3. Adam wants to buy a scooter that costs $110. He has already saved $25. Write an equation
that represents the amount of money Adam still needs to buy the scooter.

Answer:

0.222

Step-by-step explanation:

Batting average can be defined as a measure or technique used to determine the success of a player or pitcher

Batting average is determined by dividing a player's hits by his total at-bats for a number

We are told : Abraham hit 2 out of the 9 balls he was pitched.

Abraham's batting average = Number of hits/ Number of pitches

= 2/9

= 0.2222222222

Approximately ≈ 0.222

The area should be 47.5 CM.

Answer:

Step-by-step explanation:

The figure you see here is a trapezoid.

Area = \(\frac{(a + b)h}{2}\) = \(\frac{(6 + 13)(5)}{2}\) = \(\frac{(19)(5)}{2}\) = \(\frac{95}{2}\) = 47.5 cm

Answer:

f(-5) = 30

f(0) = 5

f(3) = 14

Step-by-step explanation:

=> f(x) = x²+5

for , f(-5) = (-5)² +5

=> 25 +5

=> 30

for , f(0) = (0)² +5

=> 5

for , f(3) = (3)² + 5

=> 9 + 5

=> 14

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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Answer

The distance is 13.4164078649987

Answer:

0.02

Step-by-step explanation:

Given a normal distribution :

Mean income (m) = 25000

Standard deviation of income (s) = 6000

X ≥ 12000

Using the relation to fund the standardized score :

Zscore =(x - m) / s

Zscore = ( 12000 - 25000) / 6000

Zscore = -13000 / 6000

Zscore = - 2.167

Using a z probability calculator :

P(Z ≤ - 2.167) = 0.015117

= 0.02

Answer:

see below

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y - 2 = 4(x- -1)

y - 2 = 4(x+1)

slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 4x+b

Substituting the point in

2 = 4(-1)+b

2 = -4+b

6 =b

y = 4x+6

standard form

Ax +by = c  where A is a positive integer and b and c are integers

y = 4x+6

Subtract 4x from each side

-4x+y = 6

Multiply by -1

4x -y = 6

I am not entirely sure but the answer should be 6^8

you will want to start by applying the exponent rule, (a^b)^c = a^bc

for this specific problem, it would look like this:

(6^2)^4 = 6^2x4

next you will multiply the exponents

2x4 = 8

Therefor, the answer would be 6^8

1. Chun Kumora's salary after 11 years will be $63,117.6200.

2. Chun Kumora's salary after 21 years will be $93,429.4900.

3. Chun must receive raise greater than $42,640 ($41,000 x 1.04) for the next year and greater than $44,345.6000 ($42,640 x 1.04) for the year after.

The future salaries (values) can be determined using an online finance calculator that compounds with the sum of the average inflation rate of 2% and the cost-of-living raise of 2% for 11 and 21 years, respectively.

Future Value in 11 years:

N (# of periods) = 11 years

I/Y (Interest per year) = 4% (2% x 2)

PV (Present Value) = $41,000

PMT (Periodic Payment) = $0

Results:

FV = $63,117.62 ($41,000 + $22,117.62)

Total Interest = $22,117.62

N (# of periods) = 21 years

I/Y (Interest per year) = 4% (2% x 2)

PV (Present Value) = $41,000

PMT (Periodic Payment) = $0

Results:

FV = $93,429.49 ($41,000 + $52,429.49)

Total Interest = $52,429.49

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Therefore, P(K|J) is equal to 1/5 in its simplest form.

What is fraction?

A fraction is a mathematical expression that represents a part of a whole. It is written in the form of one integer (the numerator) divided by another integer (the denominator), separated by a horizontal line. For example, the fraction 2/5 represents two parts out of a total of five parts.

The numerator represents the number of parts we are interested in, while the denominator represents the total number of equal parts that make up the whole. Fractions can be proper (the numerator is less than the denominator), improper (the numerator is greater than or equal to the denominator), or mixed (a whole number and a fraction together). Fractions are used in a wide range of mathematical operations, such as addition, subtraction, multiplication, and division.

by the question.

We can use the formula P(B/A) = P(B∩A)/P(A) to calculate P(KJ), where A is the event that J occurs, and B is the event that K and J occur.

First, we need to find P(K|J∩N). We can use the formula P(JNK) = P(KJ∩N)/P(J) to find this value.

\(P(K|J∩N) = P(JNK) * P(J) = (1/5) * (3/7) = 3/35\)

Next, we need to find P(J) = 3/7.

Finally, we can use the formula P(K|J) = P(K|J∩N)/P(J) to find P(KJ):

\(P(K|J) = P(KJ∩N)/P(J) = (3/35) / (3/7) = (3/35) * (7/3) = 1/5\)

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Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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The corresponding areas under the curves for y = 2x-x² in the interval [1, 2] and y = x³-6x²+8x in the interval [0, 4] are 2/3 unit² and 0 unit²

Given:

1. y = 2x-x² in the interval [1, 2]

2. y = x³-6x²+8x in the interval [0, 4]

In order to find  the area under the curve for these functions for the given intervals, we will take the integral of the functions and use the intervals as upper and lower limits: Thus:

y = 2x-x² in the interval [1, 2]  will be:

\(\int\limits^2_1 {2x-x^{2} } \, dx = \left[\frac{ 2x^2}{2}-\frac{ x^3}{3}\right]_1^2\)

                   \(= \left[x^{2} -\frac{ x^3}{3}\right]_1^2\)

Substitute the value of the upper and lower limits into x:

               =  [2²- 2³/3] - [1²- 1³/3]

              =   [4 - 8/3] - [ 1 - 1/3]

              =   [4/3] - [2/3]

              = 2/3 unit²

y = x³-6x²+8x in the interval [0, 4] will be:

 \(\int\limits^4_0 {x^{3} -6x^{2} + 8x } \, dx = \left[\frac{ x^4}{4}-\frac{ 6x^3}{3}+\frac{ 8x^2}{2}\right]_0^4\)

                               \(= \left[\frac{ x^4}{4}- 2x^3+4x^2\right]_0^4\)

                              = [4⁴/4 - 2(4)³ + 4(4)²] - [0⁴/4 - 2(0)³ + 4(0)²]

                              =  [ 64 - 128 + 64] - [0 - 0 -0]

                              = 0 unit²

Therefore, the areas under the curves y = 2x-x² in the interval [1, 2]

and y = x³-6x²+8x in the interval [0, 4] are 2/3 unit² and 0 unit² respectively

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The average value of 3t^3-t^2 over the interval -1<=t<=2 is 11/4

Mean Value Theorem states if a function f(x) is continuous on the interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

f '(c)=f(b)-f(a)/b-a

Average Value:

The average value of a function of a variable over a range represents the height of a rectangle of the same area as that defined by the function under the curve. This value can be calculated using a formula:

favg=1/b−a∫f(t)dt

consider f(x)=3t³-t² and limits are -1 to 2

Now, substitute these values in the above formula:

favg=1/2-(1)∫3t³-t²dt

favg=1/3∫(3/4t⁴-1/3t³)|₋₁²

favg=(12-8/3)-(3/4+1/3)

By solving the equation we get

favg=11/4

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Answer:

Uber is the best choice

Step-by-step explanation:

Uber: $0.25 × 8

          = $2.00

Lyft: $0.75 × 8

        = $6.00

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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The percentage of observations which we expect to lie between 100 and 200 is 3.38%

Given, the mean is 150 and

standard deviation(sd) = 25

what percentage of observation lie between 100 and 200.

x + 1sd = 175

x - 1sd = 125

x + 2sd = 200

x - 2sd = 100

x + 3sd = 225

x - 3sd = 7

observation between 100 and 200 lie from x + 1sd

Therefore P(x) = (100-175)÷25

= -3

=3.38%

Hence the percentage of observations that lie between 100 and 200 is 3.38%

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Answer: 15/17

Step-by-step explanation:

See attached image.

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer: The two numbers that multiply to -65 and add to -8 are -13 and 5.

Steps: Here are the steps to find two numbers that multiply to -65 and add to -8:

Write down the equation x * y = -65 where x and y are the two numbers you’re looking for.

Write down the equation x + y = -8.

Solve for one of the variables in one of the equations. For example, solving for x in the second equation gives us x = -8 - y.

Substitute this expression for x into the first equation: (-8 - y) * y = -65.

Solve this quadratic equation for y: -y^2 - 8y + 65 = 0.

Use the quadratic formula to find the values of y: y = (-(-8) +/- sqrt((-8)^2 - 4 * (-1) * 65)) / (2 * (-1)).

This gives us two possible values for y: -13 and 5.

Substitute these values back into one of the original equations to find the corresponding values of x. For example, when y = -13, we have x = -8 - (-13) = 5. When y = 5, we have x = -8 - 5 = -13.

So, the two numbers that multiply to -65 and add to -8 are -13 and 5.

Answer:

Step-by-step explanation:

While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.

The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.

The probability density function (PDF) for a Pareto Distribution is:

Xn = 1

for various Alpha levels

Where Xn is the probability value of X

As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]

Where ¶ is the Dirac Delta function.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(4.27\text{cm} \approx\boxed{4\text{cm}}\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

Recall the Rounding Rules:

⸻⸻⸻⸻

\(\underline{4.27cm}\\\\\rightarrow2\leq 4\\\\\boxed{4.27cm \approx 4cm}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Circle

Step-by-step explanation:

r = 2 cos θ

Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular.

x² + y² = 2x

x² − 2x + y² = 0

Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

This is a circle with center (1, 0) and radius 1.

The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

Given function is r = 2 cos θ

Now, Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular form;

x² + y² = 2x

x² − 2x + y² = 0

Using Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

Hence, This is a circle with a center (1, 0) and radius of 1.

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To show that the Directed Disjoint Paths Problem is NP-complete, we can use a reduction from the well-known NP-complete problem of Hamiltonian Path, which is defined as follows: given a graph G and a starting node s, does G contain a simple path that visits every node exactly once and ends at s?

We can reduce the Hamiltonian Path problem to the Directed Disjoint Paths Problem as follows. Given a graph G and a starting node s for the Hamiltonian Path problem, we can construct a new graph G' as follows:

Now, consider the k pairs of nodes (s1,t1), (s2,t2), ..., (sk,tk) in G', where si and ti are the corresponding nodes in G' for the ith node in G. We can see that G contains a Hamiltonian path from s to s if and only if G' contains k node-disjoint paths from si to ti for all i.

Since the Hamiltonian Path problem is NP-complete, and we have shown that it can be reduced to the Directed Disjoint Paths Problem in polynomial time, it follows that the Directed Disjoint Paths Problem is also NP-complete.

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Step-by-step explanation:

i assume this is the question you asked me to look at.

Well, angle 116° and y are supplementary angles

therefore,116°+y=180°

y=180°-116°=64°

Now to find x

x+y+125+72=360°

x+64+125+72=360

x+261=360

x=360-261=99°

The measure of x° is  99° and the measure of y° is 64°.

What is quadrilateral?

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

From the given figure,

116°+y°=180° (Sum of adjacent angles is 180°)

y°=180°-116°

y°=64°

Sum of interior angles of quadrilateral is 360°.

Here, x°+y°+72°+125°=360°

x°+64°+72°+125°=360°

x°+261°=360°

x°=99°

Therefore, the measure of x° is  99° and the measure of y° is 64°.

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Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.

11+13+14+16+17+18+20+20+21+24+25+29 = 228

There are 12 numbers, so divide by 12.

228/12 = 19. The mean is 19.

Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.

(Side note: yes, median and mean can be the same.)

Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.

Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.

the answer to 1 is d and the answer to 2 is 471,284. Please review this topic when you get time.hope this helps

The standard deviation of the number of toys donated by juniors is greater than that of seniors.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.

\(\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}\)

For the seniors, the mean is given as,

Mean = (5 x 2 + 35 x 2 + .... + 15 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 5)² + (26 - 5)² + (26 - 15)²] / 10

σ = 14.28

For the juniors, the mean is given as,

Mean = (40 x 2 + 25 x 2 + ....... + 40 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 40)² + (26 - 25)² + (26 - 40)²] / 10

σ = 13.19

The standard deviation of the number of toys donated by juniors is greater than that of seniors.

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The complete question is given below.