What is the measure of angle ABC?

To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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Step-by-step explanation:

complementary angle = 90 - angle

= 90- 48= 42 °

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With that information we can create the equation

10x + 5000 = 20x

where x is the number of earphones produced

10x is the cost to make each earphone, 5000 being the fixed costs of manufacturing, and 20x being the total revenue of selling each earphone for $20

Now to solve the equation:

subtract both sides by 10x

10x - 10x + 5000 = 20x - 10x

5000 = 10x

Now divide both sides by 10

5000/10 = 10/10 x

500 = x

Answer: D

Hope it helps :)

500 earphones must be produced to get the cost price of one ear phone of $20.

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question

The start-up costs for manufacturing earphones is $5,000.

Also, the cost to make earphones is $10.

Let x number of  earphones will produced to get a cost per unit of $20.

From the given conditions, we will get a linear equation in one variable

10x + 5000 = 20x

⇒ 5000 = 20x -10x

⇒ 5000 = 10x

⇒ x = 500

Hence, 500 earphones must be produced to get the cost of earphone of $20.

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Answer:

Total number of chips = 720 Favorable cases = 720 - 568

Answer:

The common difference is same = d = -9

Therefore, the data represent a linear function.

Step-by-step explanation:

Given the table

x                        y

1                         4

2                        -5

3                        -14

4                        -23

5                         -32

Finding the common difference between all the adjacent terms of y-values

d = -5 - 4 = -6,

d = -14 - (-5) = -14+5 = -9

d = -23 - (-14) = -23 + 14 = -9

d = -32 - (-23) = -32 + 23 = -9

It is clear that the common difference between all the adjacent terms is same.

Thus,

d = -9

We know that when y varies directly with x, the function is a linear function.

Here, it is clear that each x value varies 1 unit, and each y value varies -9 units.

i.e. The common difference is same = d = -9

Therefore, the data represent a linear function.

Answer:

Power Bars are cheaper!

Step-by-step explanation:

FG: $18/12 Bars = $1.50 per bar

PB: $21.75/15 Bars = $1.45 per bar

Answer:

Super Power bars

Step-by-step explanation:

In order to find the best price, we want to calculate the unit rate, or the price for each bar. Let's start with the Fee Great energy bars. Since they are $18 for 12 bars, we divide 18 by 12 to figure out how much each bar costs. We get 1.5, or $1.50 per bar. Next lets claculate the unit rate for the Super Power bars. Since its $21.75 for 15 bars, we divide 21.75 by 15. We get 1.45, or $1.45 per bar. Since the price for one bar is cheaper for the Super Power bars as $1.45 is less than $1.50, the Super Power bars are the best price for each bar.

The customer have to choose 2002 ways to taste 5 different white wine.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

The combination formula is: n! / (n-r)! r! , where n is the total number of items (14 in this case) and r is the number of items being selected at once (5 in this case),

Plugging our numbers into the formula we get:

= 14! / (14-5)! 5!

= 2002

After simplifying, we get 2002.

So, there are 2002 ways of picking 5 different white wines to taste from a group of 14 local winery bottles.

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Answer:

1. 35 pages in 7 days

2. 63 pages in 9 tables

3. 408 student on 8 buses

Step-by-step explanation:

Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.

The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:

W = F * d

where:

W is the work done in joules

F is the force in newtons

d is the distance in meters

The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.

The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.

Plugging these values into the equation for work, we get:

W = 102.8 N * 4600 m = 472320 J

The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:

472320 J / 29 kJ/mol = 162.6 mol

To one decimal place, this is 0.23 moles of ATP.

Here are the assumptions that we made in this calculation:

No friction

No mass of the bike

A flat ride with no change in altitude

These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.

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Answer:

There are 52 weeks in a year so divide that by 22,550 and you get a weekly salary of $433.65

Step-by-step explanation:

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.

We need to determine the equation, in vertex form, for the following parabolas.

We can find the parabola's equation in vertex form following two steps:

Step 1: Use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)²+k.

Step 2: Find the value of the coefficient a by substituting the coordinates of the point into the equation written in step 1 and solving for a.

Now, substitute (−2, 5) in y=a(x−h)²+k

⇒y=a(x−(-2))²+5

Now, substitute (2, 0) in y=a(x−(-2))²+5.

0=a(2+2)²+5

⇒a=-5/16

So, y=-5/16(x+2)²+5

⇒16y=-5(x²+4x+4)+5

⇒16y=-5x²-20x-20+5

⇒5x²+20x+16y-15=0.

Therefore, 5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.

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Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.

An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.

In this case, one of the measurements among the 10 is identified as an outlier.

When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.

It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.

The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.

Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.

The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.

Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.

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Answer:

$4.25

Step-by-step explanation:

Let price of drink be x

price of tub y

You have 4x+2y=32.5 (1) and

x = y -3.5                 (2)

Plug for x from (2) into (1):

4(y-3.5) + 2y = 32.5

4y -14 +2y = 32.5

6y = 14+32.5

y = (46.5)/6 = $7.75 the price of tub

x= y-3.5 = 7.75 - 3.5 = $4.25

Answer:

z=-21

Step-by-step explanation: (9-3)/2=(6+z)/5

We move all terms to the left:

(9-3)/2-((6+z)/5)=0

We add all the numbers together, and all the variables

-((z+6)/5)+6/2=0

We add all the numbers together, and all the variables

-((z+6)/5)+3=0

We multiply all the terms by the denominator

-((z+6)+3*5)=0

We calculate terms in parentheses: -((z+6)+3*5), so:

(z+6)+3*5

We add all the numbers together, and all the variables

(z+6)+15

We get rid of parentheses

z+6+15

We add all the numbers together, and all the variables

z+21

Back to the equation:

-(z+21)

We get rid of parentheses

-z-21=0

We add all the numbers together, and all the variables

-1z-21=0

We move all terms containing z to the left, all other terms to the right

-z=21

z=21/-1

z=-21

The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²

b is the coefficient of x

c is a constant term

x² + 5x + 4 = 0

We have given:

x² + 5x + 4 = 0

Comparing the equation with the standard form.

a = 1, b = 5 and c = 4

Substituting it in the formula

D = 5² - 4 × 1 + 4

By further calculation

D = 25 - 16

D = 9,

The quadratic roots are real and distinct

Therefore, the value of b² - 4ac is 9.

Hence, The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

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Using the definition,

\(f'(4) = \displaystyle \lim_{x\to4} \frac{f(x)-f(4)}{x-4}\)

The numerator in the difference quotient is

\(f(x) - f(4) = \sqrt{2x+1} - \sqrt{2\cdot4+1} = \sqrt{2x+1}-3\)

Multiply the numerator and denominator by the conjugate of this expression,

\(\displaystyle \frac{\sqrt{2x+1}-3}{x-4} \cdot \dfrac{\sqrt{2x+1}+3}{\sqrt{2x+1}+3}\)

The modified numerator reduces to a difference of squares,

\(\displaystyle \frac{\left(\sqrt{2x+1}\right)^2-3^2}{(x-4)\left(\sqrt{2x+1}+3\right)}\)

Simplify this to get

\(\displaystyle \frac{2x+1-9}{(x-4)\left(\sqrt{2x+1}+3\right)} = \frac{2(x-4)}{(x-4)\left(\sqrt{2x+1}+3\right)}\)

Since x is approaching 4, it never actually takes on the value of 4, so (x - 4)/(x - 4) reduces to 1. Then the limit is equivalent to

\(f'(4) = \displaystyle \lim_{x\to4} \frac{f(x)-f(4)}{x-4} = \lim_{x\to4}\frac2{\sqrt{2x+1}+3}\)

and the remaining limand is continuous at x = 4, so that

\(f'(4) = \dfrac2{\sqrt{2\cdot4+1}+3} = \dfrac26 = \boxed{\dfrac13}\)

Answer:x=-1

Step-by-step explanation:

4^x=1/4

x=-1

Answer: 11/16

Step-by-step explanation:

1/8=2/16

1/4=4/16

5/16=5/16

add it all together

The numerical value of 1.2 × 1.222 is approximately 1.4664.

To calculate the numerical value of 1.2 × 1.222, we multiply the two numbers together. Let's break it down step by step:

Start with the multiplication operation: 1.2 × 1.222.

Multiply the decimal numbers without considering the decimal point. We have 12 × 1222.

Perform the multiplication of the whole numbers: 12 × 1222 = 14,664.

Count the total number of decimal places in both factors. In this case, we have one decimal place in 1.2 and three decimal places in 1.222.

Add the total number of decimal places from both factors. 1 + 3 = 4.

Place the decimal point in the product by counting four places from the right of the final result obtained in step 3.

The final result is 14,664, with the decimal point placed four places from the right, giving us 1.4664. Therefore, the numerical value of 1.2 × 1.222 is approximately 1.4664.

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The population of town A is 4.5 times greater than the population of town B.

The power of a number describes how many times a number is multiplied by itself.

Given are the population of two towns A and B.

Town A has a population of 1.26×10⁵ and the population of town B is 2.8×10⁴.

To find how many times greater is the population of Town A than the population of Town B we have divide the population of town A by the population of town B which is,

= ( 1.26×10⁵)/(2.8×10⁴) times greater.

= (12.6)/(2.8).                                       ( 10⁵ divided by 10⁴ is 10¹ which is 10)

= 4.5 times greater.

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Answer:

0.9115

Step-by-step explanation:

Using a binomial probability function :

P(x =x) = nCx * p^x * (1 - p)^(n - r)

Probability of success, p = 0.55

1 - p = 1 - 0.55 = 0.45

n = 8

x = 2

P(x > 2 ) = p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) + p(x = 7) + p(x =8)

To save computation time, we could use the binomial probability calculator :

P(x > 2 ) = 0.9115

The probability of a person calling when you're thinking of them is subjective and depends on factors such as the likelihood of thinking of the person and the likelihood of the person calling, making it challenging to provide a precise estimate.

a. Likelihood of thinking of the person at a randomly selected time of day: This depends on the nature of your relationship, recent interactions or memories with the person, emotional significance, and personal thoughts. You can assign a subjective probability based on your own observations and experiences.

b. Likelihood of the person calling at a randomly selected time of day: This depends on the person's behavior, communication patterns, availability, and other relevant factors. Again, this can be subjectively estimated based on your knowledge of the person and their tendencies.

c. Compelling evidence of the combined events: To determine if the combined events provide compelling evidence that it wasn't merely a chance occurrence, you would need to establish a baseline probability of the individual events occurring independently by chance. If the combined probability significantly deviates from the expected chance occurrence, it may suggest a non-random connection between your thoughts and the person's behavior. However, a single occurrence may not provide sufficient evidence, and multiple instances would be needed to establish a pattern.

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The solution to the expression 4+(−634) is -630

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

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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Answer:

Vc. Tính giai cấp

Step-by-step explanation:

To find the derivatives of y with respect to t, we'll use the chain rule and the product rule.

y = -e^(-t) + 6

First, let's find dy/dt:

dy/dt = d/dt (-e^(-t) + 6)

= -d/dt(e^(-t)) + 0 [since the derivative of a constant is zero]

= e^(-t)

Next, let's find d^2y/dt^2 (the second derivative of y with respect to t):

d^2y/dt^2 = d/dt(dy/dt)

= d/dt(e^(-t))

= -e^(-t)

Therefore, the derivatives as functions of t are:

dy/dt = e^(-t)

d^2y/dt^2 = -e^(-t)

Note: It seems there might be a typo in the given expression for dy/dx, as the original function y is expressed in terms of t. If there was an error or if you intended to find the derivatives with respect to a different variable, please provide the correct equation for y in terms of x, and I'll be happy to help further.

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The line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.

A graph is a mathematical representation of a set of objects, called vertices or nodes, and the connections between them, called edges or arcs. Graphs are commonly used to model relationships between entities in various fields such as computer science, mathematics, physics, social sciences, and many others.

To determine the line that the angle has been reflected across, we need to find the line of reflection, which is the perpendicular bisector of the segment joining each point and its corresponding image.

We can start by finding the midpoint of the segment joining A and A', which is the point that is equidistant from these two points and lies on the line of reflection. The midpoint of AA' is:

Midpoint of AA' = ((x-coordinate of A + x-coordinate of A')/2, (y-coordinate of A + y-coordinate of A')/2)

Midpoint of AA' = ((4 + (-5))/2, (5 + (-4))/2)

Midpoint of AA' = (-1/2, 1/2)

Next, we can find the midpoint of the segment joining B and B':

Midpoint of BB' = ((x-coordinate of B + x-coordinate of B')/2, (y-coordinate of B + y-coordinate of B')/2)

Midpoint of BB' = ((1 + (-2))/2, (2 + (-1))/2)

Midpoint of BB' = (-1/2, 1/2)

We can see that the midpoint of AA' and the midpoint of BB' are the same point, which means that the line joining these midpoints is the perpendicular bisector of both segments, and therefore the line of reflection.

So, the line of reflection is the line passing through the points (-1/2, 1/2) and (-2, -1), which can be found using the slope formula:

slope of line of reflection = (y2 - y1) / (x2 - x1)

slope of line of reflection = (-1 - 1/2) / (-2 - (-1/2))

slope of line of reflection = (-3/2) / (-3/2)

slope of line of reflection = 1

We now have the slope of the line of reflection, and we can find its equation by using the point-slope form:

y - y1 = m(x - x1)

Using the point (-1/2, 1/2) and the slope 1, we get:

y - 1/2 = 1(x + 1/2)

Simplifying, we get:

y = x + 1

Therefore, the line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.

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Answer:

x=32

Step-by-step explanation:

The derivative of the given function sin(xy)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

The given equation is-

sin(xy) = 3x − 2y

Be sure to account for both sides of this argument.

d/dx(sin(xy)) = d/dx(3x − 2y)

Differentiate the equation's left side.

Set the left side equal to a right side to reform the equation.

x.cos(xy).y' + y.cos(xy) = 3

Solve for y'.

y' = 3sec(xy)/x - y/x

Thus, replace y' with dy/dx

dy/dx =  3sec(xy)/x - y/x

Thus, the derivative of the given function sin(x y)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

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