Which inequality is true?
A. 7π > 21
B. π +4<7
OC. 3π-1> 9
O ○ D. />1
SUE

The correlation coefficient is approximately 0.995, indicating a strong positive correlation between x and y.

The equation of the least squares regression line is y = 4.45 + 5.21x

We have,

To find the correlation coefficient and the least squares regression line, we need to first calculate some values based on the given data:

x  y x²   y²                 xy

0 23 0   529          0

2 26 4   676         52

3 30 9   900         90

5 33 25   1089        165

7 36 49   1296        252

8 40 64   1600        320

10 43 100   1849        430

Σx=35

Σy=231

Σx²=251

Σy² = 7889

Σxy=1309

Now,

a)

The correlation coefficient can be calculated using the formula:

r = (nΣxy - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2))

where n is the number of data points.

Substituting the values.

r = (71309 - 35231) / sqrt((7251 - 35^2)(77889 - 231^2))

= 0.995

b)

The equation of the least squares regression line can be calculated using the formulas:

b = Σxy / Σx²

a = ȳ - bẋ

where b is the slope of the line, a is the y-intercept of the line, ẋ is the mean of x, and ȳ is the mean of y.

Substituting the values.

b = 1309 / 251 = 5.21

ẋ = Σx / n = 35 / 7 = 5

ȳ = Σy / n = 231 / 7 = 33

a = 33 - 5.21(5) = 4.45

Therefore,

The correlation coefficient is approximately 0.995, indicating a strong positive correlation between x and y.

The equation of the least squares regression line is y = 4.45 + 5.21x

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The possible degree sequences for a simple graph are: b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2) c. (5, 4, 4, 4, 3, 2)

To determine which of the given degree sequences are possible for a simple graph, we can apply the Handshaking Lemma.

The Handshaking Lemma states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

Let's analyze each degree sequence:

a. (5, 3, 3, 3, 3, 2)

To check if this degree sequence is possible, we sum up all the degrees: 5 + 3 + 3 + 3 + 3 + 2 = 19. According to the Handshaking Lemma, the sum of the degrees should be twice the number of edges. Therefore, the number of edges should be 19/2 = 9.5, which is not an integer. Since the number of edges must be a whole number, this degree sequence is not possible for a simple graph.

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2)

Summing up the degrees: 6 + 5 + 5 + 5 + 4 + 4 + 3 + 2 + 2 + 2 = 38. According to the Handshaking Lemma, the number of edges should be 38/2 = 19. The number of edges being an integer, this degree sequence is possible for a simple graph.

c. (5, 4, 4, 4, 3, 2)

Summing up the degrees: 5 + 4 + 4 + 4 + 3 + 2 = 22. The number of edges should be 22/2 = 11. Since the number of edges is an integer, this degree sequence is possible for a simple graph.

d. (9, 7, 3, 3, 3, 2, 2, 1, 1)

Summing up the degrees: 9 + 7 + 3 + 3 + 3 + 2 + 2 + 1 + 1 = 31. The number of edges should be 31/2 = 15.5, which is not an integer. Therefore, this degree sequence is not possible for a simple graph.

Based on the analysis above:

a. (5, 3, 3, 3, 3, 2) is not possible.

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2) is possible.

c. (5, 4, 4, 4, 3, 2) is possible.

d. (9, 7, 3, 3, 3, 2, 2, 1, 1) is not possible.

Therefore, the possible degree sequences for a simple graph are:

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2)

c. (5, 4, 4, 4, 3, 2)

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Answer:

(x-1)(x-2)

x=1, x=2

Step-by-step explanation:

Add 100 pounds of weight to the luggage hold to balance the aircraft.

The CG is out of equilibrium forward with the existing numbers; weight must be increased, preferably to the aft portions, to bring the moment into acceptable bounds. Fuel addition will just increase weight; it won't shift the CG back.

The 100 pounds of luggage will cause the CG to shift back. Add 100 pounds to the maximum weight of everything to get a total weight of 2890 pounds.

The CG is now at the new weight as well as in balance since the aft arm of the luggage compartment increases the total moment arm by 140 pounds, to 2362 pounds, bringing it into balance.

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Answer:

12^16= 184884258895036400

12^4= 20736

Given :

John has 3 ½ = 7/2 pounds of Skittles.

He decides to give ¾ pounds of Skittles to each friend.

To Find :

How much the leftover Skittles are.

Solution :

Let, his number of bands are x.

So, amount of Skittles left is :

\(L= \dfrac{7}{2}-\dfrac{3x}{4}\\\\L = \dfrac{24-3x}{4}\)

Therefore, amount of leftover Skittles are \(\dfrac{24-3x}{4}\) pounds if number of friends are x.

Hence, this is the required solution.

The standard deviation is a measure of how a dataset is close to the mean.

The statement that is most likely true is (b) the scores from Mrs. Rijo's class are the closest to the class mean

The table entry is given as:

Class               Mean  Standard Deviation

Mrs. Jones      89            1.9

Mrs. Rijo          82            1.4

Mr. Phan         73              3.4

Mrs. Scott       90             6.1

The smaller the standard deviation, the closer the value to the mean

From the above table, we can see that Mrs. Rijo's class has the smallest standard deviation value.

Hence, the statement that is most likely true is (b) the scores from Mrs. Rijo's class are the closest to the class mean

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Answer:

it's B! :D

Step-by-step explanation:

Answer:

4.

Hope that helps!

Step-by-step explanation:

Answer:

1( 8y + 5y )

Step-by-step explanation:

The gcf of 8 and 5 is 1

Step-by-step explanation:

you can use mathaway and itll solve it for you just take a pic

The reflection over the y-axis only changes the sign of the x-component so the reflected point is A' (-3, -1)

Here we can't see the options, so I will teach you how to reflect any point over the y-axis.

Any point on the X-Y plane is defined by its coordinates (x, y).

If we reflect this point over the y-plane, we only change the sign of the x-component of the point.

So after the reflection, we get the point (-x, y).

Then if we apply that reflection to point A (3, -1). We will get the reflected point:

A' (-3, -1)

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Answer:

Step-by-step explanation:

The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.

Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.

To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.

Let's assume the loan amount is denoted by P.

The formula to calculate the future value of a loan with interest is:

FV = P(1 + r)^n

Where:

FV = Future value (total amount repaid)

P = Principal amount (maximum price of the car)

r = Interest rate per period (9.25% or 0.0925)

n = Number of periods (six years)

Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:

$210,000 = P(1 + 0.0925)^6

Now we can solve for P:

P = $210,000 / (1 + 0.0925)^6

Evaluating this expression, we find:

P ≈ $126,318.29

Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

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Answer:

y = 2x + 40

Step-by-step explanation:

slope-intercept formula: y = mx + b

x = number of months

y = total cost

slope is 2 and y-intercept is 40

The perimeter of  isosceles triangle PRQ is 24.65 units.

The lengths of its three sides and add them up. We can use the distance formula to find the length of each side.

Distance formula: The distance d between two points (x1, y1) and (x2, y2) is given by:

d = \(sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

Using this formula, we can find the lengths of the sides PR, RQ, and PQ.

PR = \(sqrt((-1 - (-7))^2 + (4 - (-1))^2) = sqrt(36 + 25) = sqrt(61)\)

RQ =\(sqrt((3 - (-1))^2 + (-1 - 4)^2) = sqrt(16 + 25) = sqrt(41)\)

PQ = \(sqrt((3 - (-7))^2 + (-1 - (-1))^2) = sqrt(100) = 10\)

Therefore, the perimeter of triangle PRQ is:

PR + RQ + PQ = \(sqrt(61) + sqrt(41) + 10 ≈ 24.65\) (rounded to two decimal places)

So, the perimeter of triangle PRQ is approximately 24.65 units.

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The answer is −x+5+q

Answer:

-x+q+5

Step-by-step explanation:

You have to combine like terms

\(3x+5-4x+q\\\\=(3x-4x)+(q)+(5)\\\\=(3-4)x+q+5\\\\=-x+q+5\)

Answer:

y = - x³ - 3x² - 3x - 4

Step-by-step explanation:

!!!!!!

The function represented in the graph is -

\(y\ =\ -\left(x+0.9\right)^{3}-3.3\)

In mathematics, if -

xⁿ = k

then -

[n] is called exponent

[x] is called base.

Logarithm is the inverse function to exponentiation. That means the logarithm of a number [x] to the base [b] is the exponent to which [b] must be raised, to produce [x]. We can write -

\(y = log_{e}x\)

We have the function as -

f(x) = x³

Refer to the graph of the function in the modified form. The function after being translated is same as the one given in the question. The function after translation is -

\(y\ =\ -\left(x+0.9\right)^{3}-3.3\)

Therefore, the function represented in the graph is -

\(y\ =\ -\left(x+0.9\right)^{3}-3.3\)

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The solution to the differential equation is y ( t ) = 100 1 + 19 e 0.09 t

This is a separable differential equation, which we can solve using separation of variables:

d y d t = 0.09 y ( 1 − y 100 )

d y 0.09 y ( 1 − y 100 ) = d t

Integrating both sides, we get:

ln | y | − 0.01 ln | 100 − y | = 0.09 t + C

where C is the constant of integration. We can solve for C using the initial condition y(0) = 5:

ln | 5 | − 0.01 ln | 100 − 5 | = 0.09 ( 0 ) + C

C = ln | 5 | − 0.01 ln | 95 |

Substituting this value of C back into our equation, we get:

ln | y | − 0.01 ln | 100 − y | = 0.09 t + ln | 5 | − 0.01 ln | 95 |

Simplifying, we get:

ln | y ( t ) | 100 − y ( t ) = 0.09 t + ln 5 95

To solve for y(t), we can take the exponential of both sides:

| y ( t ) | 100 − y ( t ) = e 0.09 t e ln 5 95

| y ( t ) | 100 − y ( t ) = e 0.09 t 5 95

y ( t ) 100 − y ( t ) = ± e 0.09 t 5 95

Solving for y(t), we get:

y ( t ) = 100 e 0.09 t 5 95 ± e 0.09 t 5 95

Using the initial condition y(0) = 5, we can determine that the sign in the solution should be positive, so we have:

y ( t ) = 100 e 0.09 t 5 95 + e 0.09 t 5 95

Simplifying, we get:

y ( t ) = 100 1 + 19 e 0.09 t

Therefore, the solution to the differential equation is:

y ( t ) = 100 1 + 19 e 0.09 t

where y(0) = 5.

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To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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When i text i mostly misspell, carrot as caroot

When i text, my autocorrect changes rat to fat.

False

True B)

Answer:

5 : x=3

Step-by-step explanation:

Answer:

15 sq m

Step-by-step explanation:

hope this helps

Answer:

15m

If you cut this shape into 2 sections you will have 2*3=6m and 3*3=9m then you add these qautities and get 15m

P is the centroid of triangle ABC, and we have AP = CP = BP, which is what we needed to prove.

Since â„“, m, and n are perpendicular bisectors of the sides of triangle ABC, they intersect at the circumcenter O of triangle ABC.

Since O is the circumcenter of triangle ABC, it lies on the perpendicular bisectors of all three sides. Therefore, OA = OB = OC.

Now, consider triangle AOC. Since OA = OC and â„“ is the perpendicular bisector of AC, â„“ passes through the midpoint of AC, which we will call D. Therefore, AD = CD.

Similarly, consider triangle BOC. Since OB = OC and n is the perpendicular bisector of BC, n passes through the midpoint of BC, which we will call E. Therefore, BE = CE.

We know that â„“, m, and n intersect at point P, so P is the intersection of lines AD, BE, and OC. Therefore, P is the centroid of triangle ABC, and we have AP = CP = BP, which is what we needed to prove.

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Answer:

9 - 15/2

10 - 9

11 - 16/3

12 - 5/6

Step-by-step explanation:

Answer:

(1/2,5/2)

Step-by-step explanation:

Given both points, K(-7,8) and J(6,-3). To find the midpoint between J and K, we can use the formula of:

\( \displaystyle{ \text{midpoint} = \left( \dfrac{x_1 + x_2}{2} ,\dfrac{y_1 + y_2}{2} \right)}\)

Therefore, substitute in:

\( \displaystyle{ \text{midpoint} = \left( \dfrac{ - 7 +6}{2} ,\dfrac{ 8 - 3}{2} \right)} \\ \\ \displaystyle{ \text{midpoint} = \left( \dfrac{ 1}{2} ,\dfrac{ 5}{2} \right)}\)

Therefore, the midpoint is (1/2,5/2)

Answer:

they are often small but intense. ... The amount of precipitation that falls around the world may range from less than ... One inch of rain falling on 1 acre of ground is equal to about 27,154 gallons

Step-by-step explanation:

Answer:

2 x 30 = 60 cents

3 x 25 = 75 cents

60 + 75 = 135 cents or 1 dollar 35 cents

Hope this helps

Step-by-step explanation:

Answer:

135 cents or $1.35

Step-by-step explanation:

30 x 2 = 60 cents for the choc

25 x 3 = 75 cents for the pb

60+75=135

The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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The lifting force if the speed is 220 miles per hour is F' = 708.53 N.

The force of light, or simply light, is the sum of all forces on an object that cause the object to move perpendicular to the direction of flow.

The most common type of lift is the wing lift. But there are many other common uses, such as propellers on airplanes and ships, rotors on helicopters, fan blades, sails on sailboats, and wind turbines.

We have,

The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. It, means that,

\(F=kAv^{2}\)

Where

k is constant

If, A = 190 Ft², v = 220 mph, F = 950 pounds

Now, find k first from the above data. So,

    \(k=\frac{F}{Av^{2} }\)

⇒ \(k=\frac{950}{190* (220)^2}\)

⇒ k = 0.0001033

It is required to find the lifting force on the wing if the plane slows down to 190 miles per hour.

Let F' is a new force. So,

    F' = 0.0001033 × 190 × (190)²

⇒ F' = 708.53 pounds.

So, the lifting force is 708.53 pounds if the plane slows down to 190 miles per hour.

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Answer:

\(a_4=19\)

Step-by-step explanation:

Given:

\(\implies a_2=a_{1}+4=7+4=11\)

\(\implies a_3=a_{2}+4=11+4=15\)

\(\implies a_4=a_{3}+4=15+4=19\)

Put values get answer

A matrix can be written as a linear combination of its columns using matrix multiplication. The columns of a matrix are vectors, and linear combinations of vectors can be formed by multiplying each vector by a scalar and adding them together.

To write a matrix A as a linear combination of its columns, we can express A as a sum of column vectors, each multiplied by the corresponding entry in a scalar vector x.

A linear combination is a sum of scalar multiples of vectors. Given a set of vectors {v₁, v₂, …, vₙ} and scalars {c₁, c₂, …, cₙ}, their linear combination is given by c₁v₁ + c₂v₂ + … + cₙvₙ.

This can be represented in matrix form as: [v₁ v₂ … vₙ] [c₁] [c₂] ⋮ [cₙ] = c₁v₁ + c₂v₂ + … + cₙvₙ = A

Where [v₁ v₂ … vₙ] is the matrix whose columns are the vectors, and [c₁ c₂ … cₙ] is the column vector of scalars.

To write A as a linear combination of its columns, we want to solve for [c₁ c₂ … cₙ]. We can do this by multiplying both sides of the equation above by the inverse of the matrix [v₁ v₂ … vₙ], which gives:[v₁ v₂ … vₙ]⁻¹ [v₁ v₂ … vₙ] [c₁] [c₂] ⋮ [cₙ] = [v₁ v₂ … vₙ]⁻¹ A c₁v₁ + c₂v₂ + … + cₙvₙ = A

Here, we used the fact that [v₁ v₂ … vₙ]⁻¹[v₁ v₂ … vₙ] = I, the identity matrix. The right-hand side is just A, and the left-hand side is the column vector [c₁ c₂ … cₙ] of scalars, which we were looking for. Thus, we have written A as a linear combination of its columns.

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