What is the y-intercept of the line 3x – 4y = 24?

Answer:2x(2yz + 5)

Step-by-step explanation:

Answer:

47.10

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

... Cos = Adjacent/Hypotenuse

The value y is the length of the hypotenuse, and the given length 35 is the side adjacent to the given angle. Thus, the cosine relationship will be helpful.

Filling in the given values, we have ...

... cos(42°) = 35/y

Multiplying by y/cos(42°), we can find y to be ...

... y = 35/cos(42°) ≈ 35/0.7431

... y ≈ 47.10

Y will be approximately  47.10 in length

Step-by-step explanation:

we will use this  form that we memorized in our schools ............. SOH CAH TOA

CAH means , Cos ∅= Adjacent/Hypotenuse

Given values

∅ =42°

hypotenuse= y

adjacent side length = 35

now putting in our values  into

Cos ∅= Adjacent/Hypotenuse

OR

cos(42°) = 35/y

by multiplying y on both sides we get

y= 35/cos( 42°)

cos(42°)= 0.743

so  y= 35/0.743    

y = 47.10632

OR

y ≈ 47.10

The correct value of p(x<8) is 1.875.

To determine how probable something is gonna occur, use probability. It is a number between 0 and 1, where 0 denotes the absence of a possibility and 1 denotes the existence of one. By dividing the number of favorable outcomes by the entire number of potential possibilities, the probability of an occurrence is determined.

To find the probability that is greater than 8, we need to integrate this probability density function from 5.5 to 20.5:

P(X < 8) = ∫[5.5,20.5] f(x) dx

= ∫[5.5,20.5] (1/8) dx

= [x/8] from 5.5 to 20.5

= (20.5/8) - (5.5/8)

= 15/8

= 1.875.

Therefore, the correct probability is 1.875.

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The value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We will use Taylor's theorem to derive this result.

Taylor's theorem, also known as the Taylor series theorem, is a mathematical formula used to represent functions as a sum of infinitely many derivatives in order to approximate them over a certain interval.

This formula allows us to derive the value of a function at a point using information about its derivatives at that point.

In essence, Taylor's theorem is a tool used in calculus to model complex functions that cannot be easily solved.

Using Taylor's theorem to solve the question:

We know that the Taylor series expansion of cos(x) is given by the formula:

cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

To get an accurate value of cos(x), we need to keep adding terms in the series until the absolute value of the next term is less than our required accuracy.

Using |x| ≤ 1/12 and rounding to 12 decimal places, we have an error tolerance of 0.000000000001.

Therefore, we need to find the smallest value of n such that \(|x^(n+1)/(n+1)!| ≤ 0.000000000001,\)

where x = 1/12.

Substituting x = 1/12,

we have |(1/12)^(n+1)/(n+1)!| ≤ 0.000000000001

Using a calculator, we can find that n = 4 satisfies this inequality.

Therefore, we need at least 5 terms in the series of cos(x) to compute the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded).

Conclusion:

To calculate the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We used Taylor's theorem to derive this result.

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Answer:

See below

Step-by-step explanation:

A)  Recursive Definition

The value of each term in a sequence that starts at 13 is reduced by 1.5 for each step in the sequence.

B)  Definition for nth Term

   D(n) = D(1)+(n-1)(-1.5)

    D(1) = 13

     D(n) = 13+(n-1)(-1.5)

Examples:

   D(5) = 13 + (5-1)*(-1.5)

   D(5) = 13 + (4)*(-1.5)

   D(5) = 13 - 6, or 7

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

    D(7) = 13 + (7-1)*(-1.5)

    D(7) = 13 + (6)*(-1.5)

    D(7) = 4

Answer: 16.308

Step-by-step explanation:brainiest please

Answer:

D

Step-by-step explanation:

The range of a set of numbers is

range = largest number - smallest number , then

range = 25 - 6 = 19 → D

A graph which represents the solution set for the compound inequality is shown in the image attached below.

In order to determine the graph which represents the solution set for the compound inequality, we would evaluate the given inequalities as follows.

Given the following inequalities:

⅓x + 10 ≥ 7

x - 10 ≥ 7

For the first inequality, we have:

⅓x + 10 ≥ 7

Multiply all through by 3;

x + 30 ≥ 21

x ≥ 21 - 30

x ≥ -9  ⇒ x < 9.

For the first inequality, we have:

x - 10 ≥ 7

x ≥ 7 + 10

x ≥ 17.

In conclusion, a graph which represents the solution set for the compound inequality is shown by using the number line in the image attached below.

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If the incomes in a certain larger population of college teachers have a normal distribution with mean of $60,000 and standard deviation of $5,000.the probability that their average salary exceeds $65,000 is 0.0228.

Probability is the tendency or likelihood that an event will happen.

First step is to find the standard deviation

Standard deviation= $5,000/√4

Standard deviation= $5,000/2

Standard deviation= $2,500

Second step is to find the z -score

Z= 65,000 - 60,000/2500

Z= 5,000/2500

Z= 2

Now let find the  pvalue of 2

pvalue of 2 = 0.0228

Therefore the probability is 0.0228.

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If Tamika adds two separate numbers at random from the collection, the likelihood that her result will be higher than Carlos' result is 4/9. To multiply two random integers from the set, Carlos chooses two more random numbers.

This event has a chance of happening or not happening.

calculation

Tamika might receive any of the following results, all of which are equally likely:

8+9=17 

8+10=18

9+10=19

The various potential values that Carlos could receive—all equally likely—are:

3 * 5=15

3 * 6=18

5 * 6=30

Because 17 is only greater than 15, the likelihood that Tamika's total would be greater than Carlos's set is 1/3.

Because 18 is only greater than 15, the likelihood that Tamika's total would be greater than Carlos's set is 1/3.

Due to the fact that 19 is greater than both 15 and 18, the likelihood that Tamika's total would be greater than Carlos's set is 2/3.

We have 1/3(1/3+1/3+2/3)=1/3(4/3)=4/9 since each sum has a 1/3 chance of being chosen.

the likelihood of the difference between Tamika's performance and Carlos' performance is 4/9.

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There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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Answer:

It must include many types of media such as different social media websites.

Step-by-step explanation:

Step-by-step explanation:

such problems are always the combination of areas of simple figures.

in our case here the simplest way seems to me to calculate the area of the whole 15×15 square (the side lengths are 15 and 9+6 = 15) and then subtract the small 6×6 square (top left), the small 6×3 triangle (bottom right) and the larger 6×9 triangle (top right).

we know that the left side of the main square is 9+6 = 15.

we know that the missing side piece (top right) is also 6 (like its left side). and the right side piece is 15-6-6 = 3.

that is how we know the side lengths of the missing pieces.

so,

15×15 = 225 cm²

the small square is

6×6 = 36 cm²

the large triangle is

6×9/2 = 3×9 = 27 cm²

the small triangle is

6×3/2 = 3×3 = 9 cm²

so, the total area of the figure is

225 - 36 - 27 - 9 = 153 cm²

Answer:

They using an Algebra calculator on your chromebook :)

Answer:

Slope: -3

y-intercept: 5

  x | y

  0 | 5

5/3 | 0

Answer:

(a) 7/15

(b) 1/3

Step-by-step explanation:

(a) teaching:

(3 1/2) / (7 1/2) = (7/2) / (15/2) = 7/2 * 2/15 = 7/15

(b) marking:

(2 1/2) / (7 1/2) = (5/2) / (15/2) = 5/2 * 2/15 = 5/15 = 1/3

We are given a point (2, 0, -1) and a plane 8x - 4y + 9z + 1 = 0. We need to find the distance from the point to the plane using Lagrange multipliers.

To find the distance from a point to a plane using Lagrange multipliers, we need to set up an optimization problem with a constraint equation representing the equation of the plane.

Let's denote the distance from the point (2, 0, -1) to a general point (x, y, z) on the plane as D. We want to minimize D subject to the constraint equation 8x - 4y + 9z + 1 = 0.

To set up the Lagrange multiplier problem, we define a function f(x, y, z) = (x - 2)² + y² + (z + 1)² as the square of the distance. We also introduce a Lagrange multiplier λ to account for the constraint.

Next, we form the Lagrangian function L(x, y, z, λ) = f(x, y, z) - λ(8x - 4y + 9z + 1). We then find the partial derivatives of L with respect to x, y, z, and λ, and set them equal to zero.

By solving the resulting system of equations, we can find the values of x, y, and z that minimize the distance. Finally, we substitute these values into the distance formula D = √((x - 2)² + y² + (z + 1)²) to obtain the minimum distance.

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The required equation is \(x^2y^4 + 4x^3y^3 - 4x^2y^2 - 12x^2y\) + 25 = 0

The direction of fastest change of a function at a point is given by the gradient of the function at that point. Therefore, to find the points at which the direction of fastest change of the function f(x, y) = \(x^2 y^2\) − 6x − 8y is in the direction of the vector i j, we need to find the gradient of f(x, y) and then find the points where the gradient is parallel to the vector i j.

The gradient of f(x, y) is given by:

∇f(x, y) = <∂f/∂x, ∂f/∂y> =\(< 2xy^2 - 6, 2x^2y - 8 >\)

To find the points at which the direction of fastest change is in the direction of i j, we need to find the points where the gradient is parallel to i j. This means that the dot product of the gradient and i j should be equal to the product of their magnitudes:

∇f(x, y) · i j = ||∇f(x, y)|| ||i j||

Substituting the values, we get:

\((2xy^2 - 6, 2x^2y - 8)\)· (1, 0) = sqrt((\(2xy^2 - 6)^2 + (2x^2y - 8)^2\)) * sqrt(\(1^2 + 0^2\))

Simplifying this equation, we get:

\(2xy^2\)- 6 = sqrt((\(2xy^2 - 6)^2\) + (\(2x^2y - 8)^2\))

Squaring both sides and simplifying, we get:

\(x^2y^4 + 4x^3y^3 - 4x^2y^2 - 12x^2y + 25 = 0\)

Therefore, the points at which the direction of fastest change of f(x, y) is in the direction of i j are given by the solution of the quartic equation above.

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Answer: I think u have to multiply all da numbers.

Step-by-step explanation:

Answer:

ooofffffffff

Step-by-step explanation:

Answer:

Cost of an adult =700

Cost of a child =500

Family paid=3100

They got 5 tickets

So,

700x+500y=3100

x+y=5

Multiplying 2nd equation to x=5-y

700(5-y)+500y=3100

y=2

x=5-2

=3

so u got the answer

If a sample includes three individuals with scores of 4, 6, and 8, the estimated population variance is (4 + 0 + 4) / 2 - 4. So, correct option is 4.

The estimated population variance formula is the sum of squared deviations from the mean divided by the degrees of freedom. In this case, the degrees of freedom would be n-1, where n is the sample size.

Using the given sample of 4, 6, and 8, we can calculate the sample mean as (4+6+8)/3 = 6.

Then, we calculate the deviations from the mean for each score:

4 - 6 = -2

6 - 6 = 0

8 - 6 = 2

We square each deviation to get 4, 0, and 4. Then, we sum the squared deviations: 4 + 0 + 4 = 8.

Since there are three scores in the sample, the degrees of freedom is 3 - 1 = 2.

Finally, we divide the sum of squared deviations by the degrees of freedom to get the estimated population variance: 8/2 = 4.

Therefore, option 4) (4 + 0 + 4) / 2 = 4 is the correct answer.

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The centroid of a quarter-circular region of radius $a$ is $\left(\frac{a^2}{2\pi}, \frac{a^2}{4}\right)$.

The centroid of a region is the point that is the average of all the points in the region. It can be found using the following formulas: xˉ=2A1​∮C​x2dyyˉ​=−2A1​∮C​y2dx

where $A$ is the area of the region, $C$ is the boundary of the region, and $x$ and $y$ are the coordinates of a point in the region.

For a quarter-circular region of radius $a$, the area is $\frac{a^2\pi}{4}$. The integrals in the formulas for the centroid can be evaluated using the following substitutions:

x = a \cos θ

y = a \sin θ

where $θ$ is the angle between the positive $x$-axis and the line segment from the origin to the point $(x,y)$.

After the integrals are evaluated, we get the following expressions for the centroid:

xˉ=a22π

yˉ=a24

Therefore, the centroid of a quarter-circular region of radius $a$ is $\left(\frac{a^2}{2\pi}, \frac{a^2}{4}\right)$.

The first step is to evaluate the integrals in the formulas for the centroid. We can do this using the substitutions $x = a \cos θ$ and $y = a \sin θ$.

The integral for $xˉ$ is:

xˉ=2A1​∮C​x2dy=2A1​∮C​a2cos2θdy

We can evaluate this integral by using the double angle formula for cosine: cos2θ=12(1+cos2θ)

This gives us: xˉ=2A1​∮C​a2(1+cos2θ)dy=2A1​∮C​a2+a2cos2θdy

The integral for $yˉ$ is:

yˉ=−2A1​∮C​y2dx=−2A1​∮C​a2sin2θdx

We can evaluate this integral by using the double angle formula for sine:

sin2θ=2sinθcosθ

This gives us:

yˉ=−2A1​∮C​a2(2sinθcosθ)dx=−2A1​∮C​a2sin2θdx

The integrals for $xˉ$ and $yˉ$ can be evaluated using the trigonometric identities and the fact that the area of the quarter-circle is $\frac{a^2\pi}{4}$.

After the integrals are evaluated, we get the following expressions for the centroid:

xˉ=a22π

yˉ=a24

Therefore, the centroid of a quarter-circular region of radius $a$ is $\left(\frac{a^2}{2\pi}, \frac{a^2}{4}\right)$.

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Answer:

323.9

Step-by-step explanation:

395/100 = 3.95 (this is each unit of the price)

3.95 x 18 = 71.1

395 - 71.1 = 323.9

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

Answer: -120

6 less than is 6 - and 3 times a number 42 is 3 x 42 so...

6 - (3 x 42) = -120

Answer:

23

Step-by-step explanation:

h(a) = 5x-2

h(5) = 5(5)-2

h(5) = 25-2

h(5) = 23

Answer:

23

Step-by-step explanation:

Plug in 5 as x

h(x) = 5x - 2

h(5) = 5(5) - 2

h(5) = 25 - 2

h(5) = 23

So, h(5) = 23

This number in scientific notation is 6.2 x 10^-3

The number is given as

0.0062

Multiply by 1

So, we have

0.0062 = 0.0062 * 1

Express 1 as 1000/1000

So, we have

0.0062 = 0.0062 * 1000/1000

This gives

0.0062 = 6.2/1000

This gives

0.0062 = 6.2/10^3

Rewrite as

0.0062 = 6.2 x 10^-3

Hence, this number in scientific notation is 6.2 x 10^-3

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Answer:

the answer is 662 feet

Step-by-step explanation:

becuase one eighth of a mile is 660 feet