in such a way that the plane cuts in a direction perpendicular to the base,what is the resulting cross section?
If a cylinder is sliced in a direction perpendicular to the base, the resulting cross section would be a rectangle.
A cylinder has a circular base, and a perpendicular slice would cut through the circular base and create a flat rectangular shape.
To visualize this, imagine a cylinder as a can of soup. If you were to cut the can of soup straight down the middle, perpendicular to the base, you would create a cross section that is a rectangle. This rectangular cross section would have a width and a length, which would be equal to the diameter of the circular base of the cylinder.
In geometry, a rectangle is defined as a quadrilateral with four right angles, and opposite sides that are equal in length. Therefore, a rectangular cross section of a cylinder would also have these properties.
In summary, if a cylinder is sliced in a direction perpendicular to the base, the resulting cross section would be a rectangle with equal width and length, and four right angles.
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There are 5 cups of oatmeal in a container. Stella eats 1/3 cup of oatmeal every day for breakfast. In how many days will Stella finish all the oatmeal in the container?
Answer:
15 days
Step-by-step explanation:
Since there are 5 cups and she eats it 1/3 times a day if you think about it, its like 5 times 3.
Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.s = 31.3, t = 13.3
The value of sin(θ) is approximately 0.921 and the value of cos(θ) is approximately 0.391.
To find the value of each variable using sine and cosine, we need to set up a right triangle with the given information. Let's label the sides of the triangle as follows:
s = 31.3 (opposite side)t = 13.3 (adjacent side)h (hypotenuse)Using the Pythagorean theorem, we can find the length of the hypotenuse:
h2 = s2 + t2
h2 = 31.32 + 13.32
h2 = 979.69 + 176.89
h2 = 1156.58
h = √1156.58
h ≈ 34.0
Now that we know the length of the hypotenuse, we can use sine and cosine to find the values of the variables:
sin(θ) = s / h
sin(θ) = 31.3 / 34.0
sin(θ) ≈ 0.921
cos(θ) = t / h
cos(θ) = 13.3 / 34.0
cos(θ) ≈ 0.391
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why is it necessary to apply the finite population correction factor when a sample is a significant part of the population? multiple choice question. if a sample is a larger part of the population, it will give a better estimate. if a sample is a larger part of the population, it will give a less accurate estimate. for a small population, samples are not independent, and thus give less accurate results.
When taking a sample from a finite population, it is important to consider the size of the sample relative to the size of the population.
If the sample is a significant part of the population, meaning that it represents a large proportion of the total population, then the finite population correction factor needs to be applied to adjust for the reduced variance in the estimate. The reason for this is that as the sample size approaches the population size, the variability in the estimate decreases. This is because the sample becomes less representative of the population and more reflective of the population itself. Therefore, the standard error of the estimate decreases, making it necessary to apply the correction factor to account for this. If the correction factor is not applied, the standard error of the estimate will be underestimated, leading to confidence intervals that are too narrow and hypothesis tests that are overly confident. This can result in incorrect conclusions being drawn from the data. It is important to note that the need for the finite population correction factor is not dependent on the accuracy of the estimate. Even if the sample is a larger part of the population and gives a better estimate, the correction factor must still be applied to account for the reduced variance in the estimate. In summary, the finite population correction factor is necessary when the sample is a significant part of the population to adjust for the reduced variance in the estimate. This ensures that confidence intervals and hypothesis tests are accurate and correct conclusions can be drawn from the data.
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I need help plsssssssssss
The ordering of the number 2/3 and 7/11 is given as 7/11 < 2/3
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic
Given the number 2/3 and 7/11 needs to have a common denominator.
Hence:
2/3 = (2/3) * (11/11) = 22/33
Also:
7/11 = (7/11) * (3/3) = 21/33
Therefore:
7/11 < 2/3 because 21/33 < 22/33
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Plz HELP!!!!!!!!!!!!!!!!!!!!!
They are Parallel, Intersecting, and perpendicular, if it's helpful let me know
1. AGES Mel is 3 years older than Rahfat
and Aurelio is twice as old as Mel. The
sum of their ages is 57. How old
is Mel?
Answer:
15
Step-by-step explanation:
Mel's Age = x
Rahfat's Age = x-3
Aurelio's Age = 2x
2x + x +x -3 = 57
4x -3 = 57
4x = 60
x = 15
Plz I need urgent help
Find each angle measure.
Answer:
1. 47 degrees
2. 119 degrees
3. 97 degrees
4. 62 degrees
Step-by-step explanation:
1. Just subtract 180 by 133 and there's your answer
2. The lines are marked as parallel which causes the two angles listed to be equal
3. Subject 83 from 180 and that's it
4. Find the x value that makes the two equal. Then plug the x value in and this is your angle
Determine the probability of precipitation (PoP) using the formula below and the following
PoP = (C * A) * 100 percent
Where C is the confidence that precipitation will occurs somewhere in the forecasted area, and A equals the percentage of the area that will receive measured precipitation if it occurs.
a. A forecaster expresses confidence that there is an 80 percent chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90 percent of the area.
b. A forecaster expresses confidence that there is a 20 percent chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10 percent of the area.
The correct answer is a) the probability of precipitation is 72%. and b) the probability of precipitation is 2%.
The given formula to determine the probability of precipitation (PoP) is PoP = (C * A) * 100 percent where C represents the confidence that precipitation will occur somewhere in the forecasted area and A represents the percentage of the area that will receive measured precipitation if it occurs.
(a) If a forecaster expresses confidence that there is an 80% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 80%A = 90%PoP = (80% * 90%) * 100%
PoP = 72%.
Therefore, the probability of precipitation is 72%.
(b) If a forecaster expresses confidence that there is a 20% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 20%A = 10%PoP = (20% * 10%) * 100%PoP = 2%
Therefore, the probability of precipitation is 2%.
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determine type of triangle PLZZ ASAP
Answer:
scalene right
Step-by-step explanation:
no side congruent and right
help me plzzzzzzzzzzzzzzzzzzzzz
Answer:
$1.25
Step-by-step explanation:
10-2.50=7.5
7.5/6=1.25
hope this helps :3
Answer: $1.25
Step-by-step explanation:
10-total
(1 notebook)-2.50, 6 pens
10-2.50=7.50
7.50/6(pens)=1.25
help me out thank you have a wonderful day!
Answer:
x= 1/4
Step-by-step explanation:
i hope this helps :)
Suppose that there are 9 faculty members in the math department and 11 in the computer science department. How many ways are there to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department
There are 9240 ways to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department.
It is given that there are 9 faculty members in the math department and 11 in the computer science department.
\(C^{9} _{3} * C^{11} _{4}\)
\(= \frac{9!}{(9-3)!3!} * \frac{11!}{(11-4)!4!}\\= 28 * 330\\= 9240\)
Therefore, there are 9240 ways to select the committee.
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A circle has a circumference of 6. It has an arc of length 1.
What is the central angle of the arc, in degrees?
The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:
6= πd and then divide both sides of the equation by π you get that d = 1.90
To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:
1 = 0.9549θ
Answer:
60
Step-by-step explanation:
1/6 x 360
Central angle is equal to measure of intercepted arc.
60 degrees
2) The box-and-whisker plot below represents the math test scores of 20 students.
HHHHHHHHHHHHHH
60
100
What percentage of the test scores are less than 722
a rectangular tank that is 1372 ft3 with a square base and open top is to be constructed of sheet steel of a given thickness. find the dimensions of the tank with minimum weight
The dimensions of the tank with minimum weight is height= 7 and width and length= 14.
The minimum surface area implies that the tank has minimum weight.
Given that the base is square, its width is equal to its length.
Let x= the base width and length of the tank.
Let h = the height .
We are given the volume of the tank that is 1372 ft^3. The formula is given by
V = hx^2
We're given that V = 1,372 ft^3, so
hx^2 = 1,372
h = 1,372 / x^2 ----------(equation 1)
Surface area can be calculated using the below given formula.
A = x^2 + 4xh
Substituting the value of euation 1, h in A, we get,
A = x^2 + 4x(1,372 / x^2)
= x^2 + 5,488 / x
To get the minimum surface area to get the minimum weight, we need to differentiate A with respect to x and equate it to zero.
dA/dx = 2x - 5,488 / x^2 = 0
2x^3 - 5,488 = 0
x =\(\sqrt[3]{\frac{5,488}{2} }\)
x= 14
We got the value of x, we substitute the value in equation 1, we get the value of h.
h = 1,372 / 14^2
h= 7
So, the dimensions of the tank with minimum weight are width and length is 14 and height is 7.
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Solve for f.
Round your answer to 2 decimals.
9f = {(12f – 2)
Answer:
f=0.67
Step-by-step explanation:
Let's solve your equation step-by-step by isolating f.
9f=12f−2
Step 1: Subtract 12f from both sides.
9f−12f=12f−2−12f
You get:
−3f=−2
Step 2: Divide both sides by -3.
−3f/−3 = −2/−3
You get:
f= 2/3, or f= 0.67
Hope this helps! :)