Assume that y varies inversely with x. If y=6.4when x=4.4, find y when x=3.2

Answers

Answer 1

Because y varies inversely with x, let
y = k/x
where k = constant.

When x=4.4, y=6.4. Therefore
k/4.4 = 6.4
k = 6.4*4.4 = 28.16

The required relation is
y = 28.16/x

When x = 3.2, obtain
y = 28.16/3.2 = 8.8

Answer: 8.8

Answer 2

the answer is 8.8

that is the answer

Related Questions

Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.

Answers

Answer:

P(x)= 0.0198

Step-by-step explanation:

Given : 65% men are knowledgeable football fans, 12 are randomly selected ,

To find : Probability that exactly four of them will consider themselves knowledgeable fans.

Solution : Let P is the success rate = 65% = 0.65

Let Q is the failure rate = 100-65= 35%= 0.35

Let n be the total number of fans selected = 12

Let r be the probability of getting exactly four = 4

Formula used : The binomial probability

[tex]P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}[/tex]

putting values in the formula we get ,

[tex]P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}[/tex]

[tex]P(x)= (495)(0.1785)(o.ooo22 )[/tex]

P(x)= 0.0198

The probability that exactly four out of the twelve randomly selected men will consider themselves knowledgeable football fans is approximately 0.236 or 23.6%.

Step 1: Model Selection (Binomial Distribution)

This scenario can be modeled using the binomial distribution if the following conditions are met:

Fixed number of trials (n): In this case, we have a fixed number of men being selected (n = 12).Binary outcome: Each man can be classified into two categories: either a "knowledgeable fan" (success) or a "not knowledgeable fan" (failure).Independent trials: The knowledge level of one man doesn't affect the selection of another.Constant probability (p): The probability (p) of a man being a knowledgeable fan remains constant throughout the random selection (given as 65%).

Since these conditions seem reasonable, the binomial distribution is a suitable model for this scenario.

Step 2: Formula and Values

The probability (P(x)) of exactly x successes (knowledgeable fans) in n trials (men selected) with probability p of success (knowledgeable fan) can be calculated using the binomial probability formula:

P(x) = nCx * p^x * (1 - p)^(n-x)

where:

n = number of trials (12 men)x = number of successes (4 knowledgeable fans - what we're interested in)p = probability of success (knowledgeable fan - 65% converted to decimal: 0.65)(1 - p) = probability of failure (not knowledgeable fan)

Step 3: Apply the Formula

We are interested in the probability of exactly 4 men being knowledgeable fans (x = 4). Substitute the known values into the formula:P(4) = 12C4 * 0.65 ^ 4 * (1 - 0.65) ^ (12 - 4)

Step 4: Calculate Using Calculator or Software

While it's possible to calculate 12C4 (combinations of 12 choosing 4) by hand, using a calculator or statistical software is often easier.12C4 = 495 (combinations of 12 elements taken 4 at a time)

Step 5: Complete the Calculation

Now you have all the values to complete the calculation:P(4) = 495 * 0.65 ^ 4 * (1 - 0.65) ^ 8Using a calculator or software, evaluate the expression. You'll get an answer around 0.236.

Factor the expression

4b^2+28b+49

Answers

(2b + 7(2b + 7) : the factor to this expression

A rectangular picture frame measures 4.0 inches by 5.5 inches. To cover
the picture inside the frame with glass costs $0.99 per square inch.
What will be the cost of the glass to cover the picture?

Answers

area = 4 x 5.5 = 22 square inches

cost is 0.99 per sq. inch

22 * 0.99 = 21.78

cost is $21.98

To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.

To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.

The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:

Total cost = 22.0 square inches × $0.99/square inch = $21.78.

Therefore, the cost of the glass to cover the picture would be $21.78.

Find the selling price of an item listed at $400 subject to a discounted series of $25%, 10%, and 5%
A. $256.50
B. $270.00
C. $225.00
D. $300.00

Answers

$400 - ($400 x 0.25) = $300

$300 - ($300 x 0.10) = $270

$270 - ($270 x 0.05) = $256.50

answer
A. $256.50

Answer:

Selling price of an item is $256.50 (A).

Step-by-step explanation:

Given : WE have given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .

To find : Find the selling price of an item.

Formula used : Selling price = marked price - discount.

Solution : We have an item listed at = $400.

Discount percentage = $25% , $10% , $5.

Discount 1 = $400 ×[tex]\frac{25}{100}[/tex] = $100.

Selling price = $400-100 = $300.

Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.

Selling price = $300-30 = $270.

Discount 3 = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.

Final selling price = $270-13.50 = $256.50.

Therefore, Selling price of an item is $256.50 (A).

determine which of the following logarithms is condensed correctly

Answers

The laws of logarithm has specific theories to be applied depending on the form of the given expression. Some of it are the following:

alogb = log b^a
log a + log b = log (ab)
log a - log b = log (a/b)

for letter A,
xlogb r + logb s - logb t = logb [(rs)^x]/t
is wrong because the s part from logb s has no x before the logb

for letter B,
xlogb r + xlogb s - logb t = logb (rs/t)^x
is wrong because the t part from logb t has no x before logb

for letter C,
logbr - xlogb s + xlogb t = logb (r)/(st)^x
is correct because after the minus sign, condensing it would form a fraction, the plus sign will form a multiplication and both s and t are raised to the power of x.
So the answer is letter C.

The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 39 inches find the lengths of the sides of the triangle

Answers

It should be 11 13 15, the sum is 39 and those are consecutive odd integers

Kenji buys 3 yards of fabric for 7.47$. Then he realizes that he needs 2 more yards. How much will the extra fabric cost?

Answers

12.47$ because one piece of fabric is 2.49$

The first thing that you would want to do is find the cost of one yard of fabric.

7.47 / 3 = 2.49

Now that we know that each yard costs $2.49, we can multiply it by the number of yards you need to buy (two).

2 • 2.49 = 4.98

Your total for two yards of fabric is $4.98

What is the value of X that makes the given equation true? 4x-16=6(3+x)

Answers

See the attached picture for how we solved it.

Find an exact value. sin(17pi/12)

a. √6 - √2 / 4
b. -√6 - √2 / 4
c. √6 + √2 / 4
d. √2 - √6 / 4

Answers

correct option is B.
feel free to ask if you have any doubts.

The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4

What are Trigonometric functions?

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric function is given in the question, as follows:

sin(17π/12)

To find the value of sin(17π/12), we can use the following trigonometric identity:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

In this case, we can write:

sin(17π/12) = sin(π/3 + π/4)

We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.

Therefore, we can use the above identity to get:

sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)

= (√3/2)(√2/2) + (1/2)(√2/2)

= (√6/4) + (√2/4)

= (√6 + √2)/4

So the answer is option (c): √6 + √2 / 4.

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Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12

Answers

There are two inequality equations to be graphed:

x + y ≥ 4
2x + 3y < 12

For the first step, let's disregard the inequality symbols and take it like any conventional algebraic equation. This is to be able to graph the lines on a Cartesian planes first.

For the first equation, x+y=4. To find the x- and y-intercepts, let the other variable be 0. For example,
x-intercept:
x+0=4
x=4
y-intercept:
0+y=4
y=4
Therefore, you can graph the equation line by plotting the intercepts (4,0) and (0,4) and connecting them together. The same thing is done to the second equation:
x-intercept:
2x + 0 = 12
x=12/2=6
y-intercept:
0 + 3y =12
y= 12/3 = 4
Therefore, you can graph the equation line by plotting the intercepts (6,0) and (0,4) and connecting them together. The graph is shown in the left side of the picture.

The next step would be testing the inequalities. Let's choose a point that does not coincide with the lines. That point could be (-5,-1).

x + y ≥ 4
-5 + -1 ≥4
-6 ≥ 4 --> this is not true. Thus, the solution of the graph must not include the area of this point. It includes everything to the right of the line denoted by the blue-shaded region.

2x + 3y < 12
2(-5) + 3(-1) <12
-13 < 12 ---> this is true. Thus, the solution would include this point. That includes all points to the left of the orange line denoted by the orange-shaded the region.

The region where blue and orange overlap is the solution of the system of equations, denoted by the green-shaded region.

How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places.

A. 0.459 radian
B. 2.178 radians
C. 1.047 radians
D. 0.955 radian

Answers

1 radian = 57.3 degrees

60 ÷ 57.3 = 1.047

correct answer: C

Answer:

Option C. 1.047 radians

Step-by-step explanation:

We have to find the measure of angle AOT in radians.

To convert measure of an angle from degree to radians we use the formula

[tex]\text{radians}=\frac{\pi(\text{degrees})}{180}[/tex]

= [tex]\frac{\pi(60)}{180}=\frac{\pi }{3}[/tex]

(Since measure of angle AOT is 60°)

= [tex]\frac{3.14}{3}[/tex] (since π = 3.14)

= 1.047 radians

Therefore, option C. 1.047 radians is the correct option.

06.01 LC)

Four graphs are shown below:
Which graph represents a positive nonlinear association between x and y?
Graph A
Graph B
Graph C
Graph D

Answers

Graph D.

Graph D is the correct answer because it represents a POSITIVE and EXPONENTIAL (non-linear) relationship.

Answer:

Step-by-step explanation:

Find all solutions in the interval [0, 2π).

sin^2 x + sin x = 0

Answers

Factoring:-

sin x( sin x + 1) = 0

sin x = 0 , or sinx + 1 = 0 giving sin x = -1

when sin x = 0 x = 0 , pi

when sin x = -1, x = pi + pi/2 = 3pi/2

solutions in given interval are 0,pi and 3pi/2

slope of -8 and Y intercept of (0, 12) in slope intercept form.

Answers

y=-8x+12 is the equation in slope intercept form

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 13 in. by 8 in.

Answers

1) To make a rectangular box you need to cut squares from the four corners of the rectangular sheet.

2) Call x the length of the sides of the squares cut off.

3) The base of the box will have dimensions: (13 - 2x) and (8 - 2x)

4) The height of the box will be x

5) The volume of the box will be the area of the base times the height:

Volume = (13 - 2x)(8 -2x)x = (4x^2 - 42x + 104)x = 4x^3 - 42x^2 + 104x

6) The maximum volume is calculated by finding the point where the derivative of the volume is zero =>

d (volume) / dx = 12x^2 - 84x + 104 = 0

7) Solve the quadratic equation 12x^2 - 84x + 104 = 0

=> 4(3x^2 - 21x + 26) = 0

=> 3x^2 - 21x + 26 = 0

=> 3 (x^2 - 7x) + 26 = 0

=> 3 [(x - 7/2)^2 - (7/2)^2] + 26 = 0

=> 3 (x - 7/2)^2 - 3* 49/4 + 26 = 0

=> 3 (x - 7/2)^2 = 3*49/4 - 26

=> (x -7/2)^2 = (49/4 - 26/3)

=> x = 7/2 +/- √(49/4 - 26/3)

x = 7/2 + √3.583 and x = 7/2 - √3.583

x = 5.393 and x = 1.607

=> Volume =

1) 4(5.393)^3 - 42(5.393)^2 + 104(5.393) = -33.26 ---> it does not have physical meaning

2) 4(1.607)^3 - 42(1.607)^2 + 104(1.607) = 75.27 ---> this is the answer

Answer: 75.27 in^3

To answer that question

Answers

First, we get ax^2+bx+c. Next, we know that the line of symmetry is -b/2a. Since we know that there is a maximum value, the parabola is facing downwards, so a is negative. For random numbers, we can say that a = -0.5 and b=-10 (b needs to be negative for -b/2a to equal -10), getting -0.5x^2-10x+c. Plugging -10 in for x (since -10 is the middle it is the max), we get -50+100=50. Since the maximum needs to be 5, not 50, we subtract 45 from the answer to get it and therefore make c = -45, getting -0.5x^2-10x-45

9log9(4) =

A. 3
B. 4
C. 9
D. 81

Answers

"9log9(4) = " What do you mean by this?

find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1

Answers

check the picture below, is a negative angle, thus, is going "clockwise"

[tex]\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{x}\implies tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{-1} \\\\\\ -1\cdot tan\left( -\frac{3\pi }{4} \right)=y\implies -1\cdot \cfrac{sin\left( -\frac{3\pi }{4} \right)}{cos\left( -\frac{3\pi }{4} \right)}=y \\\\\\ -1\cdot \cfrac{-1}{-1}=y\implies -1[/tex]

The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.

Given :

The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.

The following steps can be used in order to determine the point on the terminal side:

Step 1 - Write the given expression.

[tex]\theta = -\dfrac{3\pi}{4}[/tex]

Step 2 - The value of the trigonometric function is given by:

[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]

Step 3 - The trigonometric function can also be written as:

[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]

Step 4 - Substitute the value of 'x' in the above expression.

y = -1

So, the point on the terminal side is (1,-1).

For more information, refer to the link given below:

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Find the slopes of the asymptotes of the hyperbola with the following equation.
36 = 9x ^{2} - 4y^{2}

Answers

Final answer:

The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.

Explanation:

The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.

First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.

By comparing it with the standard equation, we see that [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.

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Determine the value of a so that the line whose equation is ax+y-4=0 is perpendicular to the line containing the points (2,-5) and (-3,2)

Answers

First, write the equation of the line containing the points (2,-5) and (-3,2).

We can use 2 point form, or point-slope form.

Let's use point-slope form.

the slope m is [tex] \frac{-5-2}{2-(-3)}= \frac{-7}{5} [/tex], then use any of the points to write the equation. (ex, pick (2, -5))

y-(-5)=(-7/5)(x-2)

y+5=(-7/5)x+14/5

y= (-7/5)x+14/5 - 5 =(-7/5)x+14/5 - 25/5 =(-7/5)x-11/5

Thus, the lines are

i) y=-ax+4 and ii) y=(-7/5)x-11/5

the slopes are the coefficients of x: -a and (-7/5),

the product of the slopes of 2 perpendicular lines is -1,

so

(-a)(-7/5)=-1

7/5a=-1

a=-1/(7/5)=-5/7

Answer: -5/7

Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?

Answers

After playing 2 matches possible outcomes are:
water polo team wins none, wins 1 or wins both games.

chance that they win both matches are:
0.44*0.44 = 0.1936 in relative value

Chance that they lose both matches are:
(1-0.44)*(1-0.44) = 0.3136 in relative value

If we multiply these relative values by number of matches and subtract that from number played double games (10000) we will get number of times they won only once.

10000 - 10000* (0.3136+ 0.1936) = 4928

Hey there! I would like some help please :) Thanks!

Answers

AC is a common side, ∠ACD = ∠ACB and CD = BC ⇒ ΔACD and ΔABC are congruent (SAS definition).

Congruent triangles have exactly the same three angles, so ∠D = ∠B.

Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
What is the length of segment QM'?

Answers

Answer: 6 units

Step-by-step explanation:

Given: Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.

Since in dilation , to calculate the distance of a point on image from center point we need to multiply scale factor to the distance of corresponding point on pre-image from center point .

Thus we have,

[tex]QM'=2\times QM\\\\\Rightarrow QM'=2\times3\\\\\Rightarrow QM'=6[/tex]

Hence, the length of segment QM' = 6 units.

Answer:

6 units

Step-by-step explanation:

True or false an inscribed angle is formed by two radii that share an endpoint

Answers

True or false an inscribed angle is formed by two radii that share an endpoint

the correct answer is : FALSE

Answer:

The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.

Step-by-step explanation:

Inscribed angle is a angle which is formed inside the circle by joining of two intersecting chords inside a circle.

The inscribed angle is explained with the help of a diagram below :

In the diagram attached below, ∠ABC is an inscribed angle with an intercepted minor arc from A to C.

Thus, the inscribed angle is not formed with the help of radii that share a common end point.

Hence, The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.

The figures in each pair are similar. Find the value of each variable. Show your work.

Answers

When a pair of figure is similar, it means the lengths have a scale factor. So we have to find what times 8 gives 16, which is the length if the bigger rectangle. 8×2=16, so we have to use the scale factor, which is 2, to multiply by the other length of the rectangle. 2×2=4, so x=4.
Next question is basically like the first one, but you have to divide instead. 12÷4=3, and so 8×3=24, so y=24. 18÷3=6, so x=6. Last one, 6÷4= 1.5. 8÷1.5=5.3 and 7÷1.5=4.6, so x=4.6 and y=5.3

We know that the figures in each pair are similar and that x,y>0, so:

The rectangle:
[tex]\frac{16}{8}=\frac{x}{2}[/tex]
[tex]2=\frac{x}{2}\quad |\cdot 2[/tex]
[tex]4=x[/tex]

The triangle I:
[tex]\frac{y}{12}=\frac{8}{4}[/tex]
[tex]\frac{y}{12}=2\quad |\cdot 12[/tex]
[tex]y=24[/tex]

[tex]\frac{12}{4}=\frac{18}{x}[/tex]
[tex]3=\frac{18}{x}\quad |\cdot x[/tex]
[tex]3x=18\quad |:3[/tex]
[tex]x=6[/tex]

The triangle II:
[tex]\frac{8}{6}=\frac{y}{4}[/tex]
[tex]32=6y\quad |:6[/tex]
[tex]y=5\frac{1}{3}[/tex]

[tex]\frac{6}{4}=\frac{7}{x}[/tex]
[tex]\frac{3}{2}=\frac{7}{x}[/tex]
[tex]3x=14[/tex]
[tex]x=4\frac{2}{3}[/tex]

:)

Write a segment addition problem using three points that asks the student to solve for x but has a solution x = 20

Answers

The segment addition problem was given below which gives the value of x as 20.

Segment addition problem:

Consider three points on a line: A, B, and C. Point B is located between points A and C.

The lengths of the line segments are as follows:

Length of segment AB: 12

Length of segment BC: x

Length of segment AC: 32

Find the value of x.

We have the equation for segment addition: AB + BC = AC

Substitute the given values:

12 + x = 32

Now, solve for x:

x = 32 - 12

x = 20

Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.

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Final answer:

To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.

Explanation:

To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:

AB + BC = AC

x + (20 - x) = 20

By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.

Here is the step-by-step problem phrased as a question:

Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.

Tim bought a soft drink for 2 dollars and 5 candy bars. He spent a total of 22 dollars. How much did the candy bar costs?

Answers

5x+2=22

Subtract 2 from both sides
5x=20

Divide both sides by 5
x=4

Final answer: $4.00

rationalize the denominator. write it in simplest terms

3
------
√12x

Answers

the idea being, you multiply top and bottom by a value that will raise the radicand in the denominator, to the same as the root, thus coming out of the root, so, let's do so

[tex]\bf \cfrac{3}{\sqrt{12x}}\cdot \cfrac{\sqrt{12x}}{\sqrt{12x}}\implies \cfrac{3\sqrt{12x}}{\sqrt{(12x)^2}}\implies \cfrac{3\sqrt{12x}}{12x}\implies \cfrac{\sqrt{12x}}{4x}[/tex]

Solve the inequality.

Answers

To solve an inequality, get the variable you're solving for on one side of the inequality and everything else on the opposite side.

[tex]\frac{2}{5} \geq x - \frac{4}{5}[/tex]

You get the x variable on it's own by undoing the operations done to it.

For example, if x is being multiplied by 5, you undo the multiplication operation by using the inverse of multiplication. Which is division.

We need to add [tex]\frac{4}{5}[/tex] to both sides of the inequality to undo the subtraction operation done to x.

[tex]\frac{2}{5} + \frac{4}{5} \geq x - \frac{4}{5} + \frac{4}{5} \\ \\ \frac{6}{5} \geq x[/tex]

Convert the improper fraction into a mixed number.

[tex]\frac{6}{5} = 1 \frac{1}{5}[/tex]

So, D 1 1/5 ≥ x is the answer.

Find the slope in line perpendicular x-y=16

Answers

Change to y = mx + b format
X - y = 16
-y = -x + 16

So slope = - 1 / 1

Other Questions

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