a hot-air balloon has a 1414-foot diameter that is being deflated at a rate of 0.250.25 feet per minute. how many minutes, xx, will it take before the balloon has shrunk to a diameter of 88 feet?

Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

How closely a value relates to the mean of a set of values is expressed by a Z-score.

The Z-score is created using standard deviations from the mean.

A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.

So, in order to determine how far the raw score deviates from the mean, the Z score is used.

The following steps are used to determine the Z score:

z = (x - μ)/σ

We know that:  x > 550 and μ = 500, σ = 40

z = 550 - 500 / 40

z = 1.25

The graph of the normal distribution indicates:

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

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question: 4m^2 - 5mn^2 + 8m^2 - 6n^2m - m^2

answer:

11m^2-11mn^2 (see pictures)

By using exponent properties we will find the equivalent expression:

(-2)⁴/(-2)² = (-2)² = 4

Here we need to use the exponent property:

xⁿ/xᵇ = xⁿ⁻ᵇ

Here the expression we have is:

(-2)⁴/(-2)²

Using the above property we can rewrite the expression as:

(-2)⁴/(-2)² = (-2)⁴⁻² = (-2)²

Now we can solve this:

(-2)² = (-2)*(-2) = 4

Then the equivalent expression is 4.

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Answer:

4

Step-by-step explanation:

 The lines are perpendicular because they intersect at a right angle.

Answer:

x=2173

Step-by-step explanation:

Answer:

He spent 4&1/10 hours

Step-by-step explanation:

2&1/2+1&3/5

=5/2+8/5

=25/10+16/10

=41/10

4&1/10

A=[e to the power of π/2-2] when the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x

Given that,

We have to draw the area that the provided curves surround. Choose x or y as the integration direction. Label the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x

We know that,

y=eˣ, x=π/2, y=cos x

Now area of the shaded region is

A=[tex]\int\limits^\pi/2_ x=0 \int\limits^e^{2} _y=cosx {dy} \, dx[/tex]

A=[tex]\int\limits^\pi/2_0 {e^{x}-cosx } \, dx[/tex]

Now we integrate with respect to x.

A=[eˣ-sinx]₀π/2

A=[e to the power of π/2- sin(π/2)]-[e⁰-sin(0)]

A=[e to the power of π/2-1]-[1-0]

A=[e to the power of π/2-1-1]

A=[e to the power of π/2-2]

Therefore, A=[e to the power of π/2-2] when the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x

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Hence, the negative solution is [tex]x=-3[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

When [tex]27[/tex] is subtracted from the square of a number, the result is [tex]6[/tex] times the number.

So we can write the equation is

[tex]x^2-27=6x\\x^2-6x-27=0\\x^2-9x+3x-27=0\\x(x-9)+3(x-9)=0\\(x+3)(x-9)=0\\x=-3,9[/tex]

Hence, the negative solution is [tex]x=-3[/tex].

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Answer: $69

Step-by-step explanation: 562-148=414 & 414/6=69

Answer:

-4v³ - v² - v - 9

Step-by-step explanation:

1. Subtract the numbers

7v - 4 - 4v³ - v² - 8v - 5

7v - 9 - 4v³ - v² - 8v

2. Combine like terms

7v - 9 - 4v³ - v² - 8v

-v - 9 - 4v³ - v²

3. Rearrange Terms

-v - 9 - 4v³ - v²

-4v³ - v² - v - 9

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Answer:

Stretches vertically by 2, shifts right by 1

Step-by-step explanation:

changes to y are direct, but you have to take the inverse for changes to x. This is because for a given value of y, with x-1, you would have to add one to x to make it the same value(to get the same point before the transformation)

Answer:

7.14 km

Step-by-step explanation:

the total time that the bus takes to travel from Deltaville to Eastwick  12:42 - 11:32 = 00:10

Convert to hours 00:10 / 60 minutes/hour = 0.17 hours.

distance = speed * time

distance = 42 km/h * 0.17 hours

distance = 7.14 km

The width of a confidence interval except increased sample size.

What is the Confidence Interval?

An area surrounding a measurement that indicates how accurate it is is called a confidence interval.

The following points clear the answer of given question:

Hence, The width of a confidence interval except increased sample size.

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Assuming that h(x) = 7x4 - 9x3 - 41x2 + 13x + 6 and h(-2) = 7, (-2) 4 - 9(-2) (-2) 3 - 41(-2) (-2) 2 + 13(-2) + 6 = 7(16) - 9(-8) (-8) - 41(4) + 13(-2) + 6 = 0;

This indicates that (x + 2) is a synthetic polynomial factor.

(7x4 - 9x3 - 41x2 + 13x + 6) ÷ (x + 2):

The balance is zero.

A polynomial of degree 3 makes up the quotient: g(x) = 7x3 - 23x2 + 5x + 3.

The Rational Zeros Theorem shows that p: 1, 3, which are factors of the constant term 3, and q: 1, 7, which are factors of the leading coefficient 7, respectively

All potential outcomes are p/q: 1, 3, 1/ 7, and 3/7 g(3) = 7. (3)

3 - 23(3) +(3)

By artificial division:

The balance is zero.

The polynomial quotient is quadratic.

7x2 - 2x - 1 = 0

Equation for quadratics = [-b (b2 - 4ac)]/2a

x = -(-2) ± √[(-2)2 - (4 × 7 × -1)]/ (2 × 7) = (2 ± √32)/14 = (1 ± 2√2)/7

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The surface area of the rectangular prism is 76cm^2

Geometry is the study of various mathematical or actual-world shapes, figures, and sizes. In geometry, we study various angles, transformations, and figure-to-figure similarities. The fundamental concepts of geometry primarily depend on point, line, angle, and plane.

The three most popular types of geometry are solid geometry (which deals with objects like the line, sphere, and polyhedron) and spherical geometry. Plane geometry deals with objects like the point, line, circle, triangle, and polygon.

According to the question:-

The surface area of the rectangular prism is:_

surface area= 2*(lb+bh+hl)

                    =2*(5*4+4*2+2*5)

                    =76 cm^2

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Answer:

y + 3 = (-5/3) × (x - 1)

Step-by-step explanation:

                     5

(1, -3); m = - -------

x₁, y₁              3

y - y₁ = m(x - x₁)

y - (-3) = (-5/3)(x - 1)

y + 3 = (-5/3)x + (5/3)

   -3                   -3

--------------------------------

y = (-5/3)x - (4/3) :Slope-intercept form

I hope this helps!

The value of r is r = -8/3, for a line that has slope -12, passes through points (-3, -6) and (r, -10)

Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.

Slope formula = (y₂-y₁)/(x₂-x₁)

Given that,

A line that has slope -12, passes through points (-3, -6) and (r, -10).

To find the slope of the line that passes through points (-3, -6) and (r, -10),

Use slope formula,

m =  (y₂-y₁) / (x₂-x₁)

m = (-10 + 6) / r - (-3)

m = -4 / (r+3)

Since a line that has slope -12 passes through the points (-3, -6) and (r, -10),

Therefore, both will have the same slope,

-4 / (r+3) = -12

r + 3 = 1/3

r = 1/3 - 3

r = -8/3

The required value of r is -8/3.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of chicken sandwiches is 60.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 6 is an equation.

We have,

Number of ham sandwiches = H

Number of chicken sandwiches = C

Cost of ham sandwiches = $3.50

Cost of chicken sandwiches = $4

Now,

The total number of sandwiches = 110

The total amount earned = $415

Now,

The two equations are:

H + C = 110 _____(1)

3.50H + 4C = 415 _____(2)

From (1) we get,

C = 110 - H _____(3)

Now,

Putting (3) in (2) we get,

3.50H + 4(110 - H) = 415

3.50H + 440 - 4H = 415

-0.5H = 415 - 440

-0.5H = -25

H = 25/0.5

H = 50

Now,

Putting H = 50 in (3) we get,

C = 110 - H

C = 110 - 50

C = 60

Thus,

The number of chicken sandwiches is 60.

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Another estimate is given as L6, R6, and M3 using the velocities at the conclusion of the time periods.

The table provides speedometer readings of velocity for a moving vehicle at 7-second intervals. t (sec) v (ft/s) 0 7 14 21 28 Using the speeds at the start of the time intervals, calculate the distance the car went during this 35-second span. travel distance in feet

Just figure out the rectangles' surface areas. Always draw the picture; it will be really helpful.

L6 = 10(0+9+31+56+71+68) \sR6 = 10(9+31+56+71+68+50) \sM3 = 20(9+56+68)

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Answer:

a. The correlation coefficient of the data is 0.817.

b. Yes, there is a correlation between the heights of daughters and mothers. The correlation coefficient of 0.817 indicates a strong positive correlation, meaning that as the height of the mother increases, the height of the daughter also increases.

Answer: I believe it is 18/5

 or Decimal Form:

3.6

or Mixed Number Form:

3 3/5

Step-by-step explanation

4/5 x 4 1/2

The required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200  which are represented in the attached graph. Company A is cheaper if the time is less than 4 hours.

As per the given question, we can write the linear functions as:

A(t) = 50t + 100

B(t) = 25t + 200

We can determine time t when both companies charge the same rate by equating the two equations.

50t + 100 = 25t + 200

Subtract 25t from both sides and subtract 100 from both sides

25t = 100

Divide both sides by 25

t = 4

At 4 hours both companies charge the same rate. So Company A is cheaper if the time is less than 4 hours.

After 4 hours, company B is cheaper.

Since both functions are linear, we only need two points to plot each one onto a graph.

Thus, the required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200  which are represented in the attached graph.

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Answer: X=0

Step-by-step explanation: X is equal to zero. This is the only way the equation can be true.

Answer: (2x + 5) (4x^2 -10 + 25)

Step-by-step explanation:

I use the equation a^3 + b^3 = (a+b) ( a^2 -ab + b^2)

You can factor the answer (2x + 5) (4x^2 -10 + 25) out to check and will get 8x^3 +125

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Answer: $4368

Step-by-step explanation:

Find 4% of 1400 by taking 1400 times 0.04 = $56

So a year he has 1456$

After 3 years just need to take 1456 times 3 = $4368

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The linear equation of the relationship is L = -8t + 40.

The amount Austin paid back each week is: $8.

A linear equation is straight line graph, which can be expressed as y = mx + b, in slope-intercept form. In the slope-intercept form, we have:

Slope = change in y / change in x.

Using two pairs of values from the table given, (1, 32) and (2, 24):

Slope (m) = (32 - 24) / (1 - 2)

m = 8/-1

m = -8.

Find the y-intercept (b) by substituting m = -8 and (x, y) = (1, 32) into y = mx + b:

32 = -8(1) + b

32 = -8 + b

32 + 8 = b

40 = b

b = 40

Substitute b = 40 and m = -8 into L = mt + b:

L = -8t + 40

Using the linear equation, the amount Austin paid back each week is: $8.

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Answer:

Step-by-step explanation:

Each of the three angles measures 75°, 65°, and 40°.

What is an angle measure?

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Let the largest angle be x degrees, the median y, and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

z = 65 - 25 = 40 degrees.

and x = 180 - 65 - 40 = 75 degrees.

Hence, each of the three angles measures 75°, 65°, and 40°.

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The measures of each of the three angles are 40,65 and 75 degrees.

What is angle ?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.

Give that:

Let us consider X,Y,Z re the largest ,medium and smallest angle in the triangle.

Sum of the measures of the angles of any triangle is 180 degrees .

                            X + Y + Z = 180 degree

The largest angle measures 55degrees less than twice the medium angle,

                            Z = 2Y - 55 degree

The smallest angle measures 25 degrees less than the medium angle,

                          X = Y - 25 degree

Now ,replace X by (Y - 25) and Z by (2Y - 55) in the first equation

Y - 25 +Y + 2Y - 55 = 180 degree

4Y = 180 + 25 + 55

4Y = 260

Y = 65   Degree of the medium angle

X = 65 - 25

X = 40   Degree of the smallest angle

Z = 2 * 65 -55

  = 130-55

Z = 75   Degree of the largest angle.

40 + 65 + 75 = 180

180 = 180

Hence proved.

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The rectangle has a length of 40 cm and width of 34 cm.

Given,

The length of a rectangle = x cm

The width of the rectangle = x - 6 cm

The perimeter of the rectangle = 148 cm

We have to find the length and width of the rectangle;

Here,

Perimeter of rectangle = 2(length + width)

That is,

148 = 2(x + x - 6)

148/2 = 2x - 6

74 = 2x - 6

74 + 6 = 2x

x = 80/2

Length, x = 40 cm

Width, x - 6 = 40 - 6 = 34 cm

Therefore,

The length of the rectangle is 40 cm and the width of the rectangle is 34 cm

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