Which function models the data in the table below?



y = -1/2x + 5

y = -2x + 5

y = -1/2x + 10

y = -2x + 10

Step-by-step explanation:

The selling price is $495.

The first washing machine:

- is marked down by 30​%

$495 - 100%

$x - 100% - 30% = 70%

Find the value of x:

x=$495*0.7=$346.50=$347

The second washing machine:

- is marked down by 20​% with an additional 10​% off

$495 - 100%

$y - 100% - 20% = 80%

Find y:

Y=$495*0.8=$396

Now,

$396 - 100%

$z - 100% - 10% = 90%

Find z:

Z=$396*0.9=$356.40=$356

the sale price of the first washing machine is $347 and the sale price of the second washing machine is $356. The second machine is more expensive.

Answer:

The sale price of the first washing machine is $308

The sale price of the second washing machine is $317

Answer:

\((244 - n)n \\ n = 3 \\ (244 - 3) \times 3 \\ = (241) \times 3 \\ = 723\)

You're looking for the percent, so your equation would be:

x% × 200 = 0.5

(x/100) × 200 = 0.5

2x = 0.5

x = 0.25

So, 0.25% of 200 is 0.5.

* You can check your work by multiplying 0.25% × 200. Surely enough, it does give you 0.5.

Answer = 0.25%

Answer:

0.25%

Step-by-step explanation:

Uhm, well I don't know how to explain but I know it's correct.

Length of hike = definite integral of velocity from 0 to 10.

What is integral ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

The total length of a piecewise-defined function represents the total distance between points on the curve. To calculate this, one can use calculus techniques, such as integration. The definite integral of the function over an interval represents the total length of the curve on that interval. To find the total length of the mountain hike from x=0 to x=10, one needs to evaluate the definite integral of the function over the interval [0,10]. This can be calculated either analytically, using calculus, or numerically, using numerical integration methods. The exact method to be used would depend on the specifics of the function and the desired level of accuracy.

Length of hike = definite integral of velocity from 0 to 10.

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Visible area = (202.8/360) × 4π × 2.1² ≈ 18.56 cm². Volume of clay = (2/3) × π × (42/2)³ = 21105 cm³

(a) The volume of clay used to prepare the dome is given by:

Volume of hemisphere = (2/3) × π × (d/2)³, where d is the diameter of the hemisphere

Therefore, Volume of clay = (2/3) × π × (42/2)³ = 21105 cm³

(b) The area of silk cloth required to prepare the chhatra can be found as follows:

The radius of the largest chhatra is 2.1 cm, so its slant height, l₁ = √(2.1² + 2.4²) = 3.076 cm (using Pythagoras theorem).

The radius of the medium chhatra is 1.4 cm, so its slant height, l₂ = √(1.4² + 2.4²) = 2.8 cm.

The radius of the smallest chhatra is 0.7 cm, so its slant height, l₃ = √(0.7² + 2.4²) = 2.5 cm.

The total area of silk cloth required to prepare the chhatras is:

Area = πr₁l₁ + πr₂l₂ + πr₃l₃, where r₁, r₂, and r₃ are the radii of the chhatras.

Substituting the values, we get:

Area = π × 2.1 × 3.076 + π × 1.4 × 2.8 + π × 0.7 × 2.5 ≈ 21.14 cm²

Hence, the answer is (ii) 5.5 cm².

(c) The area of the largest Chhatrapati to be gold-plated can be found as follows:

The largest Chhatrapati is the one with a radius of 2.1 cm. The area of this Chhatrapati is:

Area = πr² = π × 2.1² ≈ 13.85 cm²

However, since the Chhatrapati has a spherical shape, only a part of it will be visible when it is placed on the hemispherical dome. The visible area can be found as follows:

Visible area = (θ/360) × 4πr², where θ is the central angle of the spherical segment cut by the horizontal plane of the Stupa.

The radius of the sphere is the same as the radius of the largest Chhatrapati, i.e. 2.1 cm.

The height of the spherical segment can be found as follows:

h = r - (R - r), where R is the radius of the hemisphere and r is the radius of the Chhatrapati.

Substituting the values, we get:

h = 2.1 - (21 - 2.1) = 2.1 - 18.9 = -16.8 cm (negative sign indicates that the Chhatrapati is below the horizontal plane of the Stupa)

Since the Chhatrapati is below the horizontal plane, the central angle θ will be greater than 180 degrees. The angle can be found as follows:

cos(θ/2) = h/r

θ/2 = cos⁻¹(-16.8/2.1) ≈ 101.4 degrees

θ = 202.8 degrees

Substituting the values, we get:

Visible area = (202.8/360) × 4π × 2.1² ≈ 18.56 cm²

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Question:-Sanchi Stupa is a Buddhist complex in Raisen District of the state of Madhya Pradesh. A

renowned architect prepared a small-scale model which is a replica of the Stupa.

The diameter of the hemispherical dome is 42 cm. The dome is filled with clay. Three

chhatravalis are fixed on the top of the dome. These chhatravalis have radii 2.1 cm, 1.4

cm and 0.7 cm respectively. One Oopri Pradakshina Path is attached all around the

dome. The outer diameter of this path is 49 cm.

(a) The volume of clay used to prepare the dome is

(i) 16816 cm³ (ii) 17151 cm³ (iii) 19404 cm³ (iv) 21105 cm³

(b) The architect was asked to cover all the chhatravalis with a conical chhatra

(umbrella) having a radius the same as that of the Chhatrapati and a height of 2.4 cm. Find the

area of the silk cloth required to prepare the chhatra.

(i) 4.2 cm² (ii) 5.5 cm² (iii) 6.25 cm² (iv) 7.5 cm²

(c) The chhatravalis are to be gold-plated. Taking the thickness of each Chhatrapati to

be negligible, find the area of the largest Chhatrapati to be gold plated.

(i) 18.56 cm² (ii) 21.14 cm² (iii) 27.72 cm² (iv) 33.36 cm²

(d) Find the cost of fixing crystals on the surface of the dome at a rate of Rs. 5 per

cm2

.

(i) Rs. 13860 (ii) Rs. 14445 (iii) Rs. 17475 (iv) Rs. 18360

(e) Find the area of the Oopri Pradakshina Path.

(i) 201.1 cm² (ii) 363.5 cm2

(iii) 500.5 cm2

(iv) 801.1 cm2

Approximately 304,657,600 Americans were there in July 2009 based on the estimated 2008 growth rate of 0.88%.

To find the approximate US population in July 2009, we need to apply the growth rate of 0.88% to the initial population in July 2008.

Convert the growth rate from percentage to decimal:

0.88% = 0.0088
Calculate the number of people added to the population in 2008: 302,000,000 * 0.0088 = 2,657,600
Add this number to the initial population to find the population in July 2009:

302,000,000 + 2,657,600 = 304,657,600.

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Answer:

The length of a 200 meter race in inches can be calculated by converting the distance to meters and then multiplying by the number of inches per meter. Since there are 0.0254 meters in one inch, the length of a 200 meter race in inches is 200 * 0.0254 = 5.08 meters.

Usain Bolt's feet per second average speed over the 200 meter race distance can be calculated by dividing the length of the race in feet by the time it took him to run it. Since there are 3.281 feet in one meter, the length of the race in feet is 5.08 * 3.281 = 16.63 feet. Dividing this distance by Bolt's world record time of 19.19 seconds, we get a feet per second speed of 16.63 / 19.19 = 0.864 feet per second.

To convert Bolt's feet per second speed to miles per hour, we can multiply it by the number of feet in one mile and the number of seconds in one hour. Since there are 5280 feet in one mile and 3600 seconds in one hour, Bolt's speed in miles per hour is 0.864 * 5280 / 3600 = 1.3 miles per hour.

Answer:

\(5 \dfrac{2}{3}\; \textsf {pounds}\)

Step-by-step explanation:

Each dig gets 17/3 lbs of dog food

173 = 5 2/3

There is a 0.022 percent chance that a student may receive a quiz grade of 95 or above.

The z-score formula is as follows:

z = (95-85)/8.0

= 1.25

Using the z-score table, calculate the probability:

P(z >= 1.25)

= 0.022

The z-score formula can be used to determine the likelihood that a student would receive a quiz grade of 95 or higher. The data set's mean and standard deviation are considered in the formula. The mean score on the quiz in this instance is 85, and the standard deviation is 8.0. By deducting the mean from the desired score (95), the z-score can be computed by dividing the result by the standard deviation (8.0). The z-score in this instance is 1.25.  The likelihood that a student will receive a quiz grade of 95 or higher can be determined using the z-score table. The likelihood of a z-score of 1.25 or higher is 0.022, according to the table. This indicates that there is a 0.022 percent chance that a student will receive a quiz grade of 95 or above.

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The domain of the function modeling the distance swam by a swimmer as a function of time would be all positive real numbers greater than or equal to zero, representing the time spent swimming in the race.

This is because the time spent swimming in a race cannot be negative and must be greater than or equal to zero, which represents the start of the race. The domain of a function defines the set of all possible input values (in this case, time) for which the function produces a valid output (distance). In this case, the domain would be all positive real numbers greater than or equal to zero, since these are the only valid input values that can be used to calculate the distance swam by a swimmer during a race.

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Answer:

The cost of 1 gallon is $2.5

Step-by-step explanation:

Given

Cost of 14 gallons = $35

Required

Determine the cost of 1 gallon

From the given parameters, we have:

\(14\ gallons = \$35\)

Divide both sides by 14

\(\frac{14\ gallons}{14} = \frac{\$35}{14}\)

\(1\ gallon = \frac{\$35}{14}\)

\(1\ gallon = \$2.5\)

Hence,

The cost of 1 gallon is $2.5

Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

Answer:

Step-by-step explanation:

firstly, 8+d=x and y+d= -4 where d is the common difference of the AP.

Also,

x+d=y;

therefore d=y-x;

so,

8+y-x=x (from the first equation)

=>8+y=2x

=>y=2x-8

Now from the second equation,

y+d= -4

(2x-8)+(y-x)= -4

=>x-8+2x-8= -4

=>3x=12

=>x=4

similarly,

y=2(4)-8

=>y=0

The capital letter H has 2 reflectional symmetry and 2 rotational symmetry.

A figure has reflectional symmetry if it can be reflected across a line and still look the same. For the capital letter H, there is two lines of symmetry, which is the vertical line and horizontal line that divides the letter into two equal halves. Reflecting the letter across this line produces the same letter. So, the H has only 2 reflectional symmetries.

A figure has rotational symmetry if it can be rotated by some angle and still look the same. For the capital letter H, if we rotate it 180 degrees and 360 degrees about the center point of the letter, it will look the same. There is no other angle of rotation that produces the same letter. Therefore, the H has only 2 rotational symmetries.

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--The question is incomplete, answering to the question below--

"How many reflectional symmetries does this figure have?

Enter your answer

___ reflectional symmetries

How many rotational symmetries does this figure have?

Enter your answer

___ rotational symmetries"

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

True. The central limit theorem states that if the sample size n is large enough (usually considered to be at least 30), then the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution.

The sampling distribution of the mean can be approximated by the normal distribution if the sample size (n) is at least 30. This statement is based on the Central Limit Theorem, which states that the sampling distribution of the mean of a random sample drawn from any population will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. A sample size of 30 is often considered the threshold for approximating a normal distribution in such cases.

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The relative wind speed will the person sense is -5.2mph.

Speed can be explained as the  distance traveled per unit of time which is how the object is moving, and it is a  scalar quantity  having magnitude of the velocity vector.

Speed of man  =2.95 mph

Speed of wind  =-2.25 mph

Relative wind speed V_R is mathematically given directly as

Vr= Vw-Vm

=-2.25 mph -2.95 mph

= -5.2mph

Therefore, relative wind speed will the person sense is -5.2mph.

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The equation becomes of the pressure is   P = 90 + 10 sin(π/36(t +4 ))

By observation the sine function should be of form P=  90 + 10 sin(ω(t − c)) as it oscillates about 90 and with a factor of 10. Let time be represented by the variable t in hours from 12.00 AM.

At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg

Substituting it in the equation we get,

100 = 90 + 10 sin(ω(t − c))

10 = 10  sin(ω(14 − c))

1 = sin(ω(14 − c))

ω(14 − c) = π/2                           -1)

At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg

80 = 90 + 10 sin(ω(t − c))

-10 = 10 sin(ω(2 − c))

3π/2 = ω(2 − c)                           -2)

dividing 2) with 1) we get

3 = (14 − c) /(2 − c)  

6 - 3c = 14 - c

2c = -8

c = - 4

Substituting the value of c in 1) we get,

ω(14 − (-4)) = π/2

ω18 =  π/2

ω = π/36

Thus the equation becomes  P = 90 + 10 sin(π/36(t +4 ))

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When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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Answer:

x = m×p - n

Step-by-step explanation:

\(m = \frac{n + x}{p} \)

\( = > n + x = m \times p\)

\( = > x = m \times p - n\)

Answer:

x = m - n

Step-by-step explanation:

Given

m = n + x ( isolate x by subtracting n from both sides )

m - n = x

Answer:

mean = 5

median = 4.5

mode = 4

Step-by-step explanation:

Mean :

n = 8

sum of all items = 4+6+5+4+4+5+4+8

= 10+9+9+12

= 19+ 21

= 40

so,

mean = sum of all items/ n

= 40/8

= 5

mean = 5

Median:

ascending order: 4,4,4,4,5,5,6,8

n = 8

md = (n+1)/2 the term

= (8+1)/2 th term

= 9/2 th term

= 4.5 th term

= (4th + 5th) / 2

= (4+5)/2

= 9/2

= 4.5

median = 4.5

x. f.

4. 4

5. 2

6. 1

8. 1

here the highest frequency is 4 and 4 is corresponding to 4

so, mode = 4

The technique for determining an array index using only a search key and not searching is called hashing.

Hashing is a method that maps data to a fixed-size array called a hash table. In this technique, a hash function is used to generate a unique index for each search key. The hash function takes the search key as input and performs some calculations to produce the index value.

This index is then used to access the corresponding element in the array, providing direct access to the desired data without the need for further searching.

Hashing is the technique of determining an array index using only a search key.

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Answer:

Tenley will use _9_ feet of wood.

Step-by-step explanation:

The key here is to multiply 4 by 2.25. If just adding 2.25 4 times is easier, go for that. Either way the correct answer will be 9 feet.

The coefficient of the x term in the expansion of f[x] best reflects the behavior of the function for x's close to 0.

The behavior of a function for x values close to 0 can be understood by examining its expansion in powers of x. When a function is expanded in a power series, each term represents a different order of approximation to the original function. The coefficient of the x term, which is the term with the lowest power of x, provides crucial information about the behavior of the function near x = 0.

In the expansion of f[x] = a0 + a1x + a2x² + ..., where a0, a1, a2, ... are the coefficients, the term with the lowest power of x is a1x. This term captures the linear behavior of the function around x = 0. It represents the slope of the function at x = 0, indicating whether the function is increasing or decreasing and the rate at which it does so. The sign of a1 determines the direction of the slope, while its magnitude indicates the steepness.

By examining the coefficient a1, we can determine whether the function is increasing or decreasing, and how quickly it does so, as x approaches 0. A positive value of a1 indicates that the function is increasing, while a negative value suggests a decreasing behavior. The absolute value of a1 reflects the steepness of the function near x = 0.

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The height of the right triangle is 24 centimeters. This is determined by solving the equation for the area of the triangle, which is given as 96 cm², and considering that the height is 3 times the length of the base. By substituting the values and solving the equation, we find that the height is indeed 24 centimeters.

To determine the height of the right triangle, we can use the formula for the area of a triangle, which is given by the formula A = (1/2) * base * height. In this case, the area is known to be \(96 cm^2\).

Let's denote the length of the base as x. According to the problem statement, the height is 3 times the length of the base, so the height can be expressed as 3x.

Substituting these values into the area formula, we get:

\(96 = (1/2) * x * 3x\)

Simplifying the equation:

\(96 = (3/2) * x^2\)

To solve for x, we can divide both sides of the equation by (3/2):

\(64 = x^2\)

Taking the square root of both sides, we find:

x = 8

Since the height is 3 times the length of the base, the height is:

3 * 8 = 24 centimeters.

Therefore, the height of the right triangle is 24 centimeters.

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Answer:

8685 butterflies

Step-by-step explanation:

Given the logistics growth function expressed as ​f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t which describes the population of a species of butterflies t months after they are introduced to a​ non threatening habitat, to know the number of butterflies expected butterflies are expected in the habitat after 20 ​months, we will substitute t = 20 into the function.

f(20) = 440/1+13.7exp-(0.28×20)

f(20) = 440/1+13.7exp-(5.60)

f(20) = 440/1+(13.7× 0.003698)

f(20) = 440/1+0.05066

f(20) = 440/1.05066

f(20) = 8684.9

This means there will be approximately 8685 butterflies in the habitat after 20months.

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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