Find the value of x so that the line through the pair of points has the given slope.

Points: (x,4) and (5,10)
Slope: 3

What does x =?

The commission is calculated as 12% of the portion of the weekly revenue that is over $1000. So, to calculate the commission, we subtract $1000 from the weekly revenue r, and then multiply the result by 0.12. The fixed salary of $500 is then added to the commission to get the total weekly salary.

Step-by-step explanation:

The formula that describes how the salesman's weekly salary s depends on his weekly revenue r is:

s = $500 + 0.12(r - $1000)

In this formula, s represents the salesman's total weekly salary, which includes both the fixed salary of $500 and the commission based on his weekly revenue. r represents the salesman's weekly revenue.

The commission is calculated as 12% of the portion of the weekly revenue that is over $1000. So, to calculate the commission, we subtract $1000 from the weekly revenue r, and then multiply the result by 0.12. The fixed salary of $500 is then added to the commission to get the total weekly salary.

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The value of the iterated integral ∬Rf(x, y) dA= ∫-7^7 ∫-1^16xy^6 dx dy is 4116

The value of the iterated integral ∫1³ ∫2y^4-y y dx dy is 3/5.

1: Evaluate the double integral over the rectangular region R Given that the rectangular region R is

R = {(x, y): -1 ≤ x ≤ 1, -7 ≤ y ≤ 7}

and the integrand function is

f(x, y) = 6xy^6

The integral of the function f(x, y) over the rectangular region R can be expressed as:

∬Rf(x, y) dA= ∫-7^7 ∫-1^16xy^6 dxdy

= ∫-7^7 6y^6[∫-1^1 xdx]dy

= ∫-7^7 6y^6 [x^2/2]_{{-1}}^{{1}}dy

= ∫-7^7 6y^6 [(1/2) - (-1/2)]dy

= ∫-7^7 6y^6 dy

= 2 [6 (7^7)/7]

= 2 (6 (343))

= 4116

2: Evaluate the iterated integral. Given that the iterated integral is:

∫1³ ∫2y^4-y y dx dy

The limits of the inner integral with respect to x is 2y^(4 - y) ≤ x ≤ 1^3, whereas the limits of the outer integral with respect to y is 0 ≤ y ≤ 1. Now integrate the function f(x, y) = y with respect to x over the given limits, and then with respect to y, which gives,

∫1³ ∫2y^4-y y dx dy

= ∫0^1 ∫2y^4-y 1 dx dy

= ∫0^1 [x]_{{2y^4-y}}^{{1}} dy

= ∫0^1 (1 - 2y^4 + y) dy

= [y - (2/5)y^5 + (1/2)y^2]_{{0}}^{{1}}

= (1 - (2/5) + (1/2)) - 0

= 1/10 + 1/2

= 3/5

Therefore, the value of the iterated integral is 3/5.

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Answer:

Step-by-step explanation:

y - 4 = -6(x - 6)

y - 4 = -6x + 36

y = -6x + 40

Answer:

Step-by-step explanation:

Step 1: Equation at the end of step 1

Simplifying

60(x + 20) = 3x

Reorder the terms:

60(20 + x) = 3x

(20 * 60 + x * 60) = 3x

(1200 + 60x) = 3x

Solving

1200 + 60x = 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

1200 + 60x + -3x = 3x + -3x

Combine like terms: 60x + -3x = 57x

1200 + 57x = 3x + -3x

Combine like terms: 3x + -3x = 0

1200 + 57x = 0

Add '-1200' to each side of the equation.

1200 + -1200 + 57x = 0 + -1200

Combine like terms: 1200 + -1200 = 0

0 + 57x = 0 + -1200

57x = 0 + -1200

Combine like terms: 0 + -1200 = -1200

57x = -1200

Divide each side by '57'.

x = -21.05263158

Simplifying

x = -21.05263158

Given that three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. We need to determine the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite corner.

The formula for the electric potential at a point in space is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) + ….. ]where;k = Coulomb's constant (8.99 × 10^9 Nm²/C²)q1, q2, q3,…. are the charges at the cornersr1, r2, r3,…. are the distances from the corner to the point whose potential is being calculated Now we can calculate the electric potential at the empty corner as follows;The three charges can be represented as shown below:Charges at corners of a square

The distance from any corner to the opposite corner (where the positive charge is placed) is given by d = √[ (22.2 cm)² + (22.2 cm)² ] = 31.4 cmTherefore, the electric potential at the empty corner is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) ]Here, q1 = -25 nC, q2 = -55.9 nC, q3 = 79.1 nC, r1 = r2 = r3 = d = 31.4 cm = 0.314 mPlugging in the values we get;V = 8.99 × 10^9 [ (-25 × 10^-9 / 0.314) + (-55.9 × 10^-9 / 0.314) + (79.1 × 10^-9 / 0.314) ]= 8.99 × 10^9 [ -0.0795 - 0.1783 + 0.252 ]= 8.99 × 10^9 × 0.0052= 46.8 VTherefore, the value of the electric potential at the empty comer if the positive charge is placed in the opposite comer is 46.8 V.

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Answer:

35

Step-by-step explanation:

55 + x = 90

x = 90 - 55

x = 35

Answer:

39

Step-by-step explanation:

Using conditional probability, it is found that there is a 0.83 = 83% almost 0.8403  probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

Probability: -

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

Conditional Probability :

Using conditional probability, it is found that there is a 0.83 = 83% = P( A∩ B) / P(A)

In which

In this problem:

Event A: Commute to school each day.

Event B: Spends more than $25 a week.

80% indicated that they commute to school each day. of those that commute to school each day, hence , P(A) = 0.8

Of those, 83% spend more than $25 a week on gasoline, hence .

                     P(B|A) = 0.83

Thus, 0.83 = 83% probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

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Answer:

The answer could be A

Step-by-step explanation:

Got this from another Brainly user

60 forks 60÷3=$20

60 spoons 60÷4=$15

$20+$15=$35 total spent for forks and spoons

Answer:

(x-4)(x-4)

Step-by-step explanation:

Because the factors of 16 that add up to -8 can be -4 and -4.
Let's plug it in...
16 - 32 + 16 = 0

It works!!!

ANswer is (x-4)(x-4)

Answer: (x-1)(x+4)

the answer

Answer:

35

Step-by-step explanation:

m + f = 80, or f = 80 - m

2m = f + 25   Substitute

2m = (80 - m) + 25

2m = 105 - m

3m = 105

m = 35

The system of equations represents the number of male and female students are: M + F = 80  and F = 2M - 25 .

Out of total 80 students, there are 35 male students in the school band.

Let's use variables to represent the number of male and female students in the school band.

Let M represent the number of male students.

Let F represent the number of female students.

1. There are 80 students in the band:

M + F = 80

2. There are 25 fewer female students than twice the number of male students:

F = 2M - 25

So, the system of equations representing the number of male and female students in the school band is:

M + F &= 80

F &= 2M - 25

Now, solve this system of equations to find the number of male students ( M) in the band.

Substitute the second equation into the first equation:

M + (2M - 25) = 80

Combine like terms:

3M - 25 = 80

Add 25 to both sides:

3M = 105

Divide by 3:

M = 35

So, there are 35 male students in the school band.

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The chi square is a 1 by r statistic when fe's are obtained by multiplying row totals by column totals, and divided by N.

When calculating the chi square test of independence, the expected frequencies (fe's) can be obtained by multiplying the row totals by the column totals and dividing by the total sample size (N). This results in a set of expected frequencies that match the structure of the contingency table, with one expected frequency for each cell.

The chi square statistic is then calculated by summing the squared differences between observed and expected frequencies, divided by the expected frequency for each cell.

When the fe's are obtained by multiplying row totals by column totals, and divided by N, the resulting chi square statistic is a 1 by r statistic, where r is the number of rows in the contingency table.

This is because the degrees of freedom for the chi square test of independence are equal to the product of (r-1) and (c-1), where r and c are the numbers of rows and columns in the contingency table, respectively. When fe's are obtained as described above, c is reduced to 1, resulting in a 1 by r chi square statistic.

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The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer: it's the last one  It's not a function

Step-by-step explanation

Answer:

1991.759

Step-by-step explanation:

1810.69×%10=181.069

1810.69+181.069=1991.759

Answer:

14.5 exactly but 15 full weeks

Step-by-step explanation:

200-55=145

145/10=14.5

Round up to 15

Answer:

54$

Step-by-step explanation:

i took the test

The trend is slightly negative. Older adults tend to sleep a bit less than younger adults.

A trend refers to the general pattern or direction observed in the relationship between two variables. In this case, the scatterplot shows the relationship between age and the number of hours of sleep "last night" for some students.

The trend being slightly negative means that as age increases, there is a tendency for the number of hours of sleep to decrease slightly. This implies that older adults, on average, tend to sleep slightly less than younger adults.

The negative direction of the trend suggests a small negative correlation between age and sleep duration.

However, it is important to note that the trend represents a general pattern observed in the data and individual variations exist.

Not all older adults will necessarily sleep less than younger adults, as sleep patterns can be influenced by various factors such as lifestyle, health, and personal preferences.

Therefore, based on the given options, the correct answer is: The trend is slightly negative. Older adults tend to sleep a bit less than younger adults.

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Answer:

0.86 hour

Step-by-step explanation:

Jess jogs at a rate of 6 miles per hour.

The next time she jogs she increases her speed to a rate of 7 mile per hour.

The new rate of Jess's jogging is 7 miles per hour

How long will it take her to jog 6 miles?

Hence:

7 miles = 1 hour

6 miles = x hours

Cross Multiply

7 × x = 6 × 1

x = 6/7

x = 0.8571428571 hour

Approximately = 0.86 hour

It will take Jess 0.86 hour to jog for 6 miles

Answer:

Step-by-step explanation:

dont look at me go up

The procedure for revising probabilities based on additional information is referred to as Bayesian updating

The procedure for revising probabilities based on additional information is referred to as Bayesian updating. Bayesian updating is a fundamental concept in Bayesian statistics, which allows for the incorporation of new evidence or data to update and refine prior beliefs or probabilities.

In Bayesian updating, the process begins with an initial prior probability, which represents the initial belief or knowledge about an event or hypothesis before any evidence is observed. As new evidence or data becomes available, it is used to update the prior probability and generate a posterior probability. The posterior probability represents the revised belief or probability after incorporating the new information.

Bayesian updating follows the principles of Bayes' theorem, which mathematically describes the relationship between prior probabilities, likelihoods, and posterior probabilities. It involves combining the prior probability with the likelihood of observing the data given the hypothesis and then normalizing the result to obtain the posterior probability.

The beauty of Bayesian updating is that it allows for a flexible and iterative process of continuously updating beliefs and probabilities as new information emerges. It provides a framework for incorporating both subjective prior beliefs and objective data to make more informed decisions and predictions. Bayesian updating has applications in various fields, including machine learning, decision-making, and scientific research.

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Answer:

1) x = 22.5

Step-by-step explanation:

4/9 = 10/x

4 × x = 10 × 9

4x = 90

4x/4 = 90/4

x = 22.5

Answer:

2) 2.4

Step-by-step explanation:

5/2 = 6/x

5 × x = 6 × 2

5x = 12

5x/5 = 12/5

x = 2.4

Answer:

3) x = 0.8

Step-by-step explanation:

5/2 = 2/x

5 × x = 2 × 2

5x = 4

5x/5 = 4/5

x = 0.8

hope it helps!! (I'll add other answers too)

tell me if any of my answers are wrong

Answer:

1.  (5n^2 x4^n+2)/ 6

2. y=1 y=2

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\mathsf{-100\% + 0.58}\\\\\mathsf{= \dfrac{-100}{100} + \dfrac{0.58}{1}}\\\\\mathsf{= -100 \div 100 + 0.58 \div 1}\\\\\mathsf{= -1 + 0.58}\\\\\mathsf{= -0.42}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{-0.42}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

El cable experimenta un esfuerzo axial de 79577.472 pascales por el peso de la caja.

La caja tiene masa y está sometida a un campo gravitacional, por tanto, tiene un peso (W), en newtons. Por el principio de acción y reacción (tercera ley de Newton), encontramos que el cable es tensionado debido a ese peso y su área transversal experimenta un esfuerzo axial (σ), en pascales.

Asumiendo una distribución uniforme de la fuerza sobre toda la superficie transversal de la cuerda, tenemos que el esfuerzo axial se calcula mediante la siguiente expresión:

σ = W / (π · D² / 4)

Donde:

Si sabemos que W = 25 N y D = 0.02 m, entonces el esfuerzo axial aplicado a la cuerda es:

σ = 25 N / [π · (0.02 m)² / 4]

σ ≈ 79577.472 Pa

La falta de problemas verificados en español sobre esfuerzos axiales obliga a buscar uno equivalente en inglés.

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Answer:

768 m^2

Step-by-step explanation:

Separate the shapes

We can first separate the triangular pyramid from the rectangular prism.

We can calculate them separately.

Calculate

The volume of the triangular pyramid is the base multiplied by the height divided by 3. The base of the pyramid has the same base as the prism so:

8 * 8 = 64

Then we need the height which is 6 so:

64 * 6/3 = 64 * 2 = 128 m^2

Then we calculate the volum of the prism; the formula for that side times side time side:

8 * 8 * 10 = 640 m^2

The total volume is them added up:

128 + 640 = 768 m^2

The probability of getting at least 14 heads when flipping a fair coin 20 times is 0.25.

This can be calculated using the binomial distribution formula which states that the probability of obtaining exactly x successes in n trials is given by

P(x) = (n choose x) * p^x * (1-p)^(n-x),

where n is the total number of trials, p is the probability of success, and x is the number of successes.

For this problem, n=20, p=0.5, and x=14, so the probability of getting at least 14 heads is P(x) = (20 choose 14) * 0.5^14 * 0.5^6 = 0.25.

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The  equation of the line is y =  x + 6.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

= 1/-m  =1/ 4  

then,

y =  x/4 + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

hence, y =  x/4 + 6 ← equation of perpendicular line.

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