A line passes through the points (4, - 3) and (6, - 1) The equation of the line in slope -intercept form is y = mx + b . What is the value of b?

The solution for the expression 2^(x) − 2^(−x) = 5 is x = log2(10)

Substitute 2^(−x) for 5 and solve for x, which is log2(10).

The given expression ,

2^(x) − 2^(−x) = 5

2^(x) = 5 + 2^(−x)

2^(2x) = (5 + 2^(−x))^2

2^(2x) = 25 + 10*2^(−x) + 2^(−2x)

25 + 10*2^(−x) + 2^(−2x) = 2^(2x)

25 − 2^(2x) = 10*2^(−x) − 2^(−2x)

25 − 2^(2x) = 10*2^(−x) − 2^(−2x) + 2^(2x)

25 = 10*2^(−x) + 2^(2x) − 2^(−2x)

25 = 10*2^(−x) + 2^(−2x) (2^(2x) - 2^(−2x))

25/(2^(−2x) (2^(2x) − 2^(−2x))) = 10*2^(−x)

25/(2^(2x) − 2^(−2x)) = 10*2^(−x)

2^(x) = 10

x = log2(10)

Substitute 2^(−x) for 5 and solve for x, which is log2(10).

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Number of ways can this company buy them is 1623160.

Given :

a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees.

Number of ways = [tex]35_C_6[/tex] or C ( 35 , 6 )

we know that ,

C ( n , r ) = n! / ( n - r ) ! r!

substitute

= 35 ! / ( 35 - 6 ) ! 6!

= 35 * 34 * 33 * 32 * 31 * 30 * 29! / 29! * 6!

= 35 * 34 * 33 * 32 * 31 * 5 / 5 * 4 * 3 * 2 * 1

= 35 * 17 * 33 * 32 * 31 / 4 * 3

= 35 * 17 * 11 * 8 * 31

= 1623160 ways

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Answer:

Liter

Step-by-step explanation:

Milliliters are used for much smaller amounts of liquid.

The day worker's daily compensation is $160, while the concrete finisher's daily wage is $143.

A matrix is a numerical arrangement that is divided into rows and columns. Introduce yourself to matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a collection of integers that are organized in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,

Let x be the Charge for day labor and y be the charge for concrete finisher,

8x+2y=1464

x+5y=943

multiply x+5y=943 by 8,

8x+40y=7544

8x+2y=1464

subtracting them,

38y=6080

y=$160

x+5*160=943

x=943-800

x=$143

The daily wage for day worker is $160 and the daily wage for concrete finisher is $143.

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Answer: False

Step-by-step explanation:

Answer: answer below

Step-by-step explanation:

4 (a). 900 grams of flour
work 150x6=900 grams

4 (b). 3 large eggs
work 450÷150=3
5 (a). 2.99

work 11.96÷4=2.99

5 (b). 26.91

work 2.99x9=26.91

6 (a). Can't help
6 (b). 6:12
6 (c). 16:8
6 (d). 10 paws

Can't help on problem 7

Answer:

a.

Step-by-step explanation:

Answer:

The answer should be A.

Step-by-step explanation:

We can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.

According to Stoke's theorem, where C = A closed curve, "the surface integral of the curl of a function across a surface limited by a closed surface is equal to the line integral of the particular vector function over that surface."

S = Any surface bordered by C.

So, by utilizing Stokes Theorem to calculate S curl F .dS.

[tex]\iint_s c u r l F \cdot d s=\int_c F d r[/tex]

Parameterize C now.

r(t) = (3 cos t, 3 - 3 sin t)

When t is in [0 2].

Now,

[tex]\begin{aligned}& \int_c F \cdot d r=\int_0^{2 \pi} F(3 \cos t, 3-3 \sin t) \cdot r^{\prime}(t) d t \\& =\int_0^{2 \pi}\left(\left(9 \cos ^2 t\right)(27)(-3 \sin t),(\sin t) \times(-27 \cos t \cdot \sin t) \cdot(-3 \sin t, 0-3 \cos t) d t\right. \\& =27 \int_0^{2 \pi} 81 \cos ^2 t \cdot t \sin ^2 t+3 \cos ^2 t . t \sin t d t \\& =27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2 t+27\left[-\cos ^3 t\right]_0^{2 \pi}\end{aligned}[/tex]

[tex]\begin{aligned}& =27 \times \frac{81}{4} \int_0^{2 \pi}\left(\frac{1-\cos 4 t}{2}\right) \\& =\frac{2187}{8}\left[t-\frac{1}{4} \sin 4 t\right]_0^{2 \pi} \\& =\frac{2187}{8}\left[2 \pi-\frac{1}{4} \sin 4(2 \pi)-0-\frac{1}{4} \sin 4(0)\right] \\& =\frac{2187 \pi}{4}\end{aligned}[/tex]

Therefore, we can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.

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To solve this problem, we can use the standard normal distribution and the Z-score formula to find the probability that a pregnancy will last at least 300 days.

The Z-score is a measure of how many standard deviations a value is from the mean. We can use the Z-score to standardize a value, which means we can express it in terms of how many standard deviations it is from the mean of the distribution.

The Z-score formula is:

Z = (x - μ) / σ

Where x is the value we are standardizing, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

To find the probability that a pregnancy will last at least 300 days, we can use the Z-score formula to standardize 300 days:

Z = (300 - 268) / 15 = 4

This means that 300 days is 4 standard deviations above the mean of 268 days.

To find the probability that a pregnancy will last at least 300 days, we can use a Z-table or a calculator to find the area under the standard normal curve that is greater than or equal to 4 standard deviations.

Using a calculator or a Z-table, we find that the probability that a pregnancy will last at least 300 days is approximately 0.0165, which corresponds to answer choice D: 0.0165.

Hello,

I hope you and your family are doing well!

To find the point and slope given by the equation y + 2 = -7(x-1), we can start by rearranging the equation to solve for y:

y + 2 = -7(x-1)

y = -7(x-1) - 2

y = -7x + 7 + (-2)

y = -7x - 9

This is the slope-intercept form of the equation, where y = -7x - 9 is the slope and (-9, 0) is the y-intercept.

The slope of the line is -7, and the point on the line is (-9, 0).

Therefore, the point and slope given by the equation y + 2 = -7(x-1) are (-9, 0) and -7, respectively.

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Inequality #1: x + y ≤ 28

Inequality #2: 0.05x + 0.1y ≥ 2

Mav could have 5 nickles and 20 dimes.

    It's given that Mav has less than or equal to 28 coins, so we can write the following inequality:

       x + y ≤ 28

    We know that a nickel is work 0.05 and a dime is worth 0.1. Using the given information, the following inequality is true since the coins must be greater than or equal to $2 combined:

       0.05x + 0.1y ≥ 2

       Now, we will graph them. Both graphed lines will use solid lines since both include equal to. We will shade below #1 and above #2. I used Desmos Graphing Calculator, you can find it online for free. Once we type in our equations, we get the needed graph.

       The overlapping portion contains our possible solutions. There are many, but one possible solution is (5, 20), with 5 nickels and 20 dimes.

The expression that shows the number 8 in one's place will be 72.35 + 45.81 and 9.56 + 9.41. Then the correct options are B and C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The expression that shows the number 8 in one's place.

Let's check all the options, then we have

A) 34.56 + 24.89 = 59.45

In the number 59.45, the one's place is 9. So, it is incorrect.

B) 72.35 + 45.81 = 118.16

In the number 118.16, the one's place is 8. So, it is correct.

C) 9.56 + 9.41 = 18.97

In the number 18.97, the one's place is 8. So, it is correct.

D) 12.34 + 15.42 = 27.76

In the number 27.76, the one's place is 7. So, it is incorrect.

The expression that shows the number 8 in one's place will be 72.35 + 45.81 and 9.56 + 9.41. Then the correct options are B and C.

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dimensions of the poster with margin are L  =  12 in and h  = 24 in

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.

Rectangle area equals length times width.

Let call length of printed area of the poster be " x "  and  height of printed area of the poster be " y ".

Area of the poster = length and height

200 = x*y  

y = 200/x

We also know that dimensions of the poster with margin is:

L  =  x + 2   in  and     H  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )

And area as function of x is:

A(x)  =   ( x + 2 ) * ( 200/x + 4 )

A(x)  =  200 + 4*x + 400 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4 - 400/x²

By taking A´(x)  = 0

4 - 400/x² = 0 ⇒ 4*x² - 400 = 0

x² = 400 / 4

x² = 100

x = 10 in

and y = 200/x ⇒ y = 20

The second derivative A´´(x) = 400/x4 which is > 0

there is a minimum for the function at the point x = 10

As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are

L  = x  +  2   =   10  + 2  =  12 in   and

h = y  +  4   =   20  + 4  =  24  in

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The value of the notation Δy from the points (-3,-5) and (0,10) is 15

The complete question is added at the end of this solution

From the question, we have the following parameters that can be used in our computation:

Points = (-3,-5) and (0,10)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (-3,-5) and (0,10)

The notation Δy represents the change in the y values of the given points

This notation can be extended to calculate the slope of the points

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3,-5) and (0,10)

Substitute the known values in the above equation

So, we have the following equation

Slope = (10 + 5)/(0 + 3)

Evaluate the sum

Slope = 15/3

The numerator represents Δy

i.e. Δy= 15

Evaluate the quotients

Slope = 5

Hence, the slope of the line is 5 and the value of the notation Δy is 15

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Complete question

Using the given points, determine Δy

Type a numerical answer in the space provided.

(-3,-5) and (0,10)

Answer:

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.

Step-by-step explanation:

According to the described situation, the system of inequalities that  best explains whether the company can build 20 child bikes and 6 adult bikes in the week is given by:

What is the system of inequalities?

Considering the variables c and a, for the number of child and adult bikes, respectively, we have that, considering the building time:

testing time When c = 20, a = 6:

Hence, the correct option is:

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.

Using the standard deviation value of these interarrival times, the coefficient of variation is 0.012.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

The standard deviation to mean ratio, or coefficient of variation (CV), illustrates the degree of variability in proportion to the population mean. The dispersion increases with increasing CV.

Formula is given by:

[tex]CV = \frac {\sigma}{\mu}[/tex]

[tex]\sigma = 0.02[/tex]

Mean for the time of 0.02 sec is = 79 * 0.02

=1.58

CV= 0.02/1.58

=0.012

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The factor of the given expression is (C) (x + 3).

In mathematics, a divisor of an integer n, often termed a factor of n, is an integer m that may be multiplied by some number to generate n.

In this scenario, one also asserts that n is a multiple of m.

A factor is a number that is multiplied by another number to produce the desired result.

A product is a solution to a multiplication problem.

Think of a multiplication problem as components being combined to find a product.

So, we have:

3x^3+18x^2+27x

Now, take the factors out as follows:

3x^3+18x^2+27x

3x(x²+6x+9)

3x(x+3)²

Factors:  (x + 3)

Therefore, the factor of the given expression is (C) (x + 3).

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Complete question;
Which of the following is a factor of 3x3 + 18x2 + 27x?

a. 9x

b. x3

c. x + 3

d. x - 3

The current population density  is 125 people / square kilometers.

Given :

plumeria island is an island in the indian ocean. the island is 4,000 square kilometers in size. currently, 500,000 people live there. last year, 150,000 children were born and 50,000 people immigrated. 100,000 people died and 10,000 emigrated. it is believed that the island could support up to 350 people per square kilometer.

Total people =  500000

Area = 4000 square kilometers

we know that ,

Population density = total people / area

= 500000 / 4000

= 500 / 4

= 125

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The retail price of the driver of the clubs after will be $400.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A golf store buys a driver at a discount cost of $200. Mr. Nganga discovered that the driver was increased by 100 percent.

The retail price of the clubs will be given as,

⇒ $200 x (1 + 100%)

⇒ $200 x (1 + 1)

⇒ $200 x 2

⇒ $400

The retail price of the driver of the clubs after will be $400.

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In integration the bindefinite integral of 1/xlnx is

ln(|u|)+C=ln(|lnx|)+C with the aid of using parts, we've discovered whilst the specified formula.

The vital of the 2 capabilities are taken, with the aid of using thinking about the left time period as first feature and 2nd time period as the second one feature.

This technique is referred to as Ilate rule.The vital of xlnx is same to (x2/2) lnx - x2/4 + C, wherein C is the mixing constant. We can compare this vital the usage of the technique of integration with the aid of using parts.

We have the vital:

[tex]∫1xlnxdx

Use substitution. Let u=lnx so that du=1xdx . Note that each of those are presently gift withinside the vital.

∫1xlnxdx=∫(1lnx)1xdx=∫1udu

This is a not unusualplace vital:

∫1udu=ln(|u|)+C

Since u=lnx :

ln(|u|)+C=ln(|lnx|)+C[/tex]

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The distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85 is  479.97

The base cost of the rental is said to be 49.95 dollars + 1.19 per mile

The cost of the gas is $3.89. The mileage of the truck is 18 miles

There would be an extra cost of

$3.89/18 per mile.

= 0.216111

In x miles we would have the equation that is written as:

C(x) = 49.95 + (1.19 + 0.21611)x

C(X) = $724.85 this is the total cost. Hence we would have

$724.85 =  49.95 + 1.19x + 0.21611x

$724.85 -   49.95 = 1.40611x

674.9 = 1.40611x

divide through by 1.40611

674.9 / 1.40611 = x

x = 479.97

The distance traveled is  479.97

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The number of tickets they purchased is 4.

The expression that would b used to represent the total cost at the carnival is a linear expression. A linear expression is an expression that has a single variable that is raised to the power of one.

The form of the linear expressions that can be used to represent the total cost at the carnival is:

Total cost = admission fee + (price per ride x number of rides)

Total cost in option 1 = $5 + 0.30r

Total cost in option 2 = $3 + $0.80r

Where r = number of rides

When they pay the same amount of money, the linear functions would be equal:

$5 + 0.30r = $3 + $0.80r

$5 - $3 = $0.80r - 0.30r

$2 = $0.50r

r = 2 / 0.5

r = 4

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The number of seconds the ball has gone by when the ball is at its highest point is 1 second

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following axis label

The highest point on the graph is the vertex of the graph

In this case, the point is

(t, h) = (1, 4.9)

Remove the h-coordinate

t = 1

This means that the time is 1 second

Hence, the ball has gone by 1 second when the ball is at its highest point

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{x - y^2}\\\mathsf{= 3 - (-5)^2}\\\mathsf{= 3 + \bf 5^2}\\\mathsf{= 3 + \bf 5\times5}\\\mathsf{= 3 + \bf 25}\\\mathsf{= 28}\\\\\huge\text{Therefore, your answer should be: \boxed{\textsf{28}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The required amount of her commission is given as $3937.5.

Given that,
A real estate agent sold a house for $315,000 last week. The commission is 1.25% of the selling price of the home,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Commission = 1.25% of $315000
Commission = 1.25× 315000/100
Commission = $3,937.5

Thus, the required amount of her commission is given as $3937.5.

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Hello,

I hope you and your family are doing well!

To find the length of BE, we can use the Pythagorean theorem to find the length of AC, and then use the fact that DE is parallel to AC to find the length of BE.

First, we use the Pythagorean theorem to find AC:

AC^2 = AD^2 + DC^2

Substituting the known values, we get:

AC^2 = 18^2 + 12^2

AC^2 = 324

AC = sqrt(324) = 18

Since DE is parallel to AC, we can set up a proportion to find the length of BE:

BE/EC = AC/DC

Substituting the known values, we get:

BE/12 = 18/12

BE = (18/12) * 12

BE = 18/1

BE = 18

Therefore, the length of BE is 18.

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(-9, 9) domain of the vector function. A vector valued function's domain is a subset of all real numbers at which the function is well-defined.

Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.

A vector-valued function is a rule that gives each member of a subset of R1 a vector. A function's domain is the set of all possible inputs to the function. The domain of f(x)=x2 is all real numbers, for example, and the domain of g(x)=1/x is all real numbers except x=0.

r(t) = t − 1 t 1 i sin(t) j ln(81 − t2) k

Lets find the domain of  first which is given by,

t - 2 / t + 2

This function is defined at all values except, t equals to -2 as the function is not defined at,

t -= -2

Lets find the domain of  first which is given by,

sin(t),

Two trigonometry function sine and cosine defined for all real number

This function is defined at all real numbers. Hence the domain of component  j is.

Set the above argument greater than zero to find where the expression is defined.Thus,

(9 + t ) (9 - t) > 0

Therefore,

The domain of it should be (-9, 9)

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Answer:

To find the value of log1000, you can use the logarithmic property that states that log(a^b) = b * log(a). In this case, we can rewrite 1000 as 10^3, so log1000 = log(10^3) = 3 * log(10) = 3.