Help please and thanks

Answer :

To find the equation of the line containing the median that passes through point C, we first need to find the midpoint of segment AB. The coordinates of A and B are given as (-4, -2) and (4, 4) respectively, so we can find the x-coordinate of the midpoint by averaging the x-coordinates of A and B, and the y-coordinate of the midpoint by averaging the y-coordinates of A and B.

The midpoint is:

((-4+4)/2, (-2+4)/2) = (0, 1)

To find the slope of the median we will use the point slope form, which is:

y - y1 = m(x - x1)

We know that point C is (18, -8), and the midpoint is (0, 1)

The slope (m) will be:

m = (y2 - y1) / (x2 - x1) = (-8 - 1) / (18 - 0) = -9/18

We can now use point slope form and substitute the point and the slope:

y - (-8) = (-9/18) (x - 18)

To convert it to slope-intercept form we will solve for y:

y = (-9/18)x + (8/9 + 18/9) = -1/2x + 2

The equation of the line containing the median that passes through point C in slope-intercept form is y = -1/2x + 2

The surface described by the equation \(r^2 + z^2 = 4\)is a right circular cylinder with a radius of 2 units, centered along the z-axis.

The surface whose equation is given is a cylinder with a radius of 2 units and a height of 4 units, centered on the z-axis.
Hi! I'd be happy to help you identify the surface with the given equation. The equation provided is:

\(r^2 + z^2 = 4\)

This equation represents a right circular cylinder with a radius of 2 units, centered along the z-axis. Here's why:

1. Notice that the equation contains r^2 and \(z^2\) terms, which suggests a cylindrical coordinate system.
2. The equation does not contain the θ term, which implies that the surface is symmetric about the z-axis.
3. The equation is in the form \(r^2 + z^2\) = constant, which is the equation of a right circular cylinder in cylindrical coordinates.

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The value of the triple integral is -16.

Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.

The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:

∭E f(x, y, z) dV

We can set up the triple integral as follows:

∫∫∫ 16y dV

Where the limits of integration are:

0 ≤ x ≤ 2

0 ≤ y ≤ (2- \(x^2\)z)/(2y)

0 ≤ z ≤ 2/\(x^{2y\)

Note that the upper bound of integration for y is not a constant, but depends on both x and z.

Integrating with respect to y first, we get:

∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)

= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)

= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz

= ∫\(0^2 (32/x^2 - 16z)\) dz

= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz

= 16 - 16(2)

= -16

Therefore, the value of the triple integral is -16.

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Answer:

1/95

Step-by-step explanation:

2 5/7 = 19/7

1/35 divided by 2 5/7

1/35 ÷ 19/7

1/35 × 7/19

1 × 7/35 × 19

7/665 = 1/95

The expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

As per the question, we can write the expression as:

(t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9)

Using product notation, we can write this as:

Π⁷k =1 \((t^k - 9)\)

where Π represents the product of terms, k is the index of the product, and the subscript 7 indicates that the product runs from k = 1 to k = 7.

Therefore, the expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

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An equation that describes this function in slope-intercept form is y = -6x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 - 5)/(1 + 1)

Slope (m) = -12/2

Slope (m) = -6

At data point (-1, 5) and a slope of -6, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -6(x + 1)

y - 5 = -6x - 6

y = -6x - 1

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Step-by-step explanation:

In mathematics, whole numbers are the basic counting numbers 0, 1, 2, 3, 4, 5, 6, … and so on.

Answer:

Whole Number - numbers that do not include fractions, just an integer

Examples:

counting numbers

natural numbers

intergers (positive)

You can search all three of these things online to find more info.

Answer: long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend

Step-by-step explanation:

To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.

Lengthy divide as you'll with entire numbers, but positioned the decimal point in the answer at the equal place it's miles at within the dividend

What is a decimal ?

Decimal can be defined as a number in which it contains whole and fractional part.

performing long department with decimals may be very just like acting long department with entire numbers, with a few more steps along the way. The manner we technique an extended department trouble concerning decimals will rely on in which in the equation the decimal range appears; either in the dividend (the quantity under the lengthy department bracket), the divisor (the range to the left of the lengthy division bracket), or each. the position of the decimal factor within the quotient (answer) can be depending on the placement of the decimal factor within the dividend.

Therefore, lengthy divide as you'll with entire numbers, but positioned the decimal point in the answer at the equal place it's miles at within the dividend

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The p-value associated with the null hypothesis = 0.05

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours

Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.

You have the Hypothesis that "students study less than 10 hours, on average, per week"

Symbolically:

H₀:μ≥10hours

H₁:μ<10hours

The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.

The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.

Therefore,

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

The p-value associated with the null hypothesis = 0.05

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Polynomial identities can be used to rewrite the expressions efficiently as x² + 2x + 1 can be written as (x + 1)².

A mathematical fact or equation called polynomial identity allows us to easily answer equations with big integers and exponents.

Polynomial identities can be used to rewrite the expressions in a simplified manner.

For example, the polynomial x² + 2x + 1 can be written as (x + 1)².

Hence, polynomial identities can be used to rewrite the expressions efficiently as x² + 2x + 1 can be written as (x + 1)².

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Answer: c = 520

Step-by-step explanation:

     f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.

Given:

    f(x) = 4x³ + 7x² - x + c

Substitute:

    578 = 4(2)³ + 7(2)² - (2) + c

Distribute:

    578 = 4 * 2³ + 7 * 2² - 2 + c

Raise to the power of 3 and 2:

    578 = 4 * 8 + 7 * 4 - 2 + c

Multiply:

    578 = 32 + 28 - 2 + c

Add:

    578 = 60 - 2 + c

Subtract:

    578 = 58 + c

Subtract 58 from both sides:

    520 = c

Reflexive property:

   c = 520

\( \huge\mathbb{ \underline{SOLUTION :}}\)

Given:

\(\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}\)

\(\longrightarrow\sf{578= 32+28 −2+ c}\)

\(\longrightarrow\sf{578 =58+ c}\)

\(\longrightarrow\sf{c = 578-58}\)

\(\huge \mathbb{ \underline{ANSWER:}}\)

\(\longrightarrow\sf{c= 520}\)

Answer:

  99 minutes

Step-by-step explanation:

Let the variable x represent the longer part of the movie. Then the shorter part is (x-11) and the total length is the sum of the parts:

  187 = x +(x -11)

  198 = 2x

  x = 99

The length of Part 2 is 99 minutes.

Answer:

One eighth is one part of eight equal sections. Two eighths is one quarter and four eighths is a half. It's easy to split an object, like a cake, into eighths if you make them into quarters and then divide each quarter in half

Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

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The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 at a rate of 8% per year compounded 1 times per year over 16 years is $1,712.97.

Given Data

A = P + I where

P (principal) = $500.00

I (interest) = $1,212.97

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 500.00(1 + 0.08/1)^(1)(16)

A = 500.00(1 + 0.08)6(16)

A = $1,712.97

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The question was incomplete. Below you will find the missing content.
The square root function f(x) is x <= 7

Options are :

A. 7 is subtracted from the x-term inside the radical.
B. The radical is multiplied by a negative number.
C. 7 is added to the radical term.
D. The x-term inside the radical has a negative coefficient.

Option D is correct, which is : The x-term inside the radical has a negative coefficient.

Given, the domain of the square root function f(x) is x <= 7
Consider the function y = √x.
The domain of this function is x ≥ 0 and the range is y ≥ 0.
The expression inside the radical must be greater than or equal to zero.
Now, if x ≤ 7
x - 7 ≤ 0
7 - x ≥ 0
And the function y = √(7-x) will have the domain x ≤ 7.
This implies that the x-term inside the radical has a negative coefficient.
Therefore, the statement that the x-term inside the radical has a negative coefficient must be true.

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The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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Using the Poisson distribution formula, we can calculate each of these probabilities and then subtract their sum from 1 to obtain P(X ≥ 4).

One would use the Poisson distribution to calculate the probability that at least 4 customers arrive in a randomly chosen minute. The Poisson distribution models the number of occurrences of an event in a fixed interval of time or space, given a known average rate of occurrence and the assumption that the events occur independently of each other.

The probability of observing k occurrences of an event in a Poisson process with rate λ is given by the formula \(P(k) = (e^(-λ) * λ^k) / k!\), where e is the base of the natural logarithm and k! is the factorial of k.

In this case, we have λ = 1.7, the average rate of customer arrivals per minute. So, the expression to calculate the probability that at least 4 customers arrive in a randomly chosen minute would be:

P(X ≥ 4) = 1 - P(X < 4)

where X is a random variable representing the number of customer arrivals in a minute, and P(X < 4) is the cumulative probability of observing 0, 1, 2, or 3 customer arrivals in a minute:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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Answer:

4

Step-by-step explanation:

16x4=64

Answer:

4 chapters

Step-by-step explanation:

If Raj can read 1 chapter in 16 minutes you need to figure out how many times 16 goes into 64. Divide 64 by 16 and you get 4. Which means Raj can read 4 chapters in 64 minutes.

No, a and b are not independent. The joint probability of a and b does not equal the product of their individual probabilities, indicating a dependence between the two events.

To determine if a and b are independent, we need to compare the probability of their joint occurrence with the product of their individual probabilities.

If a and b are independent, then p(a and b) should equal p(a) multiplied by p(b).

p(a and b) = p(a or b) - p(a) - p(b) = 0.88 - 0.70 - 0.60 = -0.42

Since the result is negative (-0.42), it implies that p(a and b) is not equal to p(a) multiplied by p(b), indicating that a and b are dependent events.

Based on the calculation, it can be concluded that a and b are not independent events. The joint probability of a and b does not equal the product of their individual probabilities, indicating a dependence between the two events.

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If all the dimensions of a cube increase by a factor of 3/2, the surface area will increase by a factor of 9/2.

If all the dimensions of a cube increase by a factor of 3/2, then the new dimensions of the cube will be 3/2 times the original dimensions.

Let's say the original side length of the cube was "s". Then the new side length would be (3/2)*s.

The surface area of a cube is given by the formula 6s^2, where s is the side length.

So the original surface area of the cube would be:

6s^2

And the new surface area of the cube would be:

6(3/2s)^2
= 6(9/4)s^2
= 27/2 s^2

To find how many times greater the new surface area is compared to the original surface area, we can divide the new surface area by the original surface area:

(27/2 s^2) / (6s^2)
= (9/2)

So the new surface area is 9/2 times greater than the original surface area.

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To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.

To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.

For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.

You can then plot these points on the coordinate plane and connect them with a line to graph the equation.

Im really sorry that I was unable to provide a picture.  I hope this helped!

Answer:

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

Slope:

1/2

y-intercept: (0,−5)

x   y

0 −5

2 −4

Step-by-step explanation:

The given set of vectors which are represented as {(1, -4), (4, 1)} is orthogonal.

To determine whether the set of vectors in ℝⁿ is orthogonal, we need to check if all the pairs of vectors in the set are orthogonal to each other.

In this case, the set of vectors is {(1, -4), (4, 1)}. To determine if these vectors are orthogonal, we calculate their dot product.

The dot product of two vectors (a, b) and (c, d) is given by a * c + b * d.

For the first pair of vectors (1, -4) and (4, 1), the dot product is 1 * 4 + (-4) * 1 = 4 + (-4) = 0.

Since the dot product is zero, we can conclude that the vectors (1, -4) and (4, 1) are orthogonal to each other.

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Answer: D)  \(m \angle 2 = m\angle 5\)

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

Explanation:

Let's go through the answer choices to see what's true and what's false.

Answer:

140

Step-by-step explanation:

25% * x = 35

25/100 * x = 35

Multiplying both sides by 100 and dividing both sides by 25,

We have x = 35 * 100/25

x = 140

Answer: Number one is  20km. Number 2 is  I think 2.9 and number 3 ofc is 140. I'm not really sure if number 2 is correct but yeah.

Step-by-step explanation:

Answer:

Ok at do you do help  

Step-by-step explanation:

Step-by-step explanation:

a negative exponent always means 1/...

so, e.g. 6^-2 means 1/(6²).

so,

\( {w}^{6} \times {w}^{ - 4} \)

= w⁶/w⁴

that means that if w⁶w⁴ is already prefilled, we need to counteract the w⁴ in the numerator of the fraction.

it would have to be then w⁶w⁴/w⁸

because we need to end up with w⁴ in the denominator (bottom part). and the only way we can do that, if we need to keep w⁴ in the numerator (top) part, is to put these w⁴ multiplied by another w⁴ (4+4 = 8, as multiplied exponents are added).

that would give us the expanded form of

w×w×w×w×w×w×w×w×w×w

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

w×w×w×w×w×w×w×w

and the simplified form

w²/1

\( {10}^{ - 3} \times {10}^{5} \)

gives us the same problem.

it is actually 10⁵/10³

but if 10³10⁵ is already predefined, then we must use the same trick as before. we must end up with 10³ in the denominator, so to compensate for the 10³ in the numerator, we must extra multiply this into the denominator :

10³10⁵/(10³10³) = 10³10⁵/10⁶

the expanded form of this would be

10×10×10×10×10×10×10×10

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

10×10×10×10×10×10

with the simplified form

10²/1

and again similar with

\( {10x}^{3} \times {(10x)}^{ - 2} \)

which is actually

10x³/(10x)² = 10x³/100x²

again, if 10x³×(10x)² is predefined in the numerator, we need to compensate in the denominator for these extra (10x)².

so, we need then to put

10x³(10x)²/((10x)²(10x)²) = 10x³(10x)²/(10x)⁴

the expanded form would then be

10×x×x×x×10×x×10×x

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

10×x×10×x×10×x×10×x

and the simplified form would be

x/10

if these entries (as seen in the picture) in the "make exponent positive" column are from you and not predefined by your teacher, then we use the example of the first line.

and then we have as indicated

w⁶/w⁴

wwwwww / wwww

w²/1

10⁵/10³

10×10×10×10×10 / 10×10×10

10²/1

10x³/(10x)²

10×x×x×x / 10×x×10×x

x/10

Answer:

volume = 1900 cm³

Step-by-step explanation:

area of end= (12)(10) - (10)(2.5) = 95 cm²

volume = 95(20) = 1900 cm³