837÷36 with work ok ​

The equation 6x + 2ex + 4 = 0 has exactly one root.

Prove that 6x + 2ex + 4 = 0 has exactly one root by using the IVT and Rolle's theorem.

The given function is 6x + 2ex + 4.

Observe that f(−1) = 6(−1) + 2e−1 + 4

≈ 2.7133

and f(0) = 4.

As f(−1) < 0 and f(0) > 0, by the Intermediate Value Theorem, there is at least one root of the equation f(x) = 0 in the interval (−1, 0).

If possible let the equation have two distinct roots, say a and b with a < b.

By Rolle's theorem, there exists a point c ∈ (a, b) such that f'(c) = 0.

We now show that this is not possible.

Consider f(x) = 6x + 2ex + 4.

Then, f'(x) = 6 + 2ex.

The equation f'(c) = 0 implies that,

2ex = −6or

ex = −3

There is no real number x for which ex = −3. Thus, our assumption is wrong.

Therefore, there is only one real root of the equation 6x + 2ex + 4 = 0.

To know more about root visit

https://brainly.com/question/18192922

#SPJ11

Answer:

Step-by-step explanation:

Move the variables to different sides of the equation. This "substitution" metho d starts out by "solving for x" (or any other variable) in one of the ...

Answer:

The probability of her not choosing yellow is 6/22.

Step-by-step explanation:

The probability that she chooses a blue skittle is 6/23 since she eats one blue skittle the total decreases to 22. So the probability of her not choosing yellow is 6/22

Answer:

The improper fraction of the shaded parts is 7/6.

Step-by-step explanation:

1 1/6 = 1/6 + 1/6 + 1/6+ 1/6 + 1/6 + 1/6 + 1/6 = 7/6

Answer:

1 1/6=1/6+1/6+1/6+1/6+1/6+1/6+1/6

Answer:

IQR: is the length of the middle 50% of that interval of space

Step-by-step explanation:

In order to find IQR, subtract the third interquartile range - the first interquartile range

Answer:

4.15

Step-by-step explanation:

You subtract 64.14 by 59.99

Answer:

6.9% (rounded to the tenth)

Step-by-step explanation:

Subtract 64.14 from 59.99 to get 4.15.

Then divide 4.15 by 59.99 to get 0.691781964

Multiply that by 100 to get your percent

Answer:

i think it's 2.2

Step-by-step explanation:

it looks like (5,11) is a point that the line crosses so when you divide 11 by 5, would get 2.2

Given the z-table and the standard normal distribution shown in the graph, In statistics, the z-score is a standard score that shows how many standard deviations a data point is from the mean.

A z-score of 0 means that the data point is equal to the mean, a z-score of 1 means that it is one standard deviation above the mean, and a z-score of -1 means that it is one standard deviation below the mean.The z-score that represents a value that is likely to occur is usually between -2 and 2. In other words, the probability of a z-score falling between -2 and 2 is approximately 95%.

Similarly, a z-score of 3.24 has a probability of 0.9993, which means that it is very unlikely to occur, and a z-score of -3.50 has a probability of 0.0002, which means that it is extremely unlikely to occur. Therefore, the z-score that represents a value that is likely to occur is 1.49.

To know more about statistics visit:

https://brainly.com/question/32201536

#SPJ11

Answer:

The coordinates of the image triangle will be:

Please also check the attached figure.

The green triangle represents the image triangle.

Step-by-step explanation:

We know that when we reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate reveres its sign.

Thus,

The rule of reflection of the point P(x, y) across the x-axis is:

P(x, y) → P'(x, -y)

In the attached figure, let the coordinates of the triangle are:

Using the rule of reflection across the x-axis:

P(x, y) → P'(x, -y)

Thus, the coordinates of the image triangle will be:

A(-3, 1) → A'(-3, -1)

B(-3, 3) → B'(-3, -3)

C(-1, 3) → C'(-1, -3)

Therefore, the coordinates of the image triangle will be:

Please also check the attached figure.

The green triangle represents the image triangle.

If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

Learn more about null hypothesis at : https://brainly.com/question/28920252

#SPJ4

So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

It is given that the function g(x) is the inverse of f(x) so it follows:

It is given that f(-4)=9 so it follows:

So the value of g(9)-3f(-4) is given by:

Hence the value is -31.

Answer:

BECAUSE YOU ARE TRYING TO BE CONVINCE THAT THE PROOF IS TRUE,AND IT IS EASIER TO JUSTIFY

Step-by-step explanation:

Answer:

The skater has done half of the  potential energy 2750

Step-by-step explanation:

5500 divided by 2 = 2750

After 45 seconds they blink together again.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20.

Given:

One sign blinks every 9 seconds. The other sign blinks every 15 seconds.

Now, to find they blink together again we have to find the LCM of 9 and 15.

For 9 the lights will blink at seconds: 0, 9, 18, 27, 36, 45, 54, 63,

and, For 15 the lights will blink at seconds: 0, 15, 30, 45, 60, 75

Hence, they blink together at 45 seconds.

Learn more about Least Common Multiple here:

https://brainly.com/question/30060162

#SPJ1

Answer:

d.{(8,1),(−4,1),(3,5),(0,4),(−1,2)} - function

Step-by-step explanation:

a.{(2,4),(2,6),(2,8),(2,10),(2,12)}

Each value of x goes to more than one value of y- this is not a function

b. {(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)}

The value of x at -4 goes to more than one value of y- this is not a function

c.{(0,3),(−6,8),(−3,5),(0,−3),(7,11)}

The value of x at 0 goes to more than one value of y- this is not a function

d.{(8,1),(−4,1),(3,5),(0,4),(−1,2)}

 Each value of x goes to only one value of y- this is a function

Answer:

y=3x+6

Step-by-step explanation:

Just test this on like a graph or something and you will see it works. Let me know if there is a fault in my answer. Thanks! Have a good day.

The inner product is not equal to zero (495/8 ≠ 0), we can conclude that the functions x and x^2 are not orthogonal in the space P5 equipped with the given inner product.

To show that the functions x and x^2 are orthogonal in the space P5 equipped with the given inner product, we need to prove that their inner product is equal to zero.

Let's calculate the inner product of x and x^2 using the given definition:

(x, x^2) = Σx(xi) * x^2(xi) for i = 1 to 5.

First, we need to determine the values of x(xi) and x^2(xi) for each i.

Given xi = i-3/2 for i = 1, 2, 3, 4, 5:

For i = 1:

x(x1) = x(1-3/2) = x(-1/2) = -1/2

x^2(x1) = (x1)^2 = (-1/2)^2 = 1/4

For i = 2:

x(x2) = x(2-3/2) = x(1/2) = 1/2

x^2(x2) = (x2)^2 = (1/2)^2 = 1/4

For i = 3:

x(x3) = x(3-3/2) = x(3/2) = 3/2

x^2(x3) = (x3)^2 = (3/2)^2 = 9/4

For i = 4:

x(x4) = x(4-3/2) = x(5/2) = 5/2

x^2(x4) = (x4)^2 = (5/2)^2 = 25/4

For i = 5:

x(x5) = x(5-3/2) = x(7/2) = 7/2

x^2(x5) = (x5)^2 = (7/2)^2 = 49/4

Now, let's calculate the inner product:

(x, x^2) = Σx(xi) * x^2(xi) for i = 1 to 5

= (-1/2 * 1/4) + (1/2 * 1/4) + (3/2 * 9/4) + (5/2 * 25/4) + (7/2 * 49/4)

= -1/8 + 1/8 + 27/8 + 125/8 + 343/8

= 495/8

Learn more about Product

brainly.com/question/25922327

#SPJ11

For the given parallelogram ABCD where diagonals AC and BD intersect at point E and BE = x² -21 and DE = 4x then the measure of BD is equal to 56 units.

As given in the question,

In the given parallelogram ABCD,

Diagonal AC and BD intersect at point E.

BE = x² -21

DE  = 4x

In parallelogram diagonals bisects each other .

BE = DE

⇒ x² -21 = 4x

⇒ x² - 4x -21 = 0

⇒ x²  - 4x + 4 -25 = 0

⇒ ( x - 2 )² - (5)² = 0

⇒ ( x -2 -5)( x- 2 + 5) = 0

⇒ ( x -7) ( x + 3) =0

⇒ x = 7 or x = -3

x cannot be  negative.

This implies x = 7

Now,  BE = 7² -21

               = 28

               = DE

BD = BE + DE

     = 28 + 28

     = 56units

Therefore, in the parallelogram the length of the diagonal BD is equal to 56 units.

Learn more about parallelogram here

brainly.com/question/19187448

#SPJ4

Answer:

$81.15

Step-by-step explanation:

Answer:

0010110010100100001010010010101010010101010010010

001010010010100010010101000001010000101001010010

Respuesta en número binarios

To find the volume of the given solid using polar coordinates, we integrate the function over the appropriate range of values for the radial coordinate and the angle.

The given solid consists of a cone and a ring in the xy-plane. The cone is defined by the equation z = √(x² + y²), which represents a right circular cone with its vertex at the origin and opening upwards. The ring is defined by the inequality 1 ≤ x² + y² ≤ 64, which represents a circular region centered at the origin with an inner radius of 1 unit and an outer radius of 8 units.

To evaluate the volume using polar coordinates, we can express the equations in terms of the radial coordinate (r) and the angle (θ). In polar coordinates, the cone equation becomes z = r, and the ring equation becomes 1 ≤ r² ≤ 64. To set up the integral, we need to determine the range of values for r and θ. For the radial coordinate, r ranges from 1 to 8, as that corresponds to the region defined by the ring. For the angle θ, we can integrate from 0 to 2π, covering a full revolution around the origin.

The volume integral is then given by V = ∫∫∫ r dz dr dθ over the region defined by 1 ≤ r² ≤ 64 and 0 ≤ θ ≤ 2π. By evaluating this triple integral, we can find the volume of the solid.

To learn more about polar coordinates click here:

brainly.com/question/13103661

#SPJ11

There are a total of 720 permutations of the letters in the word "peppermint".

To calculate this, we use the formula n!/(r! * (n-r)!) where n is the number of objects (in this case, letters) and r is the number of objects chosen from that set. In this case, n = 10 (10 letters in "peppermint") and r = 10 (all 10 letters are chosen).

So, 10!/(10! * (10-10)!) = 10!/(10! * 0!) = 10!/(10!) = 1, which simplifies to 1. That means that there is one way to choose all 10 letters from the word "peppermint", so the total number of permutations is 1 * 10! = 10! = 3628800, or 720.

For more similar questions on permutations:

brainly.com/question/11143108

#SPJ11

Answer:

D. x = 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: Undefined

y-intercept: No y-intercept

x

y

3

0

3

1

(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x

The probability mass function p(x) can be derived from the cdf by taking differences:

p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06  x = 10.1  x = 20.17 x = 30.36  x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)

The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.

To learn more about this visit -m A branch of a certain bank has six ATMs : https://brainly.com/question/31026593

#SPJ11

There are approximately 3.65 fewer days every 10 million years and 0.365 fewer days every million years.

The Earth's rotation is gradually slowing down due to various factors such as tidal friction caused by the gravitational forces of the Moon and the Sun. As a result, the length of a day, defined as the time it takes for the Earth to complete one rotation on its axis, is gradually increasing.Based on scientific estimates, it is believed that the length of a day increases by about 1.7 milliseconds every century. This means that over a span of 10 million years, the length of a day would be approximately 17,000 milliseconds or 17 seconds longer.

To calculate the number of fewer days over 10 million years, we need to convert the 17 seconds into days. There are 86,400 seconds in a day, so 17 seconds is approximately 0.0001975 days. Dividing this by the length of a day, which is roughly 0.0027397 days, we get approximately 0.072 or 0.07 fewer days every 10 million years. Similarly, over a million years, the length of a day would be approximately 1.7 milliseconds longer, which is approximately 0.0000197 days. Dividing this by the length of a day, we get approximately 0.007 or 0.01 fewer days every million years.

These calculations demonstrate the gradual slowing down of the Earth's rotation over vast time scales, resulting in fewer days over millions of years. It is important to note that these figures are approximations and can vary due to other factors influencing the Earth's rotation.

To learn more about tidal friction click here:

brainly.com/question/6762160

#SPJ11

Answer:

$100-5(15) aka $25 still owed

The ordered pair that represents the location of vertex A after the dilation is (8, 20).

Vertex is a point in geometry that describes the location of a object in a two-dimensional or three-dimensional space. In two-dimensional space, it is a point where two lines, curves, or surfaces intersect. In three-dimensional space, it is the point where three planes intersect. In a graph, it is the point where two lines intersect.

Vertex A of the original kite is located at (6, 15).
The center of dilation is at (1, 1). To dilate the kite by a scale factor of 4/3, each point (x,y) of the kite must be multiplied by the scale factor, 4/3. In this case, vertex A will transform to (8, 20) after the dilation.
Therefore, the ordered pair that represents the location of vertex A after the dilation is (8, 20).

To learn more about vertex
https://brainly.com/question/21185651
#SPJ1