Given the equation y = mx + b, find the value of b if x = 2, m = 2, and y = 4.​

To find the value of z sub x (dz/dx) for the given implicit function xyz³ + x²y³z = x+y+z, we need to differentiate the equation implicitly with respect to x. This involves taking the partial derivative of each term in the equation with respect to x while treating y and z as independent variables. After calculating the derivative, we can substitute the values of x, y, and z to find z sub x.

To find the derivative fz at the point P(1, 0, -3) for the function Z-X f(x, y, z) = z+y, we can differentiate the function with respect to z. Since the function only depends on z and y, the derivative with respect to z will be 1. Therefore, fz at the point P is equal to 1.

To find zx for the given implicit function xyz³ + x²y³z = x+y+z, we differentiate the equation implicitly with respect to x. Treating y and z as independent variables, we calculate the partial derivative of each term with respect to x.

Taking the derivative of the first term, we have (3xyz² + 2xy³z) dx/dx. Since dx/dx is equal to 1, this term simplifies to 3xyz² + 2xy³z.

The second term, x²y³z, has a partial derivative of (2xy³z) dx/dx, which simplifies to 2xy³z.

The derivative of the right-hand side, x + y + z, with respect to x is simply 1.

Setting up the equation, we have 3xyz² + 2xy³z + 2xy³z = 1.

Simplifying further, we get 3xyz² + 4xy³z = 1.

Substituting the values of x, y, and z at the point P(1, 0, -3), we can calculate the value of zx.

To find fz at the point P(1, 0, -3) for the function Z-X f(x, y, z) = z+y, we differentiate the function with respect to z.

Since the function only depends on z and y, the derivative with respect to z is simply 1.

Therefore, fz at the point P is equal to 1.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The equation of the given slope and y-intercept is 5y = 3x - 10.

What is Slope Intercept Form?

One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfils.

Given, slope (m) = 3/5

y-intercept (c) = -2

The slope-intercept form of the equation is given by

y = mx + c

or, y = 3x/5 - 2

or, 5y = 3x - 10

Hence, the equation of the given slope and y-intercept is 5y = 3x - 10.

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The Domain is {xeR}      

Answer:

160

Step-by-step explanation:

226

-160

____

66

-64 (4 in the quotient)

____

2

Answer:

A

Step-by-step explanation:

The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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Answer:

THE SUM OF 2 OPPOSITES EQUAL 0

Step-by-step explanation:

The points of intersection occur at θ = (2πn) / 19 and θ = (π + 2πn) / 21, where n is an integer.

To find the points of intersection of the curves r = sin(θ) and r = sin(20θ), we need to set the two equations equal to each other and solve for θ.

Setting sin(θ) = sin(20θ), we can use the trigonometric identity:

sin(A) = sin(B) if and only if A = B + 2πn or A = π - B + 2πn,

where n is an integer.

Applying this identity to our equation, we have:

θ = 20θ + 2πn or θ = π - 20θ + 2πn,

Let's solve for θ in each case:

θ = 20θ + 2πn:

Rearranging the equation, we get 20θ - θ = 2πn,

which simplifies to 19θ = 2πn,

Dividing both sides by 19, we have θ = (2πn) / 19.

θ = π - 20θ + 2πn:

Rearranging the equation, we get 21θ = π + 2πn,

Dividing both sides by 21, we have θ = (π + 2πn) / 21.

Therefore, the points of intersection occur at θ = (2πn) / 19 and θ = (π + 2πn) / 21, where n is an integer.

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Answer:

Step-by-step explanation:

24+3y=56 solve for y, subtract 24 from each side

3y=32 divide each side by 3

y=32/3

Answer:

y=32/3

Step-by-step explanation:

let the number be y, then

24+3y=56 solve for y, subtract 24 from each side

3y=32 divide each side by 3

y=32/3

Answer:

the answer to x is 4

Step-by-step explanation:

.

Answer:

$201,600

Step-by-step explanation:

Multiply 34 and 84, which is 2016. Then add 2 zeros at the end because there are 2 zeros in 8400. So, the answer is 201,600 dollars.

The mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

The most appropriate measure of center to represent the data in the given line plot is the mode.

The mode is the value or values that occur most frequently in a dataset. In this case, we can observe the frequencies of the data points on the line plot:

There is one dot above 2, 4, 8, and 9.

There are two dots above 6 and 7.

There are three dots above 3.

Based on this information, the mode(s) of the dataset would be the values that have the highest frequency. In this case, the mode is 3 because it appears most frequently with a frequency of three. The other data points have frequencies of one or two.

The mode is particularly appropriate in this scenario because it represents the most common or frequently occurring value(s) in the dataset. It is useful for identifying the central tendency when the data is discrete and there are distinct peaks or clusters.

While the median and mean are also measures of center, they may not be the most appropriate in this case. The median represents the middle value and is useful when the data is ordered. However, the given line plot does not provide an ordered arrangement of the data points. The mean, on the other hand, can be affected by outliers and extreme values, which may not accurately represent the central tendency of the dataset in this scenario.

Therefore, the mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

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Answer:

-6x-10y

Step-by-step explanation:

Multiply -2 by everything in parenthesis

The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.

The area of the right-angle triangle is given as

A = 1/2 x B x H

Where B is the base and H is the height of the right triangle.

The length of PT is 10 and the angle ∠TPS is 60°.

The length of PR is given as,

PR = PT + TR

PR = 10 + 10

PR = 20

And the length of QS is given as,

QS = QT + TS

QS = 10 + 10

QS = 20

The area of the rectangle is given as,

A = Area of triangle ΔPQR + Area of triangle ΔPSR

A = 2 [(1/2) x (20 cos 60°) x (20 sin 60°)

A = 173.21 square units

The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.

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Step 1

State an expression for the probability of an event.

Number of required events = 4

Total number of events = 7

Step 2

Find the probabilities of defective batteries with replacement and without replacement

Step 3

Find the probabilities that both are defective.

Hence the probability that 2 batteries selected at random without replacement are both defective is 2/7

Answer:

2/10?

Step-by-step explanation:

Answer:

The price is 212.49

Step-by-step explanation:

sorry if wrong.

Answer:

Step-by-step explanation:

In order to solve this problem, you must find the factor to use the distributive property.

Distributive property:

→ A(B+C)=AB+AC

28r+24

4*7=28

4*6=24

Rewrite the problem down.

4*7r+4*6

Solve.

4*7r=28r

4*6=24

28r+24

I hope this helps! Let me know if you have any questions!

The wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Given that the height of the tower is 168 foot, and the angle is 30 degrees.

The wire that connects the top of the tower to the point of the ground is thus the hypotenuse.

To find the hypotenuse, we use the trigonometric ratios as follows:

Sin 30 = 168 / Hypotenuse

0.5 = 168 / Hypotenuse

Hypotenuse = (168)(0.5)

Hypotenuse = 84.

Hence, the wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

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Answer:

8

Step-by-step explanation:

let rach age be x

grandpa =7x+19

grandma=9x+3

9x+3=7x+19

9x-7x=19-3

2x=16

x=8

Rachael's age will be, 8 years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let us assume that Rachael's age will be, x

Hence, We can formulate;

Age of grandpa = 7x + 19

Age of grandma = 9x+3

Here, Rachael's grandma and grandpa are the same age.

Hence, We get;

⇒ 9x + 3 = 7x + 19

⇒ 9x - 7x = 19 - 3

⇒ 2x = 16

⇒ x = 8

Thus,  Rachael's age will be, 8 years

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

Step-by-step explanation:

Pack value for 1 = 6/2.79 = 2.1

this is better as clearly, 2.1<.27

There are 9438 different committees possible without Tarzan and Jane together.

a) To find the total number of possible committees, we need to choose 7 people out of 16 people, regardless of their gender. We can do this using the combination formula:

\(${{16}\choose{7}} = \frac{16!}{7!(16-7)!} = 11440$\)

Therefore, there are 11440 different 7-person committees possible.

b) If the committee must be made up of women only, we need to choose 7 women out of the 10 women available. We can do this using the combination formula again:

\(${{10}\choose{7}} = \frac{10!}{7!(10-7)!} = 120$\)

Therefore, there are 120 different 7-woman committees possible.

c) If the committee must be made up of 5 men and 2 women, we need to choose 5 men out of 6 men available, and 2 women out of 10 women available. We can do this using the combination formula:

\(${{6}\choose{5}} \times {{10}\choose{2}} = \frac{6!}{5!(6-5)!} \times \frac{10!}{2!(10-2)!} = 6 \times 45 \times 9 = 2430$\)

Therefore, there are 2430 different committees possible with 5 men and 2 women.

d)

i) If Tarzan and Jane must be together on the committee, we can treat them as a single entity and then choose 6 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{6}} = \frac{14!}{6!(14-6)!} = 3003$\)

Therefore, there are 3003 different committees possible with Tarzan and Jane together.

ii) If Tarzan and Jane refuse to serve on the committee, we need to choose 7 people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{7}} = \frac{14!}{7!(14-7)!} = 3432$\)

Therefore, there are 3432 different committees possible without Tarzan and Jane.

iii) If Tarzan and Jane are not on the committee together, we can count the number of committees that include both of them and subtract it from the total number of committees. The number of committees that include both Tarzan and Jane can be found by treating them as a single entity and choosing 5 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{5}} = \frac{14!}{5!(14-5)!} = 2002$\)

Therefore, the number of committees that do not include both Tarzan and Jane is:

\($11440 - 2002 = 9438$\)

Therefore, there are 9438 different committees possible without Tarzan and Jane together.

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Step-by-step explanation:

x= -2,

(x - 5) / 2= -6

( (-2) - 5) / 2= -6

(-7) / 2 = -6

-3.5 = - 6

right hand side not equal to left hand side of this equation.so,x= -2 cannot exist for this equation.

x=2,

(x - 5) / 2= -6

(2 - 5) / 2= -6

(-3) / 2= -6

-1.5 = - 6

right hand side not equal to left hand side of this equation.so,x= 2 cannot exist for this equation.

x= -17

(x - 5) / 2= -6

( ( -17) - 5) / 2= -6

(- 22) / 2= -6

-11 = -6

right hand side not equal to left hand side of this equation.so,x= -17 cannot exist for this equation.

x= -7,

(x - 5) / 2= -6

( ( -7) -5) / 2= -6

(-12) / 2= -6

-6= -6

right hand side equal to left hand side of this equation.so,x= -7 exist for this equation.

the zero property of multiplication

Explanation

the zero property of multiplication says, the product of any number and zero, is zero,

so in this case the number is (14x)

so

14x*0=0

I hope this helps you

The quadrilateral ABCD is a parallelogram as opposite sides are parallel.

Which is option A.

We have,

Based on the given coordinates of the vertices, we can determine the properties of the quadrilateral:

A. Parallelogram: Yes, opposite sides are parallel.

B. Rectangle: No, opposite sides are not both parallel and equal in length.

C. Rhombus: No, opposite sides are not equal in length.

D. Square: No, opposite sides are not both parallel and equal in length.

Thus,

The quadrilateral ABCD is a parallelogram as opposite sides are parallel.

Which is option A.

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Decide whether quadrilateral ABCD with vertices A(-2,2), B(2,5). C(2,0) and D(-2, -3) is a special quadrilateral.

Select all names that apply

A. Parallelogram

B. Rectangle

C. Rhombus

D. Square

Answer:

Let the three angles be 2x,9x & 4x

By the problem,2x+9x+4x=180

15x=180

x=180/15

x=12

there fore the angles are

2x= 2*12=24°

9x=108°

4x=48°

Step-by-step explanation: