A researcher records the odometer reading and age of used Hondas. What kind of correlation is likely to be obtained for these two variables

Answer:

Devonte is correct because the interquartile range is less for French

Step-by-step explanation:

The first box plot at the top shows scores in Spanish, while the second box plot below it shows French scores.

Variability can be ascertain by finding out the interquartile range of a data set.

The higher the value of the IQR, the more the variability, while the lower the IQR, the less the variability.

IQR = Q3 - Q1

IQR for Spanish score = 85 - 60 = 25

IQR for French score = 80 - 65 = 20

From the above, we can say that Spanish scores has more variability when compared to French scores.

Therefore, Devonte is correct because the interquartile range is less for French, which shows that the variability in French scores is lesser than that of Devonte's Spanish scores.

Answer:

Devonte is correct because the interquartile range is less for French.

Step-by-step explanation:

The scoring range indicates the deviance from the standard values. It can only be inferred that the interquartile range is very narrow. In other words, there is less variability in the scores. Thus, a smaller quartile range means that  there is less variability in the quantity being measured. The interqurtile range is the difference in the values of the the 75th percentile and the 25th percentile of a cumulative frequency distribution curve.  

To determine the longest wavelength photon which can remove an electron from mercury metal, we need to use the equation:

wavelength = hc/work function

Photons are just light particles. Photons are basic subatomic particles that convey the electromagnetic force (and so much more). The photon is the basic unit of electromagnetic radiation, or the "quantum."

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).

To determine the longest wavelength photon which can remove an electron from mercury metal, you need to use the equation:

wavelength = hc/work function

where h is the Planck constant (6.626 x 10^-34 Js), c is the speed of light (2.998 x 10^8 m/s), and work function is the minimum energy needed to remove an electron from the metal, in this case 4.475 eV.

Plugging these values into the equation gives:

wavelength = (6.626 x 10^-34 Js)(2.998 x 10^8 m/s)/(4.475 x 1.602 x 10^-19 J/eV)

This simplifies to:

wavelength = 404.4 nm

So, the longest wavelength photon which can remove an electron from mercury metal is 404.4 nm.

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Answer:

Step-by-step explanation:

Its 4.51

The answer would be ⁻\(\frac{19}{x-5\\}\)

Answer:

\(\underline{\boxed{\sf \cfrac{-19}{x-5}}}\)

Step-by-step explanation:

\(\sf \cfrac{x^2+10+25}{x+5}-\cfrac{x^2-6}{x-5}\)

First, Let's factor the expressions that are not already factored in x^2+10+25/x+5

\(\sf \cfrac{(x+5)^2}{x+5}-\cfrac{x^2-6}{x-5}\)

Now, cancel out x+5 in both numerator and denominator:-

\(\sf x+5-\cfrac{x^2-6}{x-5}\)

Expand equations to make their denominators the same before adding or subtracting them. Multiply x+5 * x-5/x-5:-

\(\sf \cfrac{(x+5)(x-5)}{x-5}-\cfrac{x^2-6}{x-5}\)

Now, Since \(\sf \frac{(x+5)(x-5)}{x-5}\) and \(\sf \frac{x^2-6}{x-5}\) and similar denominator, we'll subtrac their numerators.

\(\sf \cfrac{(x+5)(x-5)-(x^2-6)}{x-5}\)

\(\sf \cfrac{x^2-5x+5x-25-x^2+6}{x-5}\)

Combine like tems in \(\sf x^2-5x+5x-25-x^2+6\) :-

\(\sf \cfrac{-19}{x-5}\)

Therefore, your answer is D.

Answer:

3(x + 5y) - 2(x + y)

3x + 15y - 2x - 2y

x + 13y

(3x + 15y) + (-2x + -2y)

x + 13y

Answer:

c) 42 shrubs

Step-by-step explanation:

Calculation to Find the maximum number of shrubs the garden can accommodate

First step is to calculate the Area of Garden

Area of Garden = (32.2 ft)*(18 ft)

Area of Garden= 579.6ft²

Now let calculate the maximum number of shrubs the garden can accommodate using this formula

Maximum number shrubs=(579.6 ft²)/(13.8 ft² per shrub)

Maximum number shrubs = 42 shrubs

Therefore the maximum number of shrubs the garden can accommodate will be 42 shrubs

The equation given is:

We can use the property:

to break this apart. Shown below:

We can solve for k [we divide both sides by 2^x to isolate k]:

Now, let's do a little algebra. The steps are shown below:

The correct answer is

Answer:

97.6 + 77.8

Step-by-step explanation:

97.6-(-77.8)

= 97.6+77.8

97.6+77.8= 175.4

97.6-(-77.8) = 175.4

Answer:

x = 18

Step-by-step explanation:

Missing Components of triangle for angles:

A=39

B=51

C=90

Missing Components of triangle for sides:

a=11.3

b=14

x=18

To shift a function f(x) to the left in a units (where a > 0), we apply the following transformation:

In this case, we have:

• a shift to left in a = 8 units,

• the parent function f(x) = x.

Applying the transformation from above, we get:

D. g(x) = x + 8

1.) The probability that the sample mean will be greater than 48 minutes is 0.9332.

2.) The probability of the sample mean being between 44 and 49 minutes is 0.6687.

3.) The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean.

To solve this problem, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means tends to be approximately normally distributed, regardless of the shape of the original population, when the sample size is large enough.

1.) Probability of sample mean > 48 minutes:

To calculate this probability, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the population mean (μ) is 45 minutes, the population standard deviation (σ) is 12 minutes, and the sample size (n) is 36. We want to find the probability of the sample mean being greater than 48 minutes.

Calculating the z-score:

z = (48 - 45) / (12 / √36) = 3 / 2 = 1.5

Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.5 is approximately 0.9332. Therefore, the probability that the sample mean will be greater than 48 minutes is approximately 0.9332.

2.) Probability of sample mean between 44 and 49 minutes:

To calculate this probability, we need to find the z-scores for both 44 and 49 minutes and then calculate the area between those z-scores.

Calculating the z-scores:

For 44 minutes:

z1 = (44 - 45) / (12 / √36) = -1 / 2 = -0.5

For 49 minutes:

z2 = (49 - 45) / (12 / √36) = 4 / 2 = 2

Using the standard normal distribution table or calculator, we find the probabilities corresponding to z1 and z2:

P(z < -0.5) ≈ 0.3085

P(z < 2) ≈ 0.9772

The probability of the sample mean being between 44 and 49 minutes is approximately P(-0.5 < z < 2) = P(z < 2) - P(z < -0.5) ≈ 0.9772 - 0.3085 = 0.6687.

3.)Conclusion from 100 samples with a mean of 65 minutes:

If 100 samples were collected, and the sample mean was 65 minutes, we would need to assess whether this value is significantly different from the population mean of 45 minutes.

To make this assessment, we can calculate the z-score for the sample mean of 65 minutes:

z = (65 - 45) / (12 / √36) = 20 / 2 = 10

The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean. This is an extremely large deviation, suggesting that the sample mean of 65 minutes is highly unlikely to occur by chance.

Given this, we can conclude that the sample mean of 65 minutes is significantly different from the population mean. It may indicate that there is a systematic difference in the delivery times between the sample and the population, possibly due to factors such as increased demand, traffic, or other external variables

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Answer:

Step-by-step explanation:

Remark

This is a proportion question. A proportion is 2 equal ratios that requires you to solve the 4th part when you know the other 3.

Givens

1 foot scale model length

5 feet of actual length

x = length of model

65 feet of actual length

Formula

1 foot / 5 feet = x / 65 feet

Solution

1/5 = x / 65                          Cross multiply

5x = 65                                Divide by 5

5x/5 = 65/5

x = 13

Answer

The model is 13 feet long

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

0.02 × 100 = 2

Step-by-step explanation:

move the decimal 2 steps backward according to the numbers of zeros behind the multiplier(100).

0.02 × 100 = 2

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Answer:

7

Explanation:

you multiply 14 by itself again, so the exponent goes up by 1.

Answer:

Step-by-step explanation:

14⁶ × 14 =

The exponent of a number says how many times to use the number in a multiplication.

14⁶ means that 14 is multiplied by 6 times (14x14x14x14x14x14) if you add a multiplication, again by 14, you will have 14 multiplied once more, so the answer is 14⁷ ( 14x14x14x14x14x14x14).

Answer:

Substitution is when you isolate a variable-

3) We can divide the first equation by 6 to get x+y=-1, then isolate to get y=-1-x. We plug this into the second equation to have 3x+(-1-x)=-13. We simplify and get 2x=-12 so x=-6. We plug this back into the first equation and get -6+y=-1 so y=5. So the answer as an ordered pair is (-6,5).

4) We can isolate the second equation to get x=2y+11. We substitute this into the first equation to have -7(2y+11)-2y=-13. We simplify and get -16y=64 so y=-4. We plug this back into the second equation and get x+8=11 so x=3. So the answer as an ordered pair is (3,-4).

The quadratic equation that gives the height of the rocket, h = 156·t - 16·t² is evaluated at h = 60 feet to give the two times the rocket's height is 60 feet as 0.40 seconds and 9.35 seconds.

A quadratic equation is an equation of the second degree that can be expressed in the form; a·x² + b·x + c = 0, where the letters, a, and b represents the coefficients of x and c is a constant.

The initial velocity of the rocket = 156 ft./s upwards

The given equation of the rocket is: h = 156·t - 16·t²

The times when the rocket height is 60 feet are found by plugging in the value h = 60, in the equation of the vertical height of the rocket as follows:  

h = 60 = 156·t - 16·t²

156·t - 16·t² - 60 = 0

4·(39·t - 4·t² - 15) = 0

Therefore: \(39\cdot t - 4\cdot t^2 - 15 = \dfrac{0}{4} =0\)

39·t - 4·t² - 15 = 0

-4·t² + 39·t - 15 = 0

From the quadratic formula which is used to solve the quadratic equation of the form; f(x) = a·x² + b·x + c, is presented as follows;

\(x = \dfrac{-b\pm\sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

The solution of the equation, -4·t² + 39·t - 15 = 0, is therefore:

\(t = \dfrac{-39\pm\sqrt{(39)^2-4\times (-4) \times (-15)} }{2\times (-4)}= \dfrac{-39\pm\sqrt{1281} }{-8}\)

Therefore, when the height of the rocket is 60 feet, the times are: \(t = \dfrac{-39-\sqrt{1281} }{-8}\approx 9.35\) and \(t = \dfrac{-39+\sqrt{1281} }{-8}\approx 0.40\)

The times when the height of the rocket is 60 feet, the times are:

t ≈ 9.35 s, and t ≈ 0.40 s

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Answer:

Step-by-step explanation:

If the given variables are 127 hours of sleep per week for a Giant Armadillo, and 98 hours of sleep per week for a Platypus, to determine which animal gets the most sleep, first multiply the total hours of sleep of each animal per week to the total number of weeks In a year, which is 52. Once you get the answers, which are 6,604 hours of sleep in a year for the Giant Armadillo and 5,096 hours of sleep in a year for a Platypus. You subtract 6,604 and 5,096 together to get the answer, which is 1,508. Therefore we conclude that that the Giant Armadillo has 1,508 hours more hours of sleep than a Platypus in a Year.

Answer:

1508 hour I think !!!!!!!!!!

The equatiοn οf the vertical asymptοte fοr f(x) is x = -3.

The end behaviοr οf f(x) is pοsitive οr negative infinity.

The x-intercept fοr f(x) is  (5,0).

A vertical asymptοte is a line that a curve apprοaches but never tοuches οr crοsses as the input variable apprοaches a certain value. In οther wοrds, a vertical asymptοte is a vertical line οn a graph that the functiοn apprοaches as the input variable apprοaches a specific value οr set οf values.

Tο find the equatiοn οf the vertical asymptοte fοr f(x) = (4x-20)/(x+3), we need tο identify the values οf x that make the denοminatοr οf the functiοn equal tο zerο.

Setting the denοminatοr equal tο zerο, we get:

x + 3 = 0

Sοlving fοr x, we get:

x = -3

Therefοre, the equatiοn οf the vertical asymptοte fοr f(x) is x = -3.

Tο determine the end behaviοr οf f(x) as x apprοaches infinity, we can use the fact that the degree οf the numeratοr is greater than the degree οf the denοminatοr. This means that the functiοn will apprοach infinity as x apprοaches pοsitive οr negative infinity.

Tο find the x-intercept fοr f(x), we need tο set the numeratοr οf the functiοn equal tο zerο and sοlve fοr x.

Setting the numeratοr equal tο zerο, we get:

4x - 20 = 0

Sοlving fοr x, we get:

x = 5

Therefοre, the x-intercept fοr f(x) is (5,0).

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Joe earned $140 for working 20 hours

To determine the value of a single unit from a specified multiple, use the unitary technique. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.

Joe worked 14 hours  and earned = $119

Joe worked for 1 hour and earned = $ 119/ 14

Joe worked for 20 hours and earned = $ 119/ 14 x 20

                                                                 = 4140

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Answer:

D) The number that is 5 to the right of -6 on the number line

Hope this helps :)

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

  x = √65

Step-by-step explanation:

You are given a right triangle with leg lengths 4 and 7, and you are asked for the length of the hypotenuse, x.

The Pythagorean theorem relates the lengths of the sides of a right triangle. It tells you the square of the hypotenuse (x²) is the sum of the squares of the other two sides.

  x² = 4² +7² . . . . . . . . . Pythagorean relation

  x² = 16 +49 = 65 . . . evaluate the expression

  x = √65 . . . . . . . . . . take the square root

Answer:

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Step-by-step explanation:

c

Answer:

\(x\approx 59.1^\circ\)

Step-by-step explanation:

Since we want to find x and we are given the hypotenuse and the side adjacent to x, we can use the cosine ratio:

\(\displaystyle \cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\)

The adjacent side is 18 and the hypotenuse is 35. Substitute:

\(\displaystyle \cos x=\frac{18}{35}\)

Take the inverse cosine both sides. Use a calculator (make sure you're in Degrees mode!). Hence:

\(\displaystyle x=\cos^{-1}\frac{18}{35}\approx59.1^\circ\)

Answer:

1. C = $1.65p

2. $260.10 ÷ $1.65 = 157.64 because we need to round it will be rounded up to 158 pounds