Graph on the number line
7x>35
2 3 4 5 6 7 8 9 10

At the given zeros of the function (-1.5, -1, and 2), the graph will behave like a sine curve, cutting the x-axis at three points.

The given polynomial expression:

y = 2x³ + x² - 7x - 6

The zeros of a polynomial equation are the values of x at which the given function equals zero.

The first zero of the given function is at x = 2;

f(2) = 2(2)³  + (2)²  - 7(2)  - 6

     = 16   +  4  - 14  - 6

     = 20   -    20  =  0

The second zero of the given function is at x = -1;

f(-1)  = 2(-1)³  + (-1)²   - 7(-1)   -   6

      = -2    +   1   +   7   -  6

      = - 8  +  8 =  0

The third zero of the given function is at x = -1.5;

f(-1.5)  = 2(-1.5)³   +  (-1.5)²   -  7(-1.5)   -  6

          = - 6.75    +  2.25   + 10.5    -  6

          = - 12.75  + 12.75  = 0

The zeros of the given function include;

----(-1.5)-------(-1)------------------------------(2)--------

Therefore, at the given zeros of the function (-1.5, -1, and 2), the graph will behave like a sine curve, cutting the x-axis at three points.

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Suppose a person lost 10 pounds in a month. This z-score tells you that x = 10 is 2.5  standard deviations to the right of the mean 5 pounds.

To verify that the z-score when x = 10 pounds is z = 2.5, we can use the formula:

z = (x - μ) / σ

where x is the value of the random variable, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we have:

z = (10 - 5) / 2 = 2.5

This confirms that the z-score when x = 10 pounds is z = 2.5.

To determine what the z-score tells us about the location of x = 10 pounds relative to the mean, we can use the definition of a z-score:

z = (x - μ) / σ

Rearranging the formula, we have:

x = μ + zσ

So, when z = 2.5 and σ = 2, we have:

x = μ + 2.5(2) = μ + 5

This tells us that x = 10 pounds is 5 pounds above the mean. Since the z-score is positive, x = 10 pounds is to the right of the mean.

Therefore, the z-score tells us that x = 10 is 2.5 standard deviations to the right of the mean of 5 pounds.

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Step-by-step explanation:

2x + 4y = 36

2 × 4 + 4y = 36

8 + 4y = 36

4y = 36 - 8

4y = 28

y = 28 ÷ 4

y = 7

Answer: D.) 14

Step-by-step explanation:

First, you first calculate the square root of 64 , this gives you 8

Next, you calculate the square root of 36, which gives you 6

Then, since you are asked to add the two, you add 8 + 6 since this is the simplified version of the original equation.

8 + 6 = 14

Therefore, your answer is D.) 14

The percentage of the participants that shocked the learner all the way to the maximum (450-volt, xxx) level was of:

62%.

A percentage represents a fraction relative to a total amount, and this fraction is obtained dividing the value of the desired amount by the value representing the total amount, and then multiplying this value by 100%.

Hence the equation is:

Percentage = Desired amount/Total amount x 100%.

In the context of this problem, these amounts are given as follows:

Hence the percentage is obtained as follows:

P = 25/40 x 100% = 0.62 x 100% = 62%.

(rounded).

Of the 40 participants, 25 shocked the learner all the way to the maximum (450-volt, xxx) level.

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Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. Since the diameter is given as 18 units, the radius would be half of that, which is 9 units. Now, substitute the value of the radius into the formula: A = π(9^2) = 81π units^2. Therefore, the correct answer is option b) 81π units^2.


1. Use the formula A = πr^2, where A is the area and r is the radius of the circle.
2. The diameter is given as 18 units, so the radius would be half of that, which is 9 units.
3. Substitute the value of the radius into the formula: A = π(9^2) = 81π units^2.

Therefore, the area of the circle with a diameter of 18 units is 81π units^2.

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x - intercept of the lines based on the given points is :

x intercept at 22 .

Given coordinates (48 , 30) , (61 , 45) , (74 , 60)

Take any two points,

Consider (48, 30) and (61, 45).

We have to find the slope of  line joining them:

Slope = (y2 - y1)/(x2 - x1)  

= (45 - 30)/(61 - 48)

= 15/13

Since all points are in same line,  we will get same slope for (48 ,30) and (74 , 60) and to other combination .

So the equation of line joining them:

y - y1 = m(x - x1)

y - 30 = (15/13) (x - 48)

=> 13(y - 30) = 15(x - 48)

=> 15x - 13y = 330

=> (15x)/330 - (13y/330) = 1

=> x/22 + (-y/330/13) = 1

We know that  x/a + y/b = 1 .

a is x intercept and b is y intercept.

∴ x intercept is 22.

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The least distance between P and (50,0) is 25sqrt(10) units.

The line y=3x can be expressed in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, m=3 and b=0, so the equation of the line can be written as y=3x.

Let P=(x,y) be the point on the line y=3x that is closest to the point (50,0). Then the vector from P to (50,0) is orthogonal to the line y=3x. The direction vector of the line y=3x is (1,3), so the direction vector of the vector from P to (50,0) is (-3,1).

Let Q=(50,0) and R=(x,y) be the two points. The vector from Q to R is given by:

v = R - Q = (x-50, y-0) = (x-50, y)

Since the vector v is orthogonal to the direction vector (-3,1) of the line y=3x, their dot product is zero:

v . (-3,1) = 0

Substituting v and the equation y=3x, we get:

(x-50, 3x) . (-3,1) = 0

Expanding the dot product, we get:

-3(x-50) + 3x = 0

Simplifying the equation, we get:

x = 25

Substituting x=25 into the equation y=3x, we get:

y = 75

Therefore, the point P on the line y=3x that is closest to the point (50,0) is (25,75), and the least distance between P and (50,0) is the length of the vector v:

|v| = sqrt((x-50)^2 + y^2) = sqrt((25-50)^2 + 75^2) = sqrt(6250) = 25sqrt(10)

So the least distance between P and (50,0) is 25sqrt(10) units.

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The density function of √u, where u is uniformly distributed on [0,1], is f(v) = 2√v for 0 ≤ v ≤ 1.

To find the density function of √u, where u is uniformly distributed on the interval [0,1], we can use the transformation method.

Let's denote the random variable √u as v = √u. We want to find the probability density function (PDF) of v.

First, we find the cumulative distribution function (CDF) of v:

F(v) = P(v ≤ x) = P(√u ≤ x) = P(u ≤ x²) = x², for 0 ≤ x ≤ 1.

Next, we differentiate the CDF to obtain the PDF of v:

\(\begin{equation}f(v) = \frac{d}{dv} F(v) = \frac{d}{dv} (x^2) = 2x, \quad 0 \leq x \leq 1\)

However, we need to express the PDF in terms of v, not x. Since v = √u, we can substitute x = √v into the PDF:

f(v) = 2√v, for 0 ≤ v ≤ 1.

Therefore, the density function of √u is f(v) = 2√v, for 0 ≤ v ≤ 1.

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Answer:

|x| = 25

Step-by-step explanation:

Original Equation:

|x - 4| = 21

Just add 4 to both sides

|x| = 25

Hope this helped :)

Answer:

the answer is 25 or -17

5 weeks because 40 times 5 equal 200

Answer:

The answer is "21"

Step-by-step explanation:

mn + 3r

m = 5

n = 4

r = 1/3

Now just substitute the values given in the question into the equation

5(4) + 3(1/3)

Multiply 5 and 4 to get 20

20 + 3(1/3)

3(1/3) cancels out and becomes 1

20 + 1

Add 20 and 1

21

So "21" is your answer

Answer:

x=-12

Step-by-step explanation:

4x−2(x+1)=3x+10

Step 1: Simplify both sides of the equation.

4x−2(x+1)=3x+10

4x+(−2)(x)+(−2)(1)=3x+10(Distribute)

4x+−2x+−2=3x+10

(4x+−2x)+(−2)=3x+10(Combine Like Terms)

2x+−2=3x+10

2x−2=3x+10

Step 2: Subtract 3x from both sides.

2x−2−3x=3x+10−3x

−x−2=10

Step 3: Add 2 to both sides.

−x−2+2=10+2

−x=12

Step 4: Divide both sides by -1.

−x/−1=12/−1

x=−12

Answer:

x=−12

Answer:

x=-12

Step-by-step explanation:

4x-2x-2=3x+10

2x-2=3x+10

2x-2+2=3x+10+2

2x=3x+12

2x-3x=3x+12-3x

-x=12

-x/-1 = 12/-1

x= -12

the regression equation y = 5x + 23 is true.

The number 23 represents the fixed or baseline number of people attending the picnic, regardless of the number of flyers used to advertise it (x).

what is regression?

Regression in mathematics refers to a statistical analysis method used to model the relationship between variables. It aims to find the best-fitting mathematical function that describes the relationship between a dependent variable (also known as the response variable) and one or more independent variables (also known as predictor variables or features).

The purpose of regression analysis is to estimate the parameters of the mathematical function that minimize the difference between the predicted values and the actual observed values of the dependent variable. This allows us to make predictions or draw inferences about the relationship between variables based on the available data.

There are different types of regression analysis, including linear regression, polynomial regression, multiple regression, logistic regression, and more. Each type is suited for different types of relationships between variables and has its own assumptions and techniques for parameter estimation.

Regression analysis is widely used in various fields, such as economics, finance, social sciences, engineering, and machine learning, to analyze and understand the relationship between variables, make predictions, and inform decision-making processes.

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Answer:

swap the bottom two. it should be, in this order, 32+c, 0.25, 8, 0.25c

Step-by-step explanation:

Answer:

LCM = 380

HCF = 2

Step-by-step explanation:

Least common multiple (LCM) of 20 and 38 is 380

Greatest common factor (GCF) of 20 and 38 is 2

Answer:

11-8 =3

3*0.25=0.75

0.75+(0.49)8

0.75+3.92=4.67

Answer:

c

Step-by-step explanation:

i did this b4

Answer:

1296

Step-by-step explanation:

\((3^3+3^2)^2\)

( 3 * 3 * 3 + 3 * 3 )²

( 27 + 9 )²

( 36 )²

36 * 36

1296

Answer:

\((3 {}^{3} + {3}^{2} {)}^{2} \)

\(((3 \times 3 \times 3) + (3 \times 3)) {}^{2} \)

\((27 + 9 {)}^{2} \)

\( {36}^{2} \)

\(36 \times 36\)

\(1296\)

ANSWER:

1/2

EXPLANATION:

Plug this into calculator -->

(1/64) ^ (1/6) and you will get exactly

0.5 which is equal to 1/2

*Note = this can also be done by changing it to...

⁶√[1/64]

If you know this root (2⁶ = 64) then it is 2, and 1 over 2 is equal to one half

We can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

An ordered pair on the X-Y plane is written as (x, y).

Here we also have the relation:

-x + 4y = 9

If we isolate y, we get:

4y = 9 + x

y = (9 + x)/4

Now, we can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

To get the particular ones you can replace the value of x, for example, if x = 0, then:

(x, (9 + x)/4 ) = (0, 9/4)

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The required product of the function is \(8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} - 4i sin\frac{2\pi}{3}sin\frac{\pi}{3}\)

We are to find the product of the expression

\(a =4cos(\frac{2\pi}{3} )+isin(\frac{2\pi}{3})\\b=2cos(\frac{\pi}{3} )+isin(\frac{\pi}{3})\\\)

The product of the functions is expressed as;

\(ab = 4cos(\frac{2\pi}{3} )+isin(\frac{2\pi}{3})[2cos(\frac{\pi}{3} )+isin(\frac{\pi}{3}]\\ab=8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} + i^24i sin\frac{2\pi}{3}sin\frac{\pi}{3} \\ab=8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} - 4i sin\frac{2\pi}{3}sin\frac{\pi}{3}\)

Note that i² = -1

Hence the required product of the function is \(8cos\frac{2\pi}{3}cos\frac{\pi}{3}+ 4i cos\frac{2\pi}{3}sin\frac{\pi}{3} + 2i sin\frac{2\pi}{3}cos\frac{\pi}{3} - 4i sin\frac{2\pi}{3}sin\frac{\pi}{3}\)

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Answer:

D\(8[cos(\pi )+i sin(\pi )}\)

Step-by-step explanation:

Your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.

To calculate the monthly payment for a motorcycle loan, we can use the formula for the present value of an annuity. The formula is:

PMT = PV * r / (1 - (1 + r)^(-n))

Where:
PMT = Monthly payment
PV = Present value of the loan
r = Monthly interest rate
n = Number of months

In this case, the present value of the loan (PV) is $7,200, the monthly interest rate (r) is 5.54% divided by 12 (0.0554 / 12), and the number of months (n) is 60.

Plugging in these values into the formula, we get:

PMT = 7200 * (0.0554 / 12) / (1 - (1 + (0.0554 / 12))^(-60))

Evaluating this expression, the monthly payment comes out to be approximately $136.88.

Therefore, your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.

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Answer:

150

Step-by-step explanation:

150

Answer:

Take m 3 cube and find m.

The statements about least squares regression analysis is true are I and III.

The statistical technique of regression analysis demonstrates the link between two or more variables. The method evaluates the relationship between a dependent variable and independent factors, and is frequently presented as a graph.

You can anticipate the effects of the independent variable on the dependent one by creating a regression analysis. For instance, we can claim that a linear regression model can adequately account for age and height.

Here,

From the given information in the question:

The statements I and III are correct.

And the statements are:

A point with a large residual is an outlier and the removal of an influential point from the data set could change the value of the correlation coefficient.

So, the statements  I and III are correct for the given information in the question.

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The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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The probability that the council will consist of 2 females and 3 males is approximately 0.279, rounded to 3 decimal places. To find the probability that the council will consist of 2 females and 3 males, we need to calculate the number of ways this combination can occur and divide it by the total number of possible combinations.

The number of ways to choose 2 females from 8 females is given by the combination formula C(8, 2), which is equal to 28. Similarly, the number of ways to choose 3 males from 6 males is C(6, 3), which is equal to 20.

To find the total number of possible combinations for the council of 5 people, we need to calculate the combination of choosing 5 people from the total pool of 14 individuals. This can be calculated as C(14, 5), which is equal to 2002.

Now, we can calculate the probability by dividing the number of favorable outcomes (2 females and 3 males) by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

          = (C(8, 2) * C(6, 3)) / C(14, 5)

          = (28 * 20) / 2002

          ≈ 0.279

Therefore, the probability that the council will consist of 2 females and 3 males is approximately 0.279, rounded to 3 decimal places.

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The appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

The appropriate measure of variation (spread) for these data is the standard deviation. Standard deviation is a measure of how much the data values vary from the mean (average) of the data set. It is calculated by taking the square root of the variance, which is the average of the squared differences between each data value and the mean.

To calculate the standard deviation for this data set, follow these steps:

1. Find the mean of the data set by adding up all of the data values and dividing by the total number of values. In this case, the mean is (4 + 7 + 2 + 3 + 4 + 2 + 1 + 3 + 9 + 8 + 5 + 1 + 3 + 2 + 3 + 2 + 4 + 3 + 6 + 5) / 20 = 3.65

2. Find the variance by subtracting the mean from each data value, squaring the result, and then finding the average of these squared differences. The variance for this data set is ((4 - 3.65)^2 + (7 - 3.65)^2 + (2 - 3.65)^2 + ... + (6 - 3.65)^2 + (5 - 3.65)^2) / 20 = 5.2275

3. Take the square root of the variance to find the standard deviation. The standard deviation for this data set is sqrt(5.2275) = 2.287

Therefore, the appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

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