he scatterplot provided shows the gestations periods and life expectancies for several animal species. The plot contains two points that may be of concern. The point in the upper right corner of this scatterplot is for​ elephants, and the other point at the far right is for hippos.
a) By removing one of these​ points, we could make the association appear to be stronger. Which​ point? Explain.
b) Would the slope of the line increase or​ decrease?
c) Should we just keep removing animals to increase the strength of the​ model? Explain.
d) The slope of the​ scatterplot's regression line is 15.5. If we remove elephants from the​ scatterplot, the slope of the regression line becomes 11.6 days per year. Do you think elephants were an influential​ point? Explain.

The z-score associated with a 95% confidence level is approximately 1.96.

The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.

Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.

Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula

z = invNorm(1 - α/2)

where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:

z = inv Norm(1 - 0.05/2)

= inv Norm(0.975) ≈ 1.96

Therefore, the z-score is 1.96

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The inequality that represents the greatest distance that can be driven while staying within the daily budget is:

0.18x + 40 ≤ 67

Solving for x, we get:

0.18x ≤ 27

x ≤ 150

Therefore, the greatest distance that can be driven in a day while staying within the daily budget is 150 miles.

Two other two-step inequalities with the same solutions are:

0.18x ≤ 28

x ≤ 155

With the provided scale, the driveway's true length is 7/6 feet, and 1 and 1/6 feet.

The height of any unit can be converted to inches using the free online tool known as an inch calculator. Both inches and centimetres are units used to measure length; inches are abbreviated as "in" and centimeters as "cm".

To determine the real length of the driveway, we can use the provided scale.

The scale indicates that 5 inches just on illustration corresponds to 6 feet in everyday life.

Now, let's change 35 inches just on picture to feet:

35 inches / 5 inches for every 6 feet equals 7/6 feet.

The driveway is therefore 7/6 feet in length in actuality. We can condense.

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The system of equation is 100x + 72y = 1760 and 97x + 72y = 1718. The special price is $14 for hardcover books and $5 for paperback books.

Equations are declarations of equality between two mathematical expressions containing one or more variables. A linear equation is one in which the maximum power of the variable is one. Any arithmetic equation can be solved using linear equations, which can also be used to find the precise value or root of the variable that answers the question.

Let us suppose the price of hardback covers = x.

Let us suppose the price of paperback covers = y.

Given that, Mr. Howard purchased 100 new hardcover books and 72 new paperback books, which cost a total of $1,760.

100x + 72y = 1760........(1)

He also purchased 97 new hardcover books and 72 new paperback books for the adult fiction section, spending a total of $1,718.

97x + 72y = 1718.........(2)

The system of equation to describe the situation is:

100x + 72y = 1760.

97x + 72y = 1718

To find the solution subtract the two equations:

100x + 72y = 1760.

- (97x + 72y = 1718)

Thus,

3x = 42

x = 14

Substitute the value of x in equation 1:

100(14) + 72y = 1760

1400 + 72y = 1760

72y = 360

y = 5

Hence, the special price is $14 for hardcover books and $5 for paperback books.

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The total number of pages in Rhett's book is 183 pages.

A solution to an equation is a number that can be substituted for the variable to provide a valid number statement.

To find the total number of pages in Rhett's book, we need to solve for p in the equation:

p + 31 = 214

First, we can isolate p on one side of the equation by subtracting 31 from both sides:

p + 31 - 31 = 214 - 31

Simplifying:

p = 183

Therefore, the total number of pages in Rhett's book is 183 pages.

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The Taylor series for sin(x) is an infinite series expansion that represents the trigonometric function sin(x) as a sum of infinite terms involving the powers of x.

The Taylor series for sin(x) can be written as:

where n! represents the factorial of n.

The series converges for all values of x, which means that it can be used to calculate the value of sin(x) to any desired degree of accuracy. The series is based on the idea that any continuous function can be represented as an infinite sum of terms involving the function's derivatives at a particular point, in this case, x=0.

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Answer:  x= 155 degrees

Step-by-step explanation:

All angles in a triangle add up to 180. That is how we find angle a

a + b = 120 degrees as 60 degrees is taken for a straight angle or 180 degrees.

Use Algebra to find angle b

To find c we do the same thing as for a.

x is everything remaining from 180 degrees after c is taken from it.

x =  155 degrees

Answer:

Step-by-step explanation: Mean Absolute Error is a model evaluation metric used with regression models. The mean absolute error of a model with respect to a test set is the mean of the absolute values of the individual prediction errors over all instances in the test set.

The magnitude of -v is [tex]\sqrt{(89)}[/tex]

In physics and mathematics, magnitude refers to the size or quantity of a physical or mathematical property. It can be represented by a scalar value or a vector with a scalar magnitude.

In the case of scalar magnitude, it represents a property's absolute value, which is always positive. For example, the magnitude of a force, velocity, or acceleration represents its absolute value without any direction.

In contrast, vector magnitude represents the length or size of a vector, including both its magnitude and direction. It can be calculated using the Pythagorean theorem, where the magnitude of a vector V with components (Vx, Vy, Vz) is:

[tex]|V| = sqrt(Vx^2 + Vy^2 + Vz^2)[/tex]

The magnitude of a vector is always positive and can be used to determine the distance between two points in space.

Overall, magnitude is an essential concept in many fields, including physics, mathematics, engineering, and computer science, and it plays a crucial role in understanding various physical and mathematical phenomena.

The magnitude of a vector is its length, which is calculated using the Pythagorean theorem. For a vector v = (a, b), the magnitude is given by:

[tex]|v| = sqrt(a^2 + b^2)[/tex]

The negative of a vector simply reverses its direction, but not its magnitude. Therefore, the magnitude of -v is the same as the magnitude of v.

Using this information, we can calculate the magnitude of -v as follows:

[tex]|-v| = |-( -5, 8)| = |(5, -8)|\\\|-v|\ = \sqrt{(5^2 + (-8)^2)} = \sqrt{(25 + 64) }= \sqrt{(89)}Therefore, the magnitude of -v is \sqrt{(89)}[/tex]

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The coordinates of the figure are  A''(-3, 1),B''(2,2), C''(-2, -1).

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

Given that the coordinates of the points A, B, C are A(-6,-3), B(-1,-4), C(-5,-1).

The rule of a reflection across the x-axis is (x,y)→(x,-y).

After reflection across the x-axis,

A(-6,-3)→ A'(-6,3)

B(-1,-4)→B'(-1,4)

C(-5,-1)→C'(-5,1)

A rule of translation of 3 units right and 2 units down is (x,y)→(x+3,y-2).

Thus the new coordinates are:

A'(-6,3)→ A''(-6+3,3-2)=A''(-3,1)

B'(-1,4)→ B''(-1+3,4-2)=B''(2,2)

C'(-5,1)→ C''(-5+3,1-2)=C''(-2,-1)

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Daren will earn $286 for the week if he sold 122 items.

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

Darrel receives a weekly salary of $289.

And, In addition, $13 is paid for every item sold in excess of 100 items.

Hence, The cost to earn for the week if he sold 122 items is,

⇒ (122 - 100) × $13

⇒ 22 × $13

⇒ $286

Thus, Daren will earn $286 for the week if he sold 122 items.

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The measure of the arc is option (c) 140°

In geometry, an arc is a curved line that is a part of a circle's circumference. The measure of an arc can be calculated using the angle of the arc, which is measured in degrees.

In the case of EBC, the measure of the arc is 140°. This is because we can use the Angle-Side-Angle (ASA) congruence theorem, which states that two triangles are congruent if and only if two angles and the included side are equal.

In the case of EBC, we know that angle A equals 40° and angle C equals 90° so the only variable left is the measure of the arc, which is equal to 140°.

Therefore, the measure of EBC is 140°. This can be verified by drawing the triangle and measuring the arc with a protractor.

Therefore, option (c) is the right one.

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Complete Question:

What is the measure of arc  EBC when the values of Angle a nd c are 90 and 40 degree respectively.

a) 40°

b) 90°

c) 140°

d) 220°

Answer:

360 degrees

Step-by-step explanation:

I remember learning this in Math class. The rhombus angle sum will make 360 degrees.

Around 98.4 feet are equal to 30 metres.

The common formula 1 metre (m) = 3.28 feet (ft) will be used to convert measurements from metres to feet. Here, the conversion value is 3.28. To convert 10 metres to feet, for instance, multiply 10 by 3.28, which is 32.8 ft. Therefore, 10 meters = 32.8 feet.

Converting from metres to feet: 3.28084 metres are nearly equal to one metre. Add 3.28084 feet to the given metre value to convert it to feet. Add 3.28084 feet to the given metre value to convert it to feet. For instance, the conversion of 5 metres to feet is as follows: We are aware that the conversion factor for 5 metres to feet is 3.28084.

30 m * 3.280839895 ft/m =98.4251968504 ft

So, 30 metres is roughly equivalent to 98.4 ft.

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s(x) represents the value of s(x) depending on the value of x since s is a function of x.

The first thing you should be aware of in this situation is that the following is contained in the provided expression:

S: stands for a function whose value we are interested in.

In order to understand the function s, we must use the term (numerical value) represented by x.

S is therefore dependent on X.

So, we have:

As s is a function of x, its value depends on the value of x.

As s is a function of x, the value of s (x) depends on the value of x.

Consider the provided notation.

Since s is a function of x. The s(x) value depends on the x value.

For any function f(x); The independent variable is x.

i.e. it depends on the variable x.

Similarly, here s(x) is the dependent variable. which is defined for the corresponding variable x.

Hence, s(x) represents the value of s(x) depending on the value of x, since s is a function of x.

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Using the formula 1 millilitre = 10⁻³ microliters, we can convert millilitres to microliters.

The volume unit is milliliters (mL). One microliter (uL) is likewise a volume unit, although it is a smaller unit.

We already know that Milli equals 10⁻³.

As a result, we may write the relationship using the unit conversion idea.

One microliter equals 10⁻³ milliliters.

For example, if we have 2 microliters, it is equal to 2 x 10⁻³ milliliters.

Thus, we now have a standard formula that we can use to calculate the time in microliters to milliliters and milliliters to microliters.

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You are 1 meter behind the fixed point.

The total path length covered by the moving body is called distance covered.

Given is that you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters.

Total displacement = 12 + 5 - 18 = - 1

So, you are 1 meter behind the fixed point.

Therefore, you are 1 meter behind the fixed point.

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{Question in english -

Suppose you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters, the distance between the fixed point and you is}

c=25.1327

Step-by-step explanation:

c=2pir

r=1/2 d

r=4

2pi*4= 25.1327

The missing information in the square is option(b) x = 4y = 4 √(2) and y = 4.

Given square PQRS, the task is to determine the missing information. A square is a quadrilateral with four equal sides and four equal angles.

The coordinates of the vertices of a square are (x,y), (x+4,y), (x+4,y+4) and (x,y+4).

The missing information, x and y, can be found by solving the equations that represent the sides of the square. We can start by solving for x.

The equation for the side PQ is x + 4y = 2 √(2). Solving this equation for x gives x = 4y - 8 √(2).

Similarly, the equation for the side RS is x + 4y = 4 √(2). Solving this equation for x gives x = 4y = 4 √(2).

Therefore, the missing information is x = 4y = 4 √(2) and y = 4.  

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Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.

Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5   =  $29600

Median income of country A = (5+1)/2 th term = 3rd term = $29000

Mean to median ratio = 29600/ 26000= 1.02

Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800

Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000

Mean to median ratio of country B = 49800/29000 = 1.71

Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.

If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.

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The mode of the sample can be larger, smaller, or equal to the mode of the population.

The correct answer is A.

The mode is the most frequent value in a dataset. In a random sample, the mode can differ from the mode of the population because random sampling is subject to sampling variability. In other words, each random sample is likely to have different sample statistics than the population parameters. Therefore, it is possible for the mode of the sample to be larger, smaller, or equal to the mode of the population.

However, as the sample size increases, the mode of the sample becomes more likely to approach the mode of the population. This is because larger samples provide more information about the population and therefore reduce the impact of sampling variability.

Option B is incorrect because even if the sample is truly random, it is still subject to sampling variability, which means that the mode of the sample may not be equal to the mode of the population.

Option C is also incorrect because the mean of the population is a different statistic than the mode, and it is not necessarily related to the mode of the sample.

Option D is clearly incorrect, as the mode of a sample cannot be equal to the population size.

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To round 0.002391 to 2 significant figures, we need to look at the digits after the first two significant digits (which are 2 and 3 in this case).

The digit in the third decimal place is 2, which is less than 5. Therefore, we leave the second significant digit (3) as it is, and we drop all the digits after that.

So, rounding 0.002391 to 2 significant figures, we get:

0.0024

Answer:

(D.) [tex]5x^{5} -5x^{3} +4[/tex]

Step-by-step explanation:

Adding Polynomials:

To add both of these two polynomials together, all we need to do is add like terms. All of the other options are wrong, since we do not add the exponents.

[tex]5x^{5} -5x^{3} +4[/tex]

No es posible determinar si lo que dice Luis es correcto sin conocer el porcentaje de descuento aplicado en la compra de la casaca.

Si el precio original de la casaca es de $80 y después de aplicar un descuento el precio final es de $55, entonces se puede determinar el porcentaje de descuento utilizando la fórmula:

descuento = (precio original - precio final) / precio original

descuento = (80 - 55) / 80 = 0.3125 = 31.25%

Si el porcentaje de descuento es del 31.25%, entonces Luis tiene razón en su afirmación de que está comprando la casaca con un descuento. Sin embargo, si el porcentaje de descuento es diferente, entonces su afirmación podría ser incorrecta.

Por lo tanto, es importante conocer el porcentaje de descuento para determinar si lo que dice Luis es correcto o no.

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the speed of the private airplane is approximately 214.3 miles per hour. Rounding to one decimal place is not necessary but if you round it the answer will be 214 miles.

Let's call the speed of the private airplane "s". According to the problem, the speed of the commercial jet is 103 miles per hour faster than the speed of the private airplane. So, the speed of the commercial jet is:

s + 103

We know that the distance from Denver to Phoenix is the same for both planes. Let's call this distance "d".

Using the formula distance = rate x time, we can set up two equations:

For the private airplane:

d = s × 4

For the commercial jet:

d = (s + 103) × 2.7

Since both equations represent the same distance, we can set them equal to each other and solve for s:

s × 4 = (s + 103) × 2.7

4s = 2.7s + 278.1

1.3s = 278.1

s = 278.1 / 1.3

s = 214.3

Therefore, the speed of the private airplane is approximately 214.3 miles per hour.

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Answer:

I would believe inside of a race track is smaller than the outside. They are staggered so the runners all run the same distance.

Step-by-step explanation:

The next step would be to draw an arc with the compass centered at the endpoint.

This arc should intersect the segment at two points.

We have,

After Jessica places the compass on one endpoint of the segment and opens it to a width larger than half of the segment, her next step would be to draw an arc with the compass centered at the endpoint.

The concept used in Jessica's next step is the compass-and-straightedge construction method.

By opening the compass wider than half of the segment and drawing an arc with the compass centered at one endpoint, she creates two points of intersection between the arc and the segment.

These points will divide the segment into two equal halves, allowing her to bisect the segment.

Thus,

The next step would be to draw an arc with the compass centered at the endpoint.

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The value of the coefficient of the product is equal to - 30. (Correct choice: A)

The expanded form of a quadratic equation includes three real coefficients, whose definition is shown below:

(a · x + b)² = a · x² + 2 · a · b · x  + b · x²

The coefficient of the product is the element 2 · a · b of the expanded form. If we know that a = 5 and b = - 3, then the coefficient of thre product is:

2 · a · b = 2 · 5 · (- 3)

2 · a · b = - 30

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The frequency of the sine function is given as follows:

F = 0.5/π Hz.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

For the function y = sin(x), we have that B = 1, hence the period is given as follows:

P = 2π/B

P = 2π.

The frequency is one divided by the period, hence:

F = 1/P

F = 1/2π

F = 0.5/π Hz.

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Answer:

[tex]F=\dfrac{1}{2\pi}\; \sf Hz[/tex]

Step-by-step explanation:

The frequency of a sinusoidal wave refers to the rate at which the wave completes one full cycle, typically measured in Hertz (Hz), where 1 Hz signifies one complete oscillation of the wave in one second.

The period of a sinusoidal wave is the amount of time it takes for the wave to complete one complete oscillation.

The frequency (F) of a sinusoidal wave can be determined from its period (P) using the formula:

[tex]\boxed{F=\dfrac{1}{P}}[/tex]

The sine function y = sin(x) completes one full cycle over the interval [0, 2π]. Therefore, its period is P = 2π.

To calculate the frequency (F), substitute P = 2π into the frequency formula:

[tex]F=\dfrac{1}{P}=\dfrac{1}{2\pi}\; \sf Hz[/tex]