The constant of variation based on the information is one half.
How to illustrate the information?From the information given, when x is 2, y is 1, when x is 4, y is 2, etc. It should be noted that this is a direct variation.
This will be illustrated as:
y = kx
when y = 1, x = 2.
1 = 2k
Divide both side by 2.
k = 1/2
Therefore, the constant of variation is 1/2.
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Three numbers in the interval $\left[0,1\right]$ are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area
Let [tex]a,b,c[/tex] be the randomly selected lengths. Without loss of generality, suppose [tex]a
[tex]P(A + B \ge C) = P(A + B - C \ge 0)[/tex]
where [tex]A,B,C[/tex] are independent random variables with the same uniform distribution on [0, 1].
By their mutual independence, we have
[tex]P(A=a,B=b,C=c) = P(A=a) \times P(B=b) \times P(C=c)[/tex]
so that the joint density function is
[tex]P(A=a,B=b,C=c) = \begin{cases}1 & \text{if }(a,b,c)\in[0,1]^3 \\ 0 & \text{otherwise}\end{cases}[/tex]
where [tex][0,1]^3=[0,1]\times[0,1]\times[0,1][/tex] is the cube with vertices at (0, 0, 0) and (1, 1, 1).
Consider the plane
[tex]a + b - c = 0[/tex]
with [tex](a,b,c)\in\Bbb R^3[/tex]. This plane passes through (0, 0, 0), (1, 0, 1), and (0, 1, 1), and thus splits up the cube into one tetrahedral region above the plane and the rest of the cube under it. (see attached plot)
The point (0, 0, 1) (the vertex of the cube above the plane) does not belong the region [tex]a+b-c\ge0[/tex], since [tex]0+0-1=-1<0[/tex]. So the probability we want is the volume of the bottom "half" of the cube. We could integrate the joint density over this set, but integrating over the complement is simpler since it's a tetrahedron.
Then we have
[tex]\displaystyle P(A+B-C\ge0) = 1 - P(A+B-C < 0) \\\\ ~~~~~~~~ = 1 - \int_0^1\int_0^{1-a}\int_{a+b}^1 P(A=a,B=b,C=c) \, dc\,db\,da \\\\ ~~~~~~~~ = 1 - \int_0^1 \int_0^{1-a} (1 - a - b) \, db \, da \\\\ ~~~~~~~~ = 1 - \int_0^1 \frac{(1-a)^2}2\,da \\\\ ~~~~~~~~ = 1 - \frac16 = \boxed{\frac56}[/tex]
erena is writing an expression that is equivalent to 12ab – 6b, but she has not completed it.
__?__ (2 a minus 1)
What is missing from the expression?
The missing term in the expression ___( 2a-1) is 6b.
What is an Expression?An expression is an algebraic statement that consists of variables, constants, and mathematical operators.
The expression 12ab-6b is equivalent to
6b( 2a-1)
(By taking the common factors out of the given expression.)
Therefore, the missing term in the expression is 6b.
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Let R be a relation in N defined by R = { ( 1 + x , 1 +^2 ) ∶ ≤ 4, ∈ } Find
i) R ii) domain of R iii) range of R
1. R= {(2, 2), (3, 5), (4, 10), (4, 17)}
2. Domain = {1, 2, 3, 4}
3. Range = {2, 3, 4, 5, 10, 17}
What is Domain and range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
Given:
R = { ( 1 + x , 1 + x^2 ) ∶ x≤ 4, ∈ }
1) R= {(2, 2), (3, 5), (4, 10), (4, 17)}
2) Domain = {1, 2, 3, 4}
3) Range = {2, 3, 4, 5, 10, 17}
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Find the value of z.
Answer:
z = 110°
Step-by-step explanation:
Angles z and the one marked 70° form an linear pair, hence are supplementary.
z = 180° -70° = 110°
Angles where chords crossThe angle made by two chords is half the sum of the arcs intercepted by those chords. Here, that means ...
70° = 1/2(60° +x) ⇒ x = 140° -60° = 80°
The arc w completes the circle of 360°, so we have ...
w +x +79° +60° = 360° ⇒ w = 360° -219° = 141°
Finally, z is the average of w and 79°:
z = (w +79°)/2 = (141° +79°)/2 = 110° . . . as above
4(2x-1)+2x+2= 28
solve for X
Answer:
X=3
Step-by-step explanation:
First you can distribute the 4 to 2x-1 making is 8x-4
8x-4+2x+2=28
Now add like terms
8x+2x-4+2=28, 10x-2=28
Add 2 to both sides
10x=30
Divide both sides by 10
x=3
Solve the following system of equations. Express your answer as an ordered
pair in the format (a,b), with no spaces between the numbers or symbols.
2x + 7y = -1
4x - 3y = - 19
Isolate x:
2x + 7y = -1
2x = -1 -7y
x = -1/2 - 7/2y
Substitute the equation of x:
4x - 3y = -19
4(-1/2 - 7/2y) - 3y = -19
-2 - 14 - 3y = -19
-3y = -19 + 14 + 2
-3y = -3
y = 1
Substitute to find x:
2x + 7y = -1
2x + 7(1) = -1
2x = -1 - 7
2x = -8
x = -4
(-4, 1)
What are the rules of the system of equations?
Multiply one or both equations through an integer in order that one time period has the same and contrary coefficients within the equations. Add the equations to provide a single equation with one variable. clear up for the variable. alternative the variable back into one of the equations and resolve for the other variable.
Conclusion: A system of equations is fixed of 1 or greater equations related to some of the variables. The solutions to systems of equations are the variable mappings such that every one component equations are satisfied—in other phrases, the locations at which all of these equations intersect.
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why i`m very weak in maths
Answer:
your slow
Step-by-step explanation:
Step-by-step explanation:
good study habits will help! study before you plan on sleeping and designate times to do your work
I need help asap! Thank you guys
Answer:
Y intercept: (0,2) Slope: 1/3
Step-by-step explanation:
X is horizontal. Y is vertical the slope touches at (0,2).
The slope goes up by one and right by three cause it connects to the line
for the second one all you would have to do is increase the slope first number like 4/3
If the sum of three numbers is 456 and the first two numbers are 121.3 and 175.4, what
is the average of the three numbers?
Answer:
159.3
Step-by-step explanation:
456 - 121.3 = 334.7
333.7 - 175.4 = 159.3
Hope this helped
Answer:
152
Step-by-step explanation:
You actually don't need to find the thirds number. Just by taking 456 and dividing it by three, you will get your answer and the average of the three numbers.
A recipe for nut bread calls for 1/4 cup of walnuts and 2/6 cup
cup of pecans. What is
the total amount of walnuts and pecans needed for the recipe?
Answer:
[tex]\sf Total \ amount \ of \ walnuts \ and \ pecans \ needed = \dfrac{7}{12}[/tex]
Step-by-step explanation:
Fraction addition:[tex]\sf Amount \ of \ walnut \ needed = \dfrac{1}{4}[/tex]
[tex]\sf Amount \ of \ pecans \ needed =\dfrac{2}{6} =\dfrac{1}{3}[/tex]
To find the total amount of walnut and pecans, we have to add the fractions.
Find the LCM of the denominators.Find equivalent fractions using the LCMNow, add the fractionsLCM of 4 & 3 = 12
Equivalent fractions:
[tex]\sf \dfrac{1}{4}=\dfrac{1*3}{4*3}=\dfrac{3}{12}\\\\\dfrac{1}{3}=\dfrac{1*4}{3*4}=\dfrac{4}{12}[/tex]
Now, add
[tex]\sf \dfrac{3}{12}+\dfrac{4}{12}=\dfrac{3+4}{12}[/tex]
[tex]\sf = \dfrac{7}{12}[/tex]
if you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade
Answer: 42.308%
Step-by-step explanation:
Point Y is the center of dilation. Triangle A B C is dilated to form triangle A prime B prime C prime.
If CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Using the rule of dilation, 5/4, the length of C'A' is: A. 10 units.
What is Dilation?Dilation is a form of transformation that creates a new image that is similar to the original one.
The images formed are similar images shown in the diagram given, therefore, using the rule of dilation, Dy = 5/4, we would have:
CA × 5/4 = C'A'
Plug in the given value
8 × 5/4 = C'A'
10 = C'A'
C'A' = 10 units
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help meeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
80 more points ez ez!
Answer:
{(-3, -2), (-4, 3), (-1, 0), (3, -7)}
Step-by-step explanation:
When you find the inverse of a function you swap the x and the y. So let's look at a couple examples and see what happens to the x and y values
Radical:
[tex]y=\sqrt{x}[/tex]
So let's just look at perfect squares so it's a bit easier to understand
(0, 0)
(4, 2)
(9, 3)
Now let's find the inverse:
[tex]x=\sqrt{y}[/tex]
Now to make this concept a bit easier to understand let's leave it in this form. Well the first notable thing, is that any operations applied to y will now apple to x, and any operations applied to x will apply to y (in this case the square root).
So if I input 9 as the y, the x will be 3
If I input 4 as y, the x will become 2
Some points are
(0, 0)
(2, 4)
(9, 3)
You'll notice the x and y values are swapped, well it's simply because you swap the x and y's place. this is also why the domain and range are swapped
So given the points {(-2, -3), (3, -4), (0, -1), (-7, 3)} you simply swap the x and y to get: {(-3, -2), (-4, 3), (-1, 0), (3, -7)}
Answer:
D
Step-by-step explanation:
Members of the swim teams at a competition want to wash their hair. The bathroom has less than 5600 liters of water and at most 1.5 liters of shampoo.
70L+60S < 5600 represents the number of long-haired members L and short-haired members S who can wash their hair with less than 5600 liters of water.
0.02L+0.01S ≤1.50 represents the number of long-haired members and short-haired members who can wash their hair with at most 1.5 liters of shampoo.
Does the bathroom have enough water and shampoo for 35 long-haired members and 40 short-haired members? Does the bathroom have enough water and shampoo for 35 long-haired members and 40 short-haired members based on the feasible region? Why or why not?
Yes, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.
Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.
For 35 long haired and 40 short haired member.
Put this values in the given equation.
For water 70L+60S < 5600
70 x 35 + 60 x 40
2450+2400
4850 <5600
inequality holds
For shampoo 0.02L+0.01S ≤ 1.50
0.02 x 35 + 0.01 x 40
0.7 + 0.4
1.1 < 1.50
inequality holds
Thus, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.
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How would you set this problem up to find x?
Answer:
33x - 13 = 13x + 7
Step-by-step explanation:
If "G" is the midpoint of line FH, then both segments (lines FG and GH) must be the same length. Therefore, to find "x", you can set both segments equal to each other. After doing this, you can simplify and isolate to find "x".
FG = 33x - 13
GH = 13x + 7
FG = GH
33x - 13 = 13x + 7
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming that your equation should}\\\huge\textbf{look like that: }[/tex]
[tex]\mathbf{33x - 13 = 13x + 7}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathbf{33x - 13 = 13x + 7}[/tex]
[tex]\huge\textbf{SUBTRACT 13x to BOTH SIDES}[/tex]
[tex]\mathbf{33x - 13 - 13x = 13x + 7 - 13x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{20x - 13 = 7}[/tex]
[tex]\huge\textbf{ADD 13 to BOTH SIDES}[/tex]
[tex]\mathbf{20x - 13 + 12 = 7 + 13}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{20x = 20}[/tex]
[tex]\huge\textbf{DIVIDE 20 to BOTH SIDES}[/tex]
[tex]\mathbf{\dfrac{20x}{20} = \dfrac{20}{20}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = \dfrac{20}{{20}}}[/tex]
[tex]\mathbf{x = 1}[/tex]
[tex]\huge\text{Answer: \boxed{\mathsf{33x - 13 = 13x + 7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A simple random sample of size n=40 is obtained from a population with a mean of 20 and a standard deviation of 5. Is the sampling distribution normally distributed? Why?
If the sample size is n=40 ,mean of 20 and a standard deviation then the sampling distribution is normally distributed.
Given sample size is 40, sample mean is 20, sample standard deviation is 5.
We have to find whether the distribution is normally distributed or not.
Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off simultaneously towards either extreme. It may be one tailed or two tailed also.
Yes the given distribution whose sample size is 40, sample mean of 20 and sample standard deviation of 5 is normally distributed as the sample size is greater than 30.
Signs of normal distribution are:
Symmetric bell shapemean and median are equal both located at the center of the distribution68% approximately equals 68% falls within 1 standard deviation of the mean.Hence the sampling distribution is normally distributed.
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Use the quadratic formula to determine the exact solutions to the equation.
6x2+4x−3=0
ye answer's here
I need help finding the measurements I’m not good at using protractors
Answer:
a. What is the measure of ∠CAT? Answer: 70°
b. What is the measure of ∠BAR? Answer: 50°
c. What is the measure of ∠RAT? Answer: 110°
d. What is the measure of ∠CAB? Answer: 130°
e. What is the measure of ∠BAT? Answer: 60°
Step-by-step explanation:
I just looked at the degrees of the protractor.
Hope this helps!
If not, I am sorry.
PLEASE HELPPP
Which statements about this system of equations are true? Select three options.
Options in picture:
The statement about the system of of equations that are true are as follows:
x = -34 / 9y = 7 / 9How to solve system of equation?The system of equation can be solved as follows;
2x - 7y = - 13
2x + 11y = 1
18y = 14
y = 14 / 18
y = 7 / 9
2x = 1 - 11(7 / 9)
2x = 1 - 77 / 9
2x = 9 - 77 / 9
2x = -68 / 9
cross multiply
18x = -68
x = -68 / 18
x = -34 / 9
Hence, the statement about the system of of equations that are true are as follows:
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A cheerleading team plans to sell t-shirts as a fundraiser. The team's
goal is to make a profit of at least $1248. The profit on each t-shirt sold
is $6.50. The team's goal is written as the inequality shown below.
6.50t ≥1248 where t=number of t-shirts sold
Which graph represents the solution to this inequality?
Answer:
t ≥ 192
Step-by-step explanation:
To isolate t in the inequality 6.50t ≥1248, divide by 6.50 on both sides. There you are left with t ≥ 192 which means the cheerleading team must sell 192 t-shirts or more to make their profit goal. Graph this using a closed circle at 192 moving upwards. (You didn't include a picture of the given graphs in your problem)
0.127450980392 as fraction
[tex]\frac{1820728291}{14285714286}[/tex]
Prove that
1/(sec x - 1) + 1/(sec x + 1) is equal to
2cos x × cosec^2 x
Answer:
Step-by-step explanation:
[tex]1+tan^2\theta=sec^2\theta\\tan^2\theta=sec^2\theta -1 \\tan^2\theta=(sec\theta-1)(sec\theta+1)\\\implies \frac{1}{sec\theta-1} =\frac{sec\theta+1}{tan^2\theta} \\\\and \quad \frac{1}{sec\theta+1} =\frac{sec\theta-1}{tan^2\theta} \\\\ \frac{1}{sec\theta-1} + \frac{1}{sec\theta+1} = \frac{sec\theta+1}{tan^2\theta} + \frac{sec\theta-1}{tan^2\theta}\\\\=\dfrac{2sec\theta}{tan^2\theta}\\\\=\dfrac{2cos^2\theta}{cos\theta.sin^2\theta}\\\\\\=2cos\theta.cosec^2\theta[/tex]
Please help me with this question.....
[tex]\angle PYZ=116^{\circ}[/tex] (angles on a line add to 180 degrees)
[tex]\angle ZYQ=58^{\circ}[/tex] (angle bisector)
[tex]\angle XYQ=122^{\circ}[/tex] (angle addition postulate)
[tex]\angle QYP=58^{\circ}[/tex] (angle bisector)
Reflex [tex]\angle QYP=302^{\circ}[/tex] (an angle and its reflex angle add to 360 degrees)
Instructions: Find the missing segment in the image below. HELP PLEASEE !!
The missing segment in the image below is 78 units.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The ratio or two corresponding sides of similar shapes are in the same proportion.
Let x represent the missing side, hence:
(x + 26)/26 = 48/12
x =78
The missing segment in the image below is 78 units.
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The population of weights of a particular fruit is normally distributed, with a mean of 535 grams and a standard deviation of 13 grams. If 8 fruits are picked at random, then 18% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.
Pn(Z>zp)=1−p%
Given a variable X following a normal distribution with mean μ and standard deviation σ, the area below the curve that corresponds to all values that are less than a that is, X<a
is the probability P(X<a). This probability is usually calculated by converting the variable X to a standard normal variable Z (forming z scores) defined by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The variable Z follows the standard normal distribution with a mean of 0 and a standard deviation of 1.
The standard normal probabilities are typically found by using the standard normal tables or other computational means such as calculators or software.
Pn(Z>zp)=1−p%
Here Pn is the probability for the standard normal variable.
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Choose the 5 numbers that give a remainder of 5 when divided by 7 ASAp
Answer:
was there a list to choose from
Step-by-step explanation:
19, 26, 33, 40, 47
In the diagram below, all angles are given in
degrees (°).
Find the value of x.
60
x +90
X
3x
Not drawn accurately
Answer:
30°
Step-by-step explanation:
x + 90 = 2 × 60 ( angle at center = 2 × angle at circumference.)
x +90 = 120
x = 120-90
x = 30°
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29° From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 34° How high (in feet) is the mountain?
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the mountain is 3110.5767 feet.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The height of the mountain from the first point,
[tex]\tan(29^o) = \dfrac{H}{x+1000}\\\\H = (1000+x) \times \tan(29^o)[/tex]
The height of the mountain from the second point,
[tex]\tan(34^o) = \dfrac{H}{x}\\\\H = x \times \tan(34^o)[/tex]
Equating the height,
H = H
(1000+x) × tan(29°) = x tan( 34°)
x = 4611.5767 feet
Now, the height of the mountain is,
H = x tan(34°)
H = 3110.54776 feet
Hence, the height of the mountain is 3110.5767 feet.
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The number of math classes offered online in the summer is 15 less than the number of math classes offered face-to face in the summer . Let Frepresent the number of face-to face summer classes . Which of the following expressions gives the number of online math classes ?
The expressions that gives the number of online math classes is as follows:
y = x - 15
How to express an equation?The number of math classes offered online in the summer is 15 less than the number of math classes offered face-to face in the summer.
Let
the number of math classes offered face-to face = x
the number of math classes offered online = y
Therefore, the expression that gives the number of online math classes is as follows:
y = x - 15
x = y + 15
Hence,
y = x - 15
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