If we know that 1 meter (m) is approximately 1.09361 yards (yd), what is a step to
convert 18 meters to yards?
Multiply 18 m by 0.09361 yd.
Divide 18 m by 1.09361 yd.
1m
Cross multiply the proportion 1.09361 yd
Divide 1.09361 yd by 18 m.
=
18 m
x

Answer:

To find the inverse function of f(x) = 4(3x + 2), we need to solve for x in terms of f(x) and then interchange the roles of x and f(x) in the expression to obtain the inverse function.

Let y = f(x) = 4(3x + 2)

Dividing both sides by 4, we get:

y/4 = 3x + 2

Subtracting 2 from both sides, we get:

y/4 - 2 = 3x

Dividing both sides by 3, we get:

(y/4 - 2) / 3 = x

Hence, the inverse function is:

f^-1(x) = (x/4 - 2) / 3

Or we can also write it as:

f^-1(x) = (1/3)x/4 - 2/3

Therefore, the inverse function of f(x) = 4(3x + 2) is f^-1(x) = (1/3)x/4 - 2/3.

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Answer:

∡7 = 70°

Step-by-step explanation:

∡7 and ∡8 are supplementary angles

∡7 + ∡8 = 180°

If:

∡8 = 110°

Then:

∡7 = 180 - 110

∡7 = 70°

Answer:

558

Step-by-step explanation:

To find the geese population at Whitney National Park in 2000, we need to add 24% of the population in 1999 to the population in 1999.

First, we need to calculate 24% of 450:

24% of 450 = 0.24 x 450 = 108

So the increase in the geese population from 1999 to 2000 is 108.

To find the population in 2000, we need to add this increase to the population in 1999:

Population in 2000 = Population in 1999 + Increase

Population in 2000 = 450 + 108

Population in 2000 = 558

Therefore, the geese population at Whitney National Park in 2000 was 558.

This Quadrilateral is a trapezium. And the value of x is 13.

A quadrilateral is a clοsed figure and it have fοur sides, fοur vertices and fοur angles. In οrder tο create it, fοur nοn-cοllinear pοints are jοined. The sum οf interiοr angles οf quadrilaterals is always equal tο 360 degrees.

As two sides are parallel but not equal of a quadrilateral, it is conspired as trapezium.

Now, it is shown that the two adjacent angles are equal,

when two angles are qual it corresponding opposite side is equal too.

So,

30 = x + 17

Solving for x.

30 = x + 17

x = 30 - 17

x = 13

As x = 13

The longer side = x + 13 = 23 + 13 = 36

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first part.

The probability that the medicine is effective on each of three patients is 0.512 or 51.2%.

second part.

The probability that the medicine is effective on fewer than two of the next three patients is 0.104 or  10.4%.

Let p be the probability that the medicine is effective for a given patient.  p = 0.8.

6.  calculating the probability that the medicine is effective for all three patients. , we will multiply their individual probabilities of being effectively treated, because  the patients are independent

P(event 6) = p * p * p = 0.8 * 0.8 * 0.8 = 0.512 or 51.2%.

7.

event 7, we will  calculate the probability that the medicine is effective on fewer than two of the next three patients.

We apply the binomial distribution with n = 3 (the number of patients) and p = 0.8 (the probability of success).

The probability mass function for the binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

P(event 7) = P(X=0) + P(X=1)

= (3 choose 0) * 0.8^0 * 0.2^3 + (3 choose 1) * 0.8^1 * 0.2^2

= 0.008 + 0.096

= 0.104 or  10.4%.

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let's call our number hmmm Z, now, let's reduce it by 17%, so 100% - 17% = 83%, so the new size for Z is 83% off the original, hmm how much is that?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{83\% of Z}}{\left( \cfrac{83}{100} \right)Z}\implies 0.83Z[/tex]

now, let's increase it by 12%, so the new size will be 100% + 12% = 112%, so 112% of 0.83Z, let's check how much is that

[tex]\stackrel{\textit{112\% of 0.83Z}}{\left( \cfrac{112}{100} \right)0.83Z}\implies 0.9296Z[/tex]

now, let's convert that to a percent format by simply multiplying it by 100, so that'd be 100 * 0.9296Z = 92.96% of Z.  Well, hell 92.96% is less than 100%, so is really 100% - 92.96% = 7.04% less.

So, instead of all that rigamarole, we could have just reduced Z by 7.04% in one fell swoop and obtain the same thing.

Answer:

The answer to your problem is, 6a

How to find the GCF:

6a(x²+x+1)

Use that problem

The answer to your problem is, 6a

The acceleration function is a(t) = 6(t - 3).

Acceleration is the rate at which an object changes its velocity. The acceleration function is a mathematical function that gives the acceleration of an object at any given time

To find the acceleration function, we need to take the second derivative of the given velocity function f(t).

f(t) = (t - 3)^3 + t

First, let's find the first derivative of f(t)

f'(t) = 3 × (t - 3)^2 + 1

Now, let's find the second derivative of f(t) ( the acceleration function )

a(t) = f''( t )

= d/dt [3 × (t - 3)^2 + 1]

Do the derivation

= 6(t - 3)

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The given question is incomplete, the complete question is:

The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)^3 + t. find the acceleration function a(t).

The equation for a cosecant function with vertical asymptotes found at x = nπ such that n is an integer is `y = csc(x - nπ)`.

The cosecant function is the reciprocal of the sine function. The cosecant of a particular angle in a right triangle is the ratio of the hypotenuse to the side opposite the angle.

The cosecant function is written as follows: `csc(x) = 1/sin(x)`

Asymptotes are straight lines or curves that a graph approaches but never touches.

As a result, the graph of a curve gets closer and closer to the asymptote as it moves further away from the origin, but it never touches it.

For a function to have vertical asymptotes at `x = nπ`, the denominator of the function should equal zero. In the cosecant function, the denominator is equal to `sin(x - nπ)`.

Therefore, the vertical asymptotes are where `sin(x - nπ) = 0`.

The general form of the cosecant function is `y = A csc(B(x - C)) + D`.

The constants A, B, C, and D are used to alter the form of the graph of the cosecant function.

They can be used to alter the amplitude, period, phase shift, and vertical displacement of the graph, respectively.

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Answer:

an = 6 * 2^(n-1)

Step-by-step explanation:

To find the general term of the sequence 6, 12, 24, 48, ... , we need to observe that each term is obtained by multiplying the previous term by 2. Therefore, the sequence is a geometric sequence with first term a = 6 and common ratio r = 2.

The formula for the nth term of a geometric sequence is:

an = a * r^(n-1)

Substituting a = 6 and r = 2, we get:

an = 6 * 2^(n-1)

Therefore, the general term of the sequence 6, 12, 24, 48, ... is given by the formula an = 6 * 2^(n-1).

Answer:

{f(x) ∈ ℝ | f(x) ≥ –3}

Step-by-step explanation:

f(x)=|x|-3

|x| have range x≥0 .

f(x)≥0-3

f(x)≥-3

First answer {f(x) ∈ ℝ | f(x) ≥ –3}

The probability that the reporter gets an assignment in the United States or Asia is 15/37.

To find the probability that the reporter gets an assignment in the United States or Asia, we first need to determine the total number of assignments in the pool.

Total number of assignments = 8 + 29 + 15 + 22 = 74

Next, we need to determine the number of assignments that are in the United States or Asia.

Number of assignments in the United States or Asia = 8 + 22 = 30

Finally, we can calculate the probability of the reporter getting an assignment in the United States or Asia by dividing the number of assignments in the United States or Asia by the total number of assignments:

Probability of getting an assignment in the United States or Asia = (Number of assignments in the United States or Asia) / (Total number of assignments)

Probability of getting an assignment in the United States or Asia = 30/74

Therefore, the probability of the reporter getting an assignment in the United States or Asia is 30/74, which can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 2:

Probability of getting an assignment in the United States or Asia = 15/37

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Answer:

6/7

Step-by-step explanation:

First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.

Answer:

To determine which option is the most cost-effective, you can use some simple math. Let's assume you need to park for 8 hours:

Park and Ride:

Parking cost: 8 hours x £0.40 = £3.20

Bus fare: £0.60 x 2 (round trip) = £1.20

Total cost: £4.40

Free parking at the railway station:

Train fare: £3.50 x 2 (round trip) = £7.00

Total cost: £7.00

Based on the calculations above, the Park and Ride option is cheaper for an 8-hour parking period. However, you should also consider factors such as convenience and travel time when making your decision. If the railway station is closer to your destination or has more frequent train services, it may be the better option despite the higher cost.

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Answer:

(4,2) represents the number of ways to choose 2 items from a set of 4 distinct items. The formula for C(n,r) is n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values for C(4,2), we get: C(4,2) = 4! / (2! * (4-2)!) = 24 / (2 * 2) = 6 Therefore, there are 6 ways to choose 2 items from a set of 4 distinct items.

0 / 350

The value of the given combination C(4, 2) by applying the combination formula in factorial form is equals to option 6.

To evaluate C(4, 2), we use the combination formula, also known as "n choose r" or "C(n, r)",

which calculates the number of ways to choose r items from a set of n distinct items without considering their order. The formula for C(n, r) is:

C(n, r) = n! / (r! × (n - r)!)

Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

For example,

4! = 4 × 3 ×2 × 1

   = 24.

Now, let's plug the values into the formula for C(4, 2):

C(4, 2) = 4! / (2! × (4 - 2)!)

= 4! / (2! × 2!)

= (4 × 3 × 2 × 1) / ((2 × 1) × (2 × 1))

= (24) / (4)

= 6

Therefore , the value of the combination C(4, 2) equals  to option 6.

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Answer:

even

Step-by-step explanation:

It lands on 10, and 8, take that, divide by 2, and mutiply by 8.

Two examples that show the use of data and probability are an article about covid and an article about the use of predictive analysis.

Example 1: According to a recent article in The New York Times, data from the Centers for Disease Control and Prevention (CDC) shows that individuals who are fully vaccinated against COVID-19 are much less likely to be hospitalized or die from the virus. The article cites a study that found the Pfizer-BioNTech vaccine was 91 percent effective in preventing hospitalization and 95 percent effective in preventing death. This data reinforces the importance of vaccination in preventing severe illness and death from COVID-19.

Example 2: A recent article in The Wall Street Journal discusses the use of predictive analytics in the insurance industry. The article explains that insurance companies are increasingly using data and probability models to predict and mitigate risks associated with climate change, natural disasters, and other potential events that could result in insurance claims.

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Answer:

11? I only think this because it says that EBD are collinear and it equals 99 so for (9x) to equal 99, it would have to be nine times 11.

Based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graphs.

A bar graph is a chart that displays categοrical data using rectangular bars with heights οr lengths prοpοrtiοnal tο the values they represent. The bars can be οriented hοrizοntally οr vertically, and each bar represents a categοry οr grοup οf categοries.

In a bar graph, the x-axis typically represents the categοries being cοmpared, while the y-axis represents the frequency, cοunt, οr percentage οf the οbservatiοns that belοng tο each categοry. The height οr length οf each bar is determined by the value οr frequency οf the categοry it represents.

The variable that Amari used tο cοnstruct a bar graph is nοt specified. Hοwever, since a bar graph is a type οf chart that displays categοrical data with rectangular bars, it is likely that she used a variable that represents a categοrical variable, such as the type οf οrange (e.g. Valencia, Navel, Blοοd, etc.).

Therefοre, based οn the given οptiοns, it is mοst likely that Amari used the variable "Type οf οrange" tο cοnstruct the bar graph.

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(a) we can simplify the expression [tex]x^3 - 3x - 4\\[/tex]:

[tex]x^3 - 3x - 4[/tex]

(b) we cannοt simply switch the terms arοund and expect the sum tο be the same.

An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and οperatοrs, such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

(a)

The expression [tex]-(2^3)+x-3[/tex] means [tex]-(2^3) + x - 3[/tex] since the expοnent οperatοr (^) has higher precedence than the negatiοn οperatοr (-). Using the οrder οf οperatiοns, we can simplify the expressiοn:

[tex]-2^3+x-3 = -(2^3) + x - 3 = -(8) + x - 3 = x - 11[/tex]

Similarly, we can simplify the expression [tex]x^3 - 3x - 4\\[/tex]:

[tex]x^3 - 3x - 4[/tex]

(b)

The sum of [tex]-2^3+x-3[/tex] and [tex]x^3-3x-4[/tex] is not equal to the sum of [tex]x^3-3x-4[/tex]and [tex]-2x^3+x-3[/tex].This is because additiοn is nοt cοmmutative fοr nοn-like terms, meaning that changing the οrder οf the terms in a sum can change the value οf the sum.

Hence, we cannοt simply switch the terms arοund and expect the sum tο be the same.

We wοuld need tο actually perfοrm the additiοn in bοth cases tο determine if they are equal.

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The unknown angles on the straight line is as follows:

∠ZOX = 64 degrees

The sum of angles in a line segment is 180 degrees. Therefore, let's find the angle ∠ZOX as follows:

∠YOX = ∠YOZ + ∠ZOX

Therefore,

∠ZOX = ∠YOX -  ∠YOZ

∠YOX = 180°

Therefore,

5x + 6 + 3x - 2 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176 / 8

x = 22

Hence,

∠ZOX = 3x - 2

∠ZOX = 3(22) - 2

∠ZOX = 66 - 2

∠ZOX = 64 degrees

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Step-By-Step:

The height triangle has a height of 17.3 yards and a width of 12 yards. 3. Finally, connect the two triangles to create the pyramid's surface area. The surface area of the pyramid is 116.7 yards².

Answer:

116.7 yards².

Answer:

The first step is to find the area of the base triangle:

Area = (1/2) x base x height

Area = (1/2) x 20 yards x 17.3 yards

Area = 173 square yards

To find the surface area of the pyramid, we need to find the areas of the four triangular faces and add them to the base area.

Area of a triangular face = (1/2) x base x height

Area of each face = (1/2) x 20 yards x 12 yards

Area of each face = 120 square yards

Now we can add up all the areas:

Surface area = base area + area of four faces

Surface area = 173 square yards + 4 x 120 square yards

Surface area = 653 square yards

Therefore, the surface area of the pyramid is 653 square yards.

The distance between Bert and Ernie is 8.8 miles.

What is law of cosine?

According to a trigonometry rule, the square of a side in a plane triangle is equal to the total of the squares of the other sides minus twice that amount, along with the cosine of the angle that separates them.

Here using law of cosine we can find the distance between Bert and Ernie. Then,

[tex]a^2=b^2+c^2-2ab cos(A)[/tex]

Here a = BC , b = 5 mi , c = 6.5 mi and A = 100° then,

=> [tex]BC^2 = 5^2+6.5^2-2\times5\times6.5\times cos (100\textdegree)[/tex]

=> [tex]BC ^2= 25+42.25-65\times(0.1736)[/tex]

=> [tex]BC^2= 78.534[/tex]

=> BC = 8.8 miles.

Hence the distance between Bert and Ernie is 8.8 miles.

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value of variable x on the parallel line is 12.

In geometry, a co exterior angle is an angle that is formed outside of a geometric figure by extending one of its sides. More specifically, a co exterior angle is formed when a transversal intersects two parallel lines, and it is an angle that is located outside of the parallel lines and on the same side of the transversal as one of the angles formed by the intersection.

Given

m ║n

8x+6 and 9x-30 are co exterior angle

8x+6+9x-30=180°

17x-24=180°

x=12

hence, value of variable x on the parallel line is 12.

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One possible set of points: (-9, 1), (-3, 5), (3, 9) which would have a positive linear association if they were graphed in a scatterplot.

A scatterplot is a graph that displays the relationship between two quantitative variables. It is a useful tool for exploring patterns and relationships in data, and can help identify trends, outliers, and potential correlations.

In the given question,

To create a set of 3 points with a positive linear association, we want to choose three points where the y-coordinate increases as the x-coordinate increases. Here's one possible set of points:

(-9, 1), (-3, 5), (3, 9)

If we graph these points on a scatterplot, we can see that there is a clear positive trend. As x increases, y also increases, suggesting a positive linear association between the two variables.

Note that there are many other sets of points we could choose that would also have a positive linear association. The key is to choose points where the y-coordinate tends to increase as the x-coordinate increases.

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Answer:

y^10

Step-by-step explanation:

In rewriting the expression in equivalent form, C. Tony made an error in Step 3. He should have multiplied each exponent by 4 instead of adding 4.

When writing in equivalent form such that one converts the expression ( a ² b ³ /  c) ⁴, one can use the law of exponents.

In this instance, the law of exponents states that if you are taking an exponent with a certain base, to another exponent, you multiply the exponents to get the new exponent.

In step 3, Tony should have multiplied each exponent by 4 instead of adding 4.

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Backing into a driveway or an alley on the right side, none of the options are correct

A) Backing into a driveway or alley on the right side is not necessarily illegal in most states. However, some states may have specific laws or regulations related to this maneuver, so it is important to check local laws.

B) Backing into a driveway or alley on the right side can be risky and may increase the likelihood of collisions, particularly if the driver is not paying close attention or if the view is obstructed. However, it does not always cause collisions and may be necessary in certain situations.

C) The safest turnabout maneuver depends on the specific situation and the layout of the road. In some cases, backing into a driveway or alley may be the safest option, while in other situations, a three-point turn or U-turn may be safer.

D) Whether to perform a backing maneuver in heavy traffic depends on the situation. In general, it is advisable to avoid backing up in heavy traffic if possible, as it can increase the risk of collisions. However, if there is no other option, the driver should proceed with caution and take all necessary precautions to ensure safety.

Therefore, the none of the options are correct

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The given question is incomplete, the complete question is:

Backing into a driveway or an alley on the right side a.is illegal in most states b. often causes collisions .c is the safest turn about maneuver d. should be done only in heavy traffic

The measure of angle 10 is 30 degrees.

What is an angle?

we can see that angle 10 and angle 11 form a straight line, and angle 9 and angle 10 form a triangle with angle 11.

Since angle 11 is a right angle with a measure of 90 degrees, the sum of angles 9 and 10 in the triangle must be 90 degrees.

We know that the measure of angle 9 is 60 degrees, so we can solve for the measure of angle 10 as follows:

angle 9 + angle 10 = 90 degrees

60 degrees + angle 10 = 90 degrees

angle 10 = 90 degrees - 60 degrees

angle 10 = 30 degrees

Therefore, the measure of angle 10 is 30 degrees.

What is triangle ?

A triangle is a closed geometric shape that consists of three line segments that connect three non-collinear points. The points where the line segments intersect are called the vertices of the triangle, and the line segments themselves are the sides of the triangle.

Triangles are two-dimensional objects that lie flat in a plane, and they have a variety of properties and characteristics that make them important in mathematics and other fields. The angles and sides of a triangle can be measured and related to one another through various geometric formulas and theorems, and triangles are used in a wide range of applications, from basic geometry and trigonometry to engineering, physics, and computer graphics.

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Complete question is: If the measure of angle 11 is 90 degrees, and the measure of angle 9 is 60 degrees, the measure of angle 10 is 30 degrees.

the number of students who take only Physics is 15.

An equation is a mathematical statement that shows that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.

Let's denote the number of students who take only Physics by x.

We can use these equations to solve for x, the number of students who take only Physics:

Substituting the expression for the number of Physics students in terms of the number who take both, we get:

20 = number who take both + 3(number who take both)

20 = 4(number who take both)

number who take both = 5

this value in the expression for the number of Physics students, we get:

number of Physics students = 3(number who take both) = 15

Finally, we can use the first equation to solve for the number of students who take only Physics:

40 = 15 + 2(number of students who take only Physics) - 5

40 = 10 + 2(number of students who take only Physics)

number of students who take only Physics = 15

Therefore, the number of students who take only Physics is 15.

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