s2+10s+21=0 (find the equation)
​

Therefore, the covariance of 1.07x and 2y is approximately 11.984.

To find the covariance of 1.07x and 2y, we can use the property that the covariance is linear with respect to scalars. In other words, cov(aX, bY) = ab * cov(X, Y) for any constants a and b.

Given:

cov(x, y) = 5.6

Let's calculate the covariance of 1.07x and 2y:

cov(1.07x, 2y) = (1.07 * 2) * cov(x, y)

= 2.14 * 5.6

≈ 11.984

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Answer:

1:4

Step-by-step explanation:

Thats it

Answer:1/4

Step-by-step explanation:

According to the product rule we find out that there are 24 major autoroutes from Boston to Los Angeles via Detroit.

It is given to us that -

There are 4 major autoroutes from Boston to Detroit

There are 6 major autoroutes from Detroit to Los Angeles

We have to find out the number of major autoroutes from Boston to Los Angeles via Detroit.

Since it is given that there are 4 major autoroutes from Boston to Detroit, this implies that -

To travel from Boston to Detroit there are 4 ways

Similarly, since there are 6 major autoroutes from Detroit to Los Angeles, this implies that -

To travel from Detroit to Los Angeles there are 6 ways

So, the number of major autoroutes from Boston to Los Angeles via Detroit = 4 * 6 = 24 ways

Thus, through product rule we find out that there are 24 major autoroutes from Boston to Los Angeles via Detroit.

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The probability of no earthquakes occurring in one year is approximately 0.000911881965. The probability that exactly three out of the next eight years will have no earthquakes , we can apply the binomial distribution.

The probability of no earthquakes occurring in one year in the given region of California, which follows a Poisson process with a rate of seven earthquakes per year, can be calculated using the Poisson distribution formula. The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence. In this case, the average rate is seven earthquakes per year. To calculate the probability of zero earthquakes in one year, we can use the formula:

P(X = 0) = e^(-λ) * (λ^0) / 0!

where λ is the average rate of occurrence. Substituting λ = 7 into the formula, we get:

\(P(X = 0) = e^{(-7)} (7^0) / 0!\)

The exponential term \(e^{(-7)\)evaluates to approximately 0.000911881965, and 0! is equal to 1. Therefore, the probability of no earthquakes occurring in one year is approximately 0.000911881965.

To find the probability that exactly three out of the next eight years will have no earthquakes, we can apply the binomial distribution. The binomial distribution describes the probability of a certain number of successes (no earthquakes) in a fixed number of independent trials (eight years) with a constant probability of success (the probability of no earthquakes in one year). In this case, the probability of no earthquakes in one year is the value we calculated earlier: approximately 0.000911881965. The formula for the binomial distribution is:

\(P(X = k) = C(n, k) p^k (1 - p)^{(n - k)\)

where P(X = k) is the probability of exactly k successes, C(n, k) is the number of combinations of n trials taken k at a time, p is the probability of success, and n is the total number of trials. Substituting k = 3, n = 8, and p = 0.000911881965 into the formula, we can calculate the probability.

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Answer:

3x - y = 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x + 3y = 21 ( subtract x from both sides )

3y = - x + 21 ( divide all terms by 3 )

y = - \(\frac{1}{3}\) x + 7 ← in slope- intercept form

with slope m = - \(\frac{1}{3}\)

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{3} }\) = 3 , thus

y = 3x + c ← is the partial equation

To find c , substitute (1, - 3) into the partial equation

- 3 = 3 + c ⇒ c = - 3 - 3 = - 6

y = 3x - 6 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 6 ( add 6 to both sides )

6 = 3x - y , that is

3x - y = 6 ← in standard form

Answer:

3x - y = 6

Step-by-step explanation:

i got it right on my quiz

If Sean and Esteban have the same amount of drawings in their sketchbooks, then each sketchbook might have 6 groups of 3 drawings, giving a total of 18 drawings

Sean and Esteban compared the number of drawings in their sketchbooks. They came up with the equation 6×3=18. The multiplication 6×3 indicates that there are 6 groups of 3 drawings. This is the equivalent of the 18 drawings which they have altogether.

There is no information on how many drawings Sean or Esteban have.

However, it does reveal that if Sean and Esteban have the same amount of drawings in their sketchbook ,then each sketchbook might have 6 groups of 3 drawings, giving a total of 18 drawings.

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Answer:

It is about 15.8, so B.

Step-by-step explanation:

If you multiply 15.8 by 15.8, you'll get 249.64. Closest to 250.

C is just 250 divided by 2. Not square root of.

D doesn't even make sense.

25 times 25 is 625, not 250. So not A.

Answer:

-3

Step-by-step explanation:

Let the first term be a-d, second term be a and third term be a+d

d is the common difference

If each term, starting with the 3rd term, is found by multiplying the previous two terms then:

a(a-d) = a+d

a²+ad-a-d = 0

a(a+d)-1(a+d) = 0

(a+d)(a-1) = 0

a-1 = 0

a= 1

a+d = 0

1+d = 0

d = 0-1

d = -1

Get the sixth term

nth term of a sequence is expressed as

Tn = a+(n-1)d

T6 = 1+(6-1)(-1)

T6 = 1+5(-1)

T6 = 1-5

T6 = -4

Get the third term T3

T3 = a+2d

T3 = 1+2(-1)

T3 = 1-2

T3 = -1

difference between the 6th and 3rd terms in the sequence is expressed as;

Difference = T6-T3

Difference = -4-(-1)

Difference = -4+1

Difference = -3

Answer: 0.65

Step-by-step explanation:

Step-by-step explanation:

as the formula says for the acid of symmetry :

x = -b/2a

in the function m(x) = 2x² + 8x +3

we have

a = 2

b = 8

c = 3

the axis of symmetry is

x = -8/(2×2) = -8/4 = -2

the vertex is (h, k) out of the form

m(x) = a(x - h)² + k

we know already, a = 2

for the rest we do all the multiplications and then we compare it with the original function :

m(x) = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k

a = 2

-2ah = 8

-2×2×h = 8

-4h = 8

h = -2

ah² + k = 3

2×(-2)² + k = 3

8 + k = 3

k = -5

so, the vertex is (-2, -5)

The percentage of data that falls between 1.9 inches and 2.3 inches of rainfall is roughly (D) 68% if the distribution is normal.

In essence, percentages are fractions with 100 as the denominator.

We place the percent symbol (%) next to the number to indicate that the number is a percentage.

For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

So, we determine each's z-score:

z-score = (x-mean)/SD

z1 = (1.9-2.1)/0.2 = -1

z2 = (2.3-2.1)/0.2 = 1

Then, the percentage we want to determine is:

P(-1<x<1)

For this, we utilize the normal scoring table:

P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269

= 68%

Therefore, the percentage of data that falls between 1.9 inches and 2.3 inches of rainfall is roughly (D) 68% if the distribution is normal.

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Complete question:
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%

The volume of the cylinder with a height of 8in and a radius of 6in is approximately 904.32 cubic inches.

To find the volume of a cylinder, we use the formula V=πr²h, where V is the volume, r is the radius, and h is the height.

Given a cylinder with a height of 8 inches and a radius of 6 inches, we can substitute these values into the formula to find the volume:

V = π(6²)(8)

V = π(36)(8)

V = 904.32 cubic inches (rounded to two decimal places)

The formula for the volume of a cylinder is derived by multiplying the area of the base of the cylinder (which is πr²) by the height of the cylinder. In this case, the radius of the cylinder is 6 inches, so the area of the base is π(6²) = 36π square inches. Multiplying this by the height of 8 inches gives us the volume of the cylinder.

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Answer:

B

Step-by-step explanation:

im pretty sure it's B because it's a negitive

Answer:

the answer is side angle side (sas)

Answer: SAS

Step-by-step explanation: You know to sides are congruent so the included angle between them must also be congruent.

The gradient of a function points in the direction in which the function increases the fastest because it represents the direction of greatest increase of the function.

The gradient of a function is a vector that points in the direction of the steepest increase of the function at a particular point. This means that if we move in the direction of the gradient, the value of the function increases the fastest.

To understand why this is true, let's consider the definition of the gradient. The gradient of a function f(x) is defined as a vector of partial derivatives:

∇f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)

Each component of the gradient vector represents the rate of change of the function with respect to the corresponding variable. In other words, the gradient tells us how much the function changes as we move a small distance in each direction.

When we take the norm (or magnitude) of the gradient vector, we get the rate of change of the function in the direction of the gradient. This means that if we move in the direction of the gradient, the value of the function changes the fastest, because this is the direction in which the function is most sensitive to changes in the input variables.

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Answer:

Step-by-step explanation:

To use the regression function on your calculator, first hit STAT then choose 1:Edit by pressing ENTER. Then a table pops up. If it's not clear, arrow up to L1, hit CLEAR then ENTER and the table empties. Do the same with L2. Arrow left and right as needed to get from one column to the other. Then in L1 enter the x values one at a time, hitting ENTER after each. When all the x values are in, arrow over to L2 and enter the y values in the same way.

Next, hit STAT again, then right arrow over to CALC. Choose 6:CubicReg by either arrowing down to it or by pressing 6. If you have a TI 83+, the equation comes right up for you; if you have a TI 84+ or 84+CE, you have to arrow down to CALCULATE and hit ENTER to get your equation. The equation is

\(-2x^3+2x^2-4x+3\) with a coefficient correlation (r-squared) value of 1 which means this is a perfect equation for this data and all the points you entered into the table fall perfectly on this curve.

Angle for this inequality is approximately (11) 0.46 radians or 26.57 degrees. (12) 1.32 radians or 75.52 degrees and 4.96 radians or 284.48 degrees. (16)1.37 radians or 78.46 degrees and 4.77 radians or 273.54 degrees.  

What is radians ?

Radians are a unit of measurement for angles. One radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

11. cos x > 1/2 (sin x)

We can start by dividing both sides by cos(x) (assuming cos(x) ≠ 0) to get:

tan x > 1/2

Using a calculator, we can find the reference angle for this inequality is approximately 0.46 radians or 26.57 degrees.

12. tan x < 2 sin x

We can rearrange the inequality to get:

tan x - 2 sin x < 0

Using trigonometric identities, we can write this as:

sin x (cos x - 2) < 0

This inequality is satisfied when either sin x < 0 and cos x > 2 or sin x > 0 and cos x < 2. Using a calculator, we can find the reference angles for cos x = 2 are approximately 1.32 radians or 75.52 degrees and 4.96 radians or 284.48 degrees.

16. cos 2x ≥ 5 - cos x

We can start by using the double angle formula for cosine to get:

2 \(cos^2\) x - cos x - 5 ≥ 0

This quadratic inequality can be factored as:

(2 cos x - 5) (cos x + 1) ≥ 0

The inequality is satisfied when either 2 cos x - 5 ≥ 0 and cos x + 1 ≥ 0 or 2 cos x - 5 ≤ 0 and cos x + 1 ≤ 0. Using a calculator, we can find the reference angles for 2 cos x - 5 = 0 are approximately 1.37 radians or 78.46 degrees and 4.77 radians or 273.54 degrees.

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Answer:

3x+2

Step-by-step explanation:

khan told me that my explanation

The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90.

1/90

The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90. This is because there are only 9 possible digits (1, 2, 3, 4, 5, 6, 7, 8, 9) to choose from, and each of these digits can be multiplied by itself twice to give 9 possible combinations. Therefore, there are 9 three-digit numbers that satisfy the given condition, and these 9 numbers can be chosen from a total of 900 three-digit numbers (10 x 10 x 10 = 1000, minus the 100 numbers beginning with 0). Thus, the probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 9/900, which can be simplified to 1/90.

The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90.

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Answer:

slope = 2 , y- intercept = -8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

- 4x + 2y = - 16 ( add 4x to both sides )

2y = 4x - 16 ( divide both sides by 2 )

y = 2x - 8 ← in slope- intercept form

with slope m = 2 and y- intercept c = - 8

Answer:

the slope is 2 and y-intercept is (0,-8)

Step-by-step explanation:

Step 1: is to subtract 2y from both sides, -4x+2y-2y=-16-2y

Step 2: Simplify, -4= -16-2y

Step 3: Divide both sides by -4, -4x/4=-16/-4-2y/-4

4x/4=x=1

Answer:

x= 8 km

Step-by-step explanation:

measurement used:

When getting measurement the missing side occupies 1 more than a half of 15km

Answer:

x = 8km

Step-by-step explanation:

Use Pythagorean Theorem:

c2 = a2 + b2

In the diagram given, the hypotenuse (c) is 17 so substitute these values into the equation

17^2 = x^2 + 15^2

Take 15 to the power 2, to the other side.

17^2 - 15^2 = x^2

Solve to get

64 = x2

Square root both sides so

x = 8

Th matrix is missing. The matrix is :

\(\begin{bmatrix}1 &-4 &4 \\ -4 &16 & 4 \end{bmatrix}\)

Solution :

The column of the matrix are \(\begin{bmatrix}1\\ -4\end{bmatrix}\) , \(\begin{bmatrix}-4\\ 16\end{bmatrix}\), \(\begin{bmatrix}4\\ 4\end{bmatrix}\)

Now each of them are vectors in \($IR^2$\). But  \($IR^2$\) has dimensions of 2. But there are 3 column vectors, hence they are linearly dependent.

Therefore, the column of the given matrix does not form the \(\text{linearly independent set}\) as the set contains \(\text{more vectors}\) than there are entries in each vector.

Therefore, option (D) is correct.

Answer:

     j/k + 6

Step-by-step explanation:

Add 6 to the quotient of j and k comes out to:

                                  j/k + 6

The probability of and odds for being dealt a two or black card in a 52-card deck are approximately 27/52 or 0.5192 and 1.08 : 0.93, respectively.

A 52-card deck has 26 red cards and 26 black cards. There are four twos in the deck, with two of them being red and two being black.

Therefore, the probability of being dealt a two or a black card is:P(two or black card) = P(two) + P(black card) - P(two and black)P(two)

P(two or black card)  = 4/52 = 1/13, as there are four twos in a 52-card deck.

P(black card) = 26/52 = 1/2, as there are 26 black cards in a 52-card deck.

P(two and black) = 2/52 = 1/26, as there are two cards in the deck that are both a two and black card.

So, substituting these values into the formula above:P(two or black card) = 1/13 + 1/2 - 1/26

P(two or black card) = 27/52 or approximately 0.5192

As for the odds of being dealt a two or a black card, the formula for odds is:P(success) : P(failure)

The probability of success in this case is 27/52, and the probability of failure is 25/52 (since there are 25 non-black twos in the deck).

So, the odds of being dealt a two or a black card are:27/25 : 25/27 or approximately 1.08 : 0.93.

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Answer:

1. Parallel

2. Neither

3. Perpendicular

4. Perpendicular

5. Neither

6. Same Line

7. Perpendicular

8. Parallel

9. Same Line

10. Perpendicular

11. Parallel

12. Perpendicular

13. Parallel

14. Same Line

15. Perpendicular

16. Parallel

17. Neither

18. Parallel

19. Parallel

20. Parallel

Answer:

Around 376.99

Step-by-step explanation:

the formula is 2πrh+2πr²

so if we plug in everything we get 2π(4)(11)+2π(4)²

When we simplify that, we would get 376.99

Answer:

d yes that is the correct answer

This function is Exponential

Hope that helps!

The length of the diagonal cannot be determined with the given information.

The question provides information about the perimeter of the rhombus and the lengths of two sides (15 and 30). However, this information is not sufficient to determine the length of the diagonal. In a rhombus, the diagonals are not necessarily equal in length unless specified.

Therefore, without additional information about the angles or side lengths of the rhombus, it is not possible to determine the length of the diagonal. The answer cannot be determined based on the information provided.

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