Find the slope of a line that passes through the points (-8, 3) and (-20, -18). *

A. 7/4
B. 4/7
C. -7/4
D. -4/7

Answer:

The least degree of the polynomial that assures an error smaller than 0.001 is 4.

The Lagrange error bound for the Taylor polynomial of degree n centered at x=2 for e^x is given by:

```

|e^x - T_n(x)| < \frac{e^2}{(n+1)!}|x-2|^{n+1}

```

where T_n(x) is the Taylor polynomial of degree n centered at x=2.

We want the error to be less than 0.001, so we have:

```

\frac{e^2}{(n+1)!}|x-2|^{n+1} < 0.001

```

We can solve for n to get:

```

n+1 > \frac{e^2 \cdot 1000}{|x-2|}

```

We know that |x-2| = 0.45, so we have:

```

n+1 > \frac{e^2 \cdot 1000}{0.45} \approx 6900

```

Therefore, n > 6899.

The least integer greater than 6899 is 6900, so the least degree of the polynomial that assures an error smaller than 0.001 is 4.

The fourth-degree Taylor polynomial centered at x=2 for e^x is given by:

```

T_4(x) = 1 + 2x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24}

```

We can use this polynomial to estimate e^1.45 as follows:

```

e^1.45 \approx T_4(1.45) = 4.38201

```

The actual value of e^1.45 is 4.38202, so the error in this approximation is less than 0.001.

Step-by-step explanation:

Answer:

w = 0.5

Step-by-step explanation:

w represents the width of the frame

Area of the picture and the frame is

(2 + 2w)2

Area of picture is

22

Area of the frame is

(2 + 2w)2 - 4 = 5

(2 + 2w)2 = 9

2 + 2w = 3

2w = 1

The length of the sides of the frame is 2.5 ft

Area is the term used to define the amount of space taken up by a 2D shape or surface.

Given that, you are making a square frame of uniform width for a square picture that has side lengths of 2 feet, the total area of the frame is 5 square feet.

Since, the width of picture is uniform and is = 2ft

Therefore, width of frame = 2ft

Area of frame = length*width

5 = l*2

l = 5/2 = 2.5ft

Hence, The length of the sides of the frame is 2.5 ft

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The sample correlation coefficient would be closest to -0.9.

Here's why:

Correlation Coefficient: The correlation coefficient is a statistical measure of the degree of correlation (linear relationship) between two variables. Pearson’s correlation coefficient is the most widely used correlation coefficient to assess the correlation between variables.

Pearson’s correlation coefficient (r) ranges from -1 to 1. A value of -1 denotes a perfect negative correlation, 1 denotes a perfect positive correlation, and 0 denotes no correlation. There is a negative correlation between speed and time. As the speed of the car increases, the time needed to traverse the segment decreases. So, the sample correlation coefficient would be negative.

Since the sample size is large enough, the sample correlation coefficient should be close to the population correlation coefficient. The population correlation coefficient between speed and time should be close to -1, which implies that the sample correlation coefficient should be close to -1.

Therefore, the sample correlation coefficient would be closest to -0.9.

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The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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The compound inequality statement for the weight of cartons that would be inspected is 630 > X > 690

Weight of empty carton = 20 oz

Acceptable range of weight per bag of peanut :

Number of peanut bags per carton = 20 bags

Therefore,

The lower limit for weight of carton after being filled will be :

The Upper limit for weight of carton after being filled will be :

Therefore, the compound inequality for the cartons that will be inspected is : 630 > X > 690

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the answer would be -6

Answer:

the answer is B

Step-by-step explanation:

when you take the first answer and subtract the second answer from it you get a negitive number of -1.1080325x10+28

Answer:

True

Step-by-step explanation:

Linear equations are often used to model the relationship between the dependent variable that is affected by changes in the independent variable.  

For instance, the linear function: f(x) = 2x + 3, where f(x) is the output (dependent variable) depends on the value of the input, x (independent variable).  

Therefore, the correct answer is True.      

x=74°

look at the given picture for stepwise

Answer:

RV = 49 units

Step-by-step explanation:

in parallelogram RSTU , the diagonals bisect each other, then

TV = RV , that is

3y - 17 = y + 27 ( subtract y from both sides )

2y - 17 = 27 ( add 17 to both sides )

2y = 44 ( divide both sides by 2 )

y = 22

Then

RV = y + 27 = 22 + 27 = 49 units

Answer:

The Coefficients in this expression are 10 and 3, while the constants are 5 and 1.

Step-by-step explanation:

Coefficients = The number that is in front of the variable.

Constant = Any number without a variable.

(Variables are the letters that you may find in an equation or function.)

Hope this helps you :)

Answer:

The coefficient are 10 and  3

The constants are 5 and 1

Step-by-step explanation:

A coefficient is the number in front of any known term.

A constant is a number by itself.

So the coefficient are 10 and  3

The constants are 5 and 1

Answer:

Hello! the answer is CD is 17,0 (-2,19)

\(\text {Hello! Let's Solve this Problem!}\)

\(\text {\underline {The First Step is to Add 4}}\)

\(\text {3x-4+4=14+4}\)

\(\text {3x=18}\)

\(\text {\underline {The Final Step is to Divide 3}}\)

\(\text {3x/3=18/3}\)

\(\text {Your Answer Would Be:}\)

\(\Huge\boxed {x=6}\)

\(\text {Best of Luck!}\)

\(\huge\text{$x=\boxed{6}$}\)

We can solve for the variable \(x\) by isolating it on one side of the equals sign.

Start by adding \(4\) to both sides to cancel out the \(-4\) on the left side of the equation.

\(\begin{aligned}3x-4+4&=14+4\\3x&=18\end{aligned}\)

Now divide both sides of the equation by \(3\) since \(3x\) is the same as \(3*x\) and we want to isolate \(x\), keeping in mind that anything multiplied by \(1\) is itself.

\(\begin{aligned}3x&=18\\3*x&=18\\3*x\div3&=18\div3\\x*3\div3&=18\div3\\x*1&=6\\x&=\boxed{6}\end{aligned}\)

Answer:

Mark a line or colors from the left of 2 on the x until arrive on the point of 2

Step-by-step explanation:

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Answer:

<4

Step-by-step explanation:

Answer:

Area of shaded region is 160.14m²

Step-by-step explanation:

To find the area of the shaded region, subtract the area of inner circle from the area of outer one

a=πr²

(3.14)7²=153.86

(3.14)10²=314

314-153.86=160.14

Answer:

Your answer is:

(x+2)^2

Factor x2+4x+4

x2+4x+4

The middle number is 4 and the last number is 4.

Add together to get 4

Multiply together to get 4

2+2 = 4

2*2 = 4

(x+2)(x+2) or (x+2)^2

The solution to the equation log₄(x) = 2 is x = 16.

Given the equation in the question:

log₄(x) = 2

To solve the equation log₄(x) = 2, we can use the properties of logarithms.

Using the property:

If x and n are positive real numbers and b ≠ 1, then logₙ(x) = a is equivalent to:

bᵃ = x

Applying this definition:

Rewrite log₄(x) = 2 as an exponential function

4² = x

x = 4²

x = 16

Therefore, the value of x is 16.

Option D) 16 is the correct answer.

The question is:

What is the value of x in the equation log₄(x) = 2

Options: A)1, B)2, C)4, D)16, E)64

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10% had both an internship and a summer class, events "friend had an internship" and "friend took a summer class" are dependent, and 60% did none of the three activities using percentages.

Let I, C, and R represent the events that a friend had an internship, took a summer class, or took a road trip, respectively. We are given:

P(I) = 0.4

P(C) = 0.2

P(R) = 0.5

P(I U C) = 0.5

P(I U R) = 0.7

P(C U R) = 0.6

P(I ∩ C ∩ R) = 0.05

(a) We can use the inclusion-exclusion principle to find the number of friends who had both an internship and a summer class:

P(I ∩ C) = P(I U C) - P(I) - P(C) = 0.5 - 0.4 - 0.2 = 0.1

So, 10% of your friends had both an internship and a summer class.

(b) To check if the events "your friend had an internship" and "your friend took a summer class" are independent, we need to verify if:

P(I ∩ C) = P(I) * P(C)

Using the result from part (a), we have:

P(I ∩ C) = 0.1

P(I) = 0.4

P(C) = 0.2

So, we have:

P(I ∩ C) = 0.1 ≠ 0.08 = P(I) * P(C)

Since the probability of the intersection is not equal to the product of the individual probabilities, the events are dependent.

(c) To find the number of friends who did none of the three activities, we can use the complement rule:

P(not (I U C U R)) = 1 - P(I U C U R)

Using the inclusion-exclusion principle, we have:

P(I U C U R) = P(I) + P(C) + P(R) - P(I ∩ C) - P(I ∩ R) - P(C ∩ R) + P(I ∩ C ∩ R)

= 0.4 + 0.2 + 0.5 - 0.1 - 0.15 - 0.2 + 0.05 = 0.4

So, we have:

P(not (I U C U R)) = 1 - P(I U C U R) = 1 - 0.4 = 0.6

Therefore, 60% of your friends did none of the three activities.

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Another accepted answer is -5-i, but if your teacher wants only one answer, then I'd go for 5+i

======================================================

Work Shown:

\(\sqrt{24+10i} = a+bi\\\\\left(\sqrt{24+10i}\right)^2 = (a+bi)^2\\\\24+10i = a^2+2abi+b^2i^2\\\\24+10i = a^2+2abi+b^2(-1)\\\\24+10i = a^2+2abi-b^2\\\\24+10i = (a^2-b^2)+(2ab)i\\\\\)

Equating terms, we have this system

\(\begin{cases}24 = a^2-b^2\ \text{.... real terms}\\10 = 2ab\ \text{.... imaginary terms}\end{cases}\)

Solve the second equation for b to get b = 5/a

Plug that into the first equation to solve for 'a'

\(24 = a^2-b^2\\\\24 = a^2-\left(\frac{5}{a}\right)^2\\\\24 = a^2-\frac{25}{a^2}\\\\24a^2 = a^4-25\\\\0 = a^4-24a^2-25\\\\a^4-24a^2-25 = 0\\\\(a^2-25)(a^2+1) = 0\\\\(a-5)(a+5)(a^2+1) = 0\\\\\)

Setting each factor equal to zero would lead to...

We're told that 'a' is a real number, so we ignore the solutions "a = i and a = -i". The only possible solutions are a = 5 and a = -5

If a = 5, then,

b = 5/a = 5/5 = 1

So

\(\sqrt{24+10i} = a+bi = 5+1i = 5+i\)

or in short,

\(\sqrt{24+10i} = 5+i\)

-----------------

If a = -5, then b = 5/a = 5/(-5) = -1

So it's very possible that we could also say

\(\sqrt{24+10i} = -5-i\\\\\)

If you wanted to combine the two we would use the plus/minus notation like so

\(\sqrt{24+10i} = \pm(5+i)\\\\\)

This is due to (5+i)^2 and (-5-i)^2 both having the same result of 24+10i. Hence the plus/minus. If your teacher wants one answer only, then I'd go for 5+i, as we could consider it a "principal" square root in a sense.

The greatest possible number of intersection points for four circles of different sizes is 12.

The greatest possible number of intersection points of four circles of different sizes can be calculated by considering the maximum number of intersection points each pair of circles can have and then summing them up.

When two circles intersect, they can have a maximum of two intersection points. So, if we have four circles, we can find the maximum number of intersection points by considering each pair of circles separately.

For the first circle, it can intersect with the other three circles at most two times each, giving us a total of 2 * 3 = 6 intersection points.

For the second circle, it can intersect with the remaining two circles at most two times each, giving us a total of 2 * 2 = 4 intersection points.

The third circle can intersect with the last remaining circle at most two times, giving us a total of 2 * 1 = 2 intersection points.

Finally, the fourth circle doesn't have any other circle left to intersect with, so it doesn't contribute any additional intersection points.

Now, we can sum up the intersection points from each pair of circles: 6 + 4 + 2 + 0 = 12.

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Answer:

The slope is -1/2

Answer:

-(1/2) or -0.5

Step-by-step explanation:

select two coordinates. for example, (2,2) and (4,1).

do (y2 - y1) ÷ (x2 - x1).

in this case, (1 - 2) ÷ (4 - 2). you should end up with -(1/2), or -0.5

Answer:

16

Step-by-step explanation:

Since the ratio is constant, you can do divisions here.

4/3 = 4/3

6/8 = 4/3

Etc.

From here, you take 12, and multiple it by 4/3, and get 16.

Answer:

16 is the missing number.

Step-by-step explanation:

Have a great day. :-)

and can I please have brainliest?

Answer:

30

Step-by-step explanation:

(x + 37) + (x + 67) + 90 = 180 by the Triangle Angle Sum Theorem

(x + 37) + (x + 67) = 90

2x + 104 = 90

2x = -14

x = -7

(-7 + 37) = angle A

angle A = 30

Answer:

<a = 30

Step-by-step explanation:

x + 37 + x + 67 + 90 = 180

<A + <B + <C = 180

*take each angle, add them, and equal them to 180*

x + 37 + x + 67 + 90 = 180

*solve for x*

2x + 194 = 180

      -194   -194

2x = -14

x = -7

<a = x + 37

<a = (-7) + 37

<a = 30

<b = x + 67

<b = (-7) + 67

<b = 60

<c = 90

After addition of the given unlike fractions 9/5 and 14/7 will be 133/35 after converting them to like fractions and then adding them.

As per the question statement, Rita and Sigmund are assigned to solve a problem involving the addition of two unlike fractions 9/5 and 14/7.

Our first step will be to convert the given pair of fractions to like fraction.

9/5 + 14/7 = 9*7/35 + 14*5/35

In the above step, we made the pair of fractions into like fraction by using the LCM of 5 and 7.

9/5 + 14/7 = 9*7/35 + 14*5/35

                = (63+70)/35

                = 133/35

Hence, after addition of the given unlike fractions 9/5 and 14/7 will be 133/35 after converting them to like fractions and then adding them.

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Therefore, the surveyor is approximately 61 meters away from the base of the cliff. Rounded to the nearest meter, the answer is 61 meters.

Distance is a numerical measurement of the physical space between two points or objects. It is often expressed in units such as meters, feet, miles, or kilometers, depending on the system of measurement being used. Distance is a scalar quantity, meaning that it has only magnitude and no direction. It is different from displacement, which is the vector quantity that describes the overall change in position of an object, taking into account both magnitude and direction. Distance can be calculated using various methods depending on the context, such as using a ruler or tape measure for small distances or using GPS or other advanced technologies for larger distances.

by the question.

We can use trigonometry to solve this problem. Let's call the distance from the surveyor to the base of the cliff "x". Then, we can use the tangent function to find x:

\(tan(71°) = opposite/adjacent\)

In this case, the opposite side is the height of the cliff (160 meters) and the adjacent side is x, so we have:

\(tan(71°) = 160/x\)

To solve for x, we can multiply both sides by x and divide both sides by tan (71°):

\(x = 160 / tan(71°)\)

Using a calculator, we find that tan (71°) is approximately 2.62, so:

\(x = 160 / 2.62\)

x ≈ 61.07 meters

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The beta of the portfolio, considering $1 with a beta of 3% and $2 with a beta of 7% and a weight of 0.1 (w1), is 6.6%.


The beta of a portfolio measures its sensitivity to overall market movements. To calculate the beta of a portfolio, we need the individual asset weights and betas of each asset. Given that $1 has a beta of 3% and $2 has a beta of 7%, with a weight of 0.1 (w1), we can determine the beta of the portfolio.

To calculate the beta of the portfolio, we use the following formula:

β(portfolio) = (w1 * β1) + (w2 * β2) + ...

In this case, the portfolio contains two assets, so the formula becomes:

β(portfolio) = (w1 * β1) + (w2 * β2)

Substituting the given values:

β(portfolio) = (0.1 * 3%) + (0.9 * 7%)

β(portfolio) = 0.3% + 6.3%

β(portfolio) = 6.6%

Therefore, the beta of the portfolio is 6.6%.

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