4) Ella drives 60 miles per hour. How far will she drive in 2% hours?​

The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x))​ is 1

Given that

f(x) = 3 - 2x

Rewrite as

g(x) = -x² + x + 1

Express as vertex form

g(x) = -(x - 0.5)² + 1.25

Express as equation and swap x & y

x = -(y - 0.5)² + 1.25

Make y the subject

y = 0.5 + √(1.25 - x)

So, the inverse is

g⁻¹(x) = 0.5 + √(1.25 - x)

Here, we have

f(g(x)) = g(f(x))​

This means that

f(g(x)) = 3 - 2(-x² + x + 1)

g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1

Using a graphing tool, we have

f(g(x)) = g(f(x))​ when x = 1

Hence, the value of x is 1

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Complete question

f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers

Find the inverse of G and the value for x for which f(g(x)) = g(f(x))​.

The rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches is 4.96 square inches per second.

The surface area of a spherical balloon and the volume of the balloon are related by the equation [tex]A³ - 36πV²[/tex], where A is in square inches and V is in cubic inches. To find the rate at which the surface area of the balloon is increasing, we can use derivatives. We start by taking the derivative of the equation [tex]A³ - 36πV²[/tex] with respect to time (t).

[tex]d/dt[A³ - 36πV²] = 3A²dA/dt - 72πVdV/dt[/tex]

Given the rate at which the balloon is being inflated with gas (dV/dt) and the area and volume of the balloon (A, V) at the given instant, we can solve for the rate at which the area is increasing (dA/dt).

[tex]dA/dt = (3A² - 72πV)dV/dt / 36πV[/tex]

Plugging in the given values for A, V, and [tex]dV/dt,[/tex]we can calculate dA/dt:

[tex]dA/dt = (3(153.24)² - 72π(178.37))(18)/(36π(178.37)) ≈ 4.96[/tex]

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The z-score for Keenan is 0.71, rounded up to the hundredth.

The Z-score determines the standard deviations by which the measure deviates from the mean. After calculating the Z-score, we look at the z-score table to ascertain the p-value associated with it. This p-value represents the percentile of X or the probability that the measure's value is smaller than X. You may get the likelihood that the value of the measure is greater than X by subtracting 1 from the p-value.

The formula for calculating the z-score is as follows: The z-score is the number of standard deviations an individual's score deviates from the mean.

z = (x - μ) / σ

where the mean score is, the standard deviation is, and x is the individual's score.

About Keenan's test:

z = (80 - 77) / 4.2

z = 0.71

Keenan's z-score is 0.71 as a result, rounded to the nearest hundredth.

Any decimal number is rounded to the nearest hundredth value when it is expressed as a fraction. A hundredth is 1/100 or 0.01 in decimal form. For instance, 2.17 is the result of rounding 2.167 to the nearest tenth.

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The price after discount is $33 and option 1 is the correct answer.

A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.

Given that, one-day discount rate of 45% is applied.

Thus,

Discount = 60.20 * 0.45 = 27.09

Price after discount = 60.20 - 27.09 = 33.11

Hence, the price after discount is $33 and option 1 is the correct answer.

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To find the point on the given plane that is closest to the given point (5,6,2), we can use Lagrange multipliers.

Let f be the function that represents the plane x-y+z=3 and let g be the function that represents the point (5,6,2). Then, the point on the plane closest to (5,6,2) is the point that minimizes g=x2+y2+z2. We can use the method of Lagrange multipliers to solve this problem.

Let lambda be the Lagrange multiplier. Then, we need to solve the system of equations given by:
x2+y2+z2-2x-2y-2z=0x-y+z-3=0

By solving this system of equations, we obtain the point 13/14x=7/7y=11/7z=5/7, which is the closest point on the plane to the given point (5,6,2).

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Answer:

The answer is letter D.

Step-by-step explanation:

Ye

Answer:

The answer is C

x -10 < -20

x < -20 + 10

x< -10

The sign won't change to the other side because the variable we were asked to find is in the positive form.

we can use the notation P(A) and apply the definition of probability: P(A) = P(B), P (A ∩ B), and P (A ∪ B) if we have the necessary information.

I believe you meant to say, "Venn diagram". A Venn diagram is a type of graphical representation used to illustrate relationships between sets or groups of objects, concepts, or ideas. It consists of a series of overlapping circles or other closed shapes, with each circle representing a set or group and the overlapping areas representing the relationships or intersections between them.

by the question.

Let A be the event that a student is a cast member of Seussical, and let B be the event that a student is a cast member of Wizard of Oz. Then, we can define the following:

A ∩ B: The event that a student is a cast member of both Seussical and Wizard of Oz.

A ∪ B: The event that a student is a cast member of either Seussical, Wizard of Oz, or both.

A': The event that a student is not a cast member of Seussical.

B': The event that a student is not a cast member of Wizard of Oz.

Based on the information given, we do not know how many students are in each of these events, but we can still make some general observations. For example:

If A and B have no students in common (i.e., A ∩ B = ∅), then the number of students in A ∪ B is equal to the sum of the number of students in A and the number of students in B.

If some students are in both A and B (i.e., A ∩ B is not empty), then the number of students in A ∪ B is equal to the sum of the number of students in A, the number of students in B, and the number of students in A ∩ B. In other words, some students are counted twice when we add up the number of students in A and the number of students in B, so we need to subtract the number of students in A ∩ B to avoid double-counting.

We do not know whether the events A and B are mutually exclusive (i.e., whether A ∩ B = ∅) or not. If they are mutually exclusive, then P(A ∩ B) = 0, and we can use the addition rule of probability to find P (A ∪ B) = P(A) + P(B). If they are not mutually exclusive, then we need to use the general addition rule of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Finally, if we want to find the probability that a student chosen at random is a cast member of Seussical,

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Ann has 60 $1 bills, 5 $10 bills, and 20 $20 bills.

Let's assume Ann has $1x, $10y, and $20z bills.

From the given information, we can write two equations based on the relationships between the numbers of bills:

z = 4y (Ann has four times as many $20 bills as $10 bills)

x = 3z (Ann has three times as many $1 bills as $20 bills)

We know that the total amount of money Ann has is $204, so we can write a third equation:

x + 10y + 20z = 204

Now we can use substitution method here, substitute equation 2 into equation 1 to get:

z = 4y

x = 3z

x = 3(4y) = 12y

Substituting these equations into equation 3, we get:

12y + 10y + 20(4y) = 204

42y = 204

y = 4.86

Since y must be a whole number (representing the number of $10 bills), we can round up to y = 5.

Using equation 1, we can find that z = 4y = 20 (representing the number of $20 bills).

Using equation 2, we can find that x = 3z = 60 (representing the number of $1 bills).

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The given question is incomplete, the complete question is:

Ann has $ 1, $10, and $20 bills. She has 4 times as many $20 bills as $10 bills. She has 3 times as many $1 bills as $20 bills. She has a total of $204 .What is the number of $1, $10, and $ 20 bills she has

Given that the graph is falling downward, it can be seen that the graph is negative.

Before the tank's water level starts to drop, there are 120 gallons there.

Finding the slope of the graph will give us the amount of water that was lost every minute.

Slope is equal to a climb or a run.

increase = water in gallons

run equals time in minutes.

Slope equals y2 - y1 / x2 - x1

Two points will be chosen from the graph.

( 30, 80) and (60, 40) (60, 40)

Let x1=30, y1=80, x2=60, and y2=40.

Slope = 40 - 80 / 60 - 30

Slope = -40 / 30

Slope = -4/3

The result in the negative represents a loss in gallons of water per minute.

According to the line of best fit, a gallon of water was lost every minute or so.

The graph indicates that the tank will be empty in around 60 minutes.

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Answer: 8 mangoes

Step-by-step explanation:

1. To find the total number of mangoes Peter had, add 8 and 24 which gives you 32. 8 + 24 = 32.

2. If Peter had an equal number of mangoes in each bag, and a total number of 32 mangoes, then you must divide the total number of mangoes by the number of bags, which is 4. 32 ÷ 4 = 8. Therefore, there were 8 mangoes in each bag.

Answer:

The answer  is 8 mangoes

Answer: 6

Step-by-step explanation:

Average rate of change is the same as slope.

To find the average rate of change between two points, use the formula y2 - y1 / x2 - x1

Plug in the (0, 7) and (6, 43) coordinates.

43 - 7 / 6 - 0 = 6

Answer: The total surface area of the cylinder is 850π m².

Step-by-step explanation:

The cylinder has a curved surface area of 408π m², which is the area of the lateral surface of the cylinder. The lateral surface of a cylinder is the curved surface that connects the top and bottom bases of the cylinder.

The formula for the lateral surface area of a cylinder is given by: Lateral Surface Area = 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder.

We are given that the length of the cylinder is 17 m. Since the length of a cylinder is the same as its height, we can substitute h = 17 m into the formula for the lateral surface area to get:

408π m² = 2πr(17 m)

Simplifying this equation, we get:

r = 12 m

Now that we know the radius of the cylinder, we can find the total surface area of the cylinder. The formula for the total surface area of a cylinder is given by:

Total Surface Area = 2πr(r + h)

Substituting r = 12 m and h = 17 m into this formula, we get:

Total Surface Area = 2π(12 m)(12 m + 17 m) = 850π m²

Therefore, the total surface area of the cylinder is 850π m².

The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

Answer:28

Step-by-step explanation:

Answer: 28

Explanation:  Look for a pattern or reason for the following number in the sequence. In this case 3+1=4, 4+3=7, 7+5=12, 12+7=19, so the probable answer is to add the following odd number to the last one in the line to get the next. (19+9=28)

The value of X is 42.5 and Y is 90.98.

How to solve equations?

To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:

Simplify both sides of the equation by combining like terms and following the order of operations.

Add or subtract the same value from both sides of the equation to isolate the variable term.

Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.

Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.

Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:

[tex]10x/10 = 425/10[/tex]

Simplifying the left side of the equation gives:

[tex]x = 42.5[/tex]

Therefore, X is 42.5.

To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:

[tex]81729 = 898.12 \times Y[/tex]

Simplifying the right side of the equation gives:

[tex]Y = 81729 / 898.12[/tex]

[tex]Y = 90.98[/tex]

Therefore, Y is 90.98.

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Answer:

Y=x^2+7x-3

complete the square to re-write the quadratic function in vertex form.

pls help

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.

y = x^2 + 7x - 3

y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)

y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)

y = (x + 7/2)^2 - 49/4 - 3

y = (x + 7/2)^2 - 61/4

So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).

The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).

The volume of any cylinder can be calculated using the formula,

V = πr²h

(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)

As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:

Volume of oil = (1/5) x Total Volume

Substituting the given values, we have:

Total Volume =  π(80cm)²(200cm) = 4,031,240 cm³

Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³

Converting cm³ to litres, we have:

1 litre = 1000 cm³

Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres

Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.

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Answer:

40.4026226 aka 40.403

Step-by-step explanation:

tan 22 degrees = h/100

Denote by X the arrival time of the first guest. The time of arrival of the first guest at a bank is modeled by the Poisson distribution, where the arrival rate is λ. Thus, the number of arrivals during time t is Poisson(λt).

Therefore, the distribution of X is Exponential(λ), which means that its probability density function is

f(x) = λe−λx, x > 0.

The expected value of X is E[X] = 1/λ and the variance is Var(X) = 1/λ².

b. Denote by Y the arrival time of the second guest.

The number of arrivals during time t is Poisson(λt). The first guest arrived at time X, so the number of arrivals from time X to time t is Poisson(λ(t - X)).

Thus, the arrival time of the second guest has the conditional probability density function:

f(y | X) = λe^(−λ(y−x)), y > x

Therefore, the unconditional probability density function of Y is obtained through the law of total probability:

f(y) = ∫f(y | x)f(x)dx

= ∫λe^(−λ(y−x))λe^(−λx)dx

= λ²e^(−λy), y > 0

Therefore, the distribution of Y is Exponential(λ), which is the same as that of X.

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The angles of △ABC can be determined by dividing 360 degrees by the number of congruent triangles. Therefore, each angle of △ABC measures 90 degrees as all the sides are congruent.

Since triangle ABC is isosceles, we know that angle BAC is equal to angle BCA. By drawing the perpendicular bisector of AC from point D, we can see that it intersects AC at its midpoint M. Therefore, we have AD = MC, and angle AMD is equal to angle CMD. Similarly, by drawing the perpendicular bisector of AC from point F, we have FC = CE, and angle CFE is equal to angle ECF. Since AD = DE and BF = EF, we have angle ADE = angle DEF and angle BEF = angle BFE. Therefore, we have four congruent triangles: △AMD, △BME, △ECF, and △FBC. Each of these triangles has angles that add up to 180 degrees, so we can find the measures of the angles of △ABC by dividing 360 degrees by the number of congruent triangles. Thus, each angle of △ABC measures 90 degrees.

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The beam is 7.8 feet far away from the base of the house

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

It involves the use of trigonometric functions such as sine, cosine and tangent.

Using the attached image:

Let b represent the distance from the base of the house to the beam. We can say:

cos 71° = b/24 (adjacent/hypotenuse)

b = 24 * cos 71°

b = 7.8 feet  

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Answer:

Step-by-step explanation:\Write an expression for the sequence of operations describe below Add C and the quotient of 2 and D do not simplify any part of the expression

a

=

334

a

73

Write the problem as a mathematical expression.

a

=

334

a

73

Subtract

334

a

73

from both sides of the equation.

a

−

334

a

73

=

0

Factor

a

out of

a

−

334

a

73

.

Tap for more steps...

a

(

1

−

334

a

72

)

=

0

If any individual factor on the left side of the equation is equal to

0

, the entire expression will be equal to

0

.

a

=

0

1

−

334

a

72

=

0

Set

a

equal to

0

.

a

=

0

Set

1

−

334

a

72

equal to

0

and solve for

a

.

Tap for more steps...

a

=

1

72

√

334

,

−

1

72

√

334

The final solution is all the values that make

a

(

1

−

334

a

72

)

=

0

true.

a

=

0

,

1

72

√

334

,

−

1

72

√

334

The result can be shown in multiple forms.

Exact Form:

a

=

0

,

1

72

√

334

,

−

1

72

√

334

A skater has a mean score of 7. 25 points. An equation to determine the skaters total scores received from eight judges is equals to the x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

Mean is called the average of the values and is calculated by dividing the addition of values by the total number of values. It is denoted by [tex]\bar X[/tex]. That is bar above X represents mean of x number of values. Mathematically, Mean = (Sum of all the values/Total number of values).We have in a skating compotion where each skater receives score from eight judges. Now, Mean or average of score points obtained by a skater = 7.25 points. Let the skater's received score from eight judges be equals to x₁,x₂,x₃,x₄,x₅,x₆,x₇, x₈. Total score received by skater = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ and we have to write the equation to determine the skaters total scores. Now, in this case mean of scores means the sum of scores received by skaters from eight judges divided by eight (judges).

=> 7.25 = (x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈)/8

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 8× 7.25

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 58

which is equation of 8 variables for total score. Therefore, the required equation is x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

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Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

[tex]3[/tex] days [tex]0[/tex] hours. The answer is three because the function [tex]W[/tex] that solves the differential equation gives the number of weeds in a large garden.

A number is calculated and represented using a decimal, which is an algebra quantity. In handwriting, numerical symbols like "3" are used to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.

Vets Day and Memorial Day are commonly celebrated on November 11 in the United States and overseas, respectively. The history, mythology, and mathematical importance of this particular time and date are all explained here.

[tex]\frac{dw}{dt}=\frac{1}{12}(-318+24W)[/tex]

[tex]\frac{d^{2}W }{dt^{2} }=\frac{d}{dt}[\frac{1}{12} (-318+24W)][/tex]

When [tex]W=14, \frac{dW}{dt}[/tex]

[tex]=\frac{1}{12}(-318+24*14)[/tex]

[tex]=\frac{18}{12}=1.5[/tex]

[tex]=2\frac{dW}{dt}=2*1.5[/tex]

[tex]=3[/tex]

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Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.y has a mean of 203 and a variance of 85.

A function, in mathematics, is a reIationship between a set of possibIe inputs and an equaIIy IikeIy set of outputs, where each input is associated to exactIy one outcome. Functions are commonIy represented as equations or graphs, and they are used to modeI many reaI-worId processes in domains such as physics, engineering, and economics.

Function types incIude Iinear, quadratic, trigonometric, and exponentiaI functions, among others. CaIcuIus, a fieId of mathematics that investigates how quantities change over time or space, heaviIy reIies on functions.

given

The foIIowing is the MacIaurin series for the function g(x) = (1+x)e(-x):

g(x) = ∑[n=0 to ∞] ((-1)ⁿ*xⁿ) / n!

We may simpIify and pIug in the first few vaIues of n to determine the first four nonzero terms of this series:

n = 0: ((-1)⁰*x⁰) / 0! = 1

n = 1: ((-1)¹*x¹) / 1! = -x

n = 2: ((-1)²*x²) / 2! = x²/2

n = 3: ((-1)³*x³) / 3! = -x³/6

The MacIaurin series for g(x) therefore has the foIIowing first four nonzero terms:

1 - x + x²/2 - x³/6

Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.  y has a mean of 203 and a variance of 85.

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Answer:

The midpoint of the diameter is (4, 1)

This is the center of the circle

=====================================================

Explanation:

Add up the x coordinates and divide in half

(-1+9)/2 = 8/2 = 4

The x coordinate of the midpoint is x = 4

Repeat for the y coordinates

(4 + (-2))/2 = (4-2)/2 = 2/2 = 1

The y coordinate of the midpoint is y = 1

The midpoint is located at (x,y) = (4,1)

The midpoint of any diameter is the center of the circle. This is because all diameters go through the center.

The distance from the center to either endpoint represents the radius of the circle (aka half the diameter).