An angle is bisected. Each resulting angle is 78 degree. how is the original angle
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Using the properties of arithmetic mean and average we get the value of 'w' is 22.

We know that mean is calculated by dividing the sum by the frequency.

Here n= 3

Sum = 5+6+7+w = 18+w

Now , (18+w )/4 = 10 which is the mean

or, 18 + w = 40

or, w = 40 - 18

or, w = 22

The value of w is 22.

By adding together all the observations and then dividing the sum by the same total sample sizes, the arithmetic mean of the supplied data can be calculated.

In order to determine the data's central tendency, an arithmetic mean formula computes the mean, or average, of the numbers. It can alternatively be described as the total number of observations multiplied by the sum of all the observations that were provided.

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Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.

Proportion refers to the quantity of a value or variable contained in another value.

Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.

Proportions are depicted using fractions, decimals, or percentages.

The number of avocados required for 4 orders of guacamole = 6.5

The total number of orders of guacamole required = 14

The number of avocados to make 1 order = 6.5/4

The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)

Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.

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⇒Note this is a fraction.

⇒For a fraction to be undefined that is of when the denominator is equal to 0

⇒Now equate what is  in the denominator with 0

⇒ [tex]k+3=0\\k=-3[/tex]

⇒So that the denominator is 0 that is of when k is equal to -3..it is then that the whole expression will be undefined.

⇒The expression is undefined when k=-3

Answer:

y = x - 3

Step-by-step explanation:

Consider the equation "y = mx + b" :

y = mx + b

Since the slope is 1, you could input that into the equation:

y = (1)x + b

The variable "b" represents the y-intercept, therefore, to find the y - intercept, you would have to subtract 7 from each side of the coordinate points to get 0 as the x - coordinate to find the y - intercept:

(7    4)

-7 || -7

(0, -3)

Therefore, the y - intercept would be -3 and the equation would be:

y = x - 3

Graph for the equation ( y = -300x +  1200 ) below

y-intercept = ( 0, 1200 )

x-intercept = ( 4, 0 )

Hope this helps! :)

The y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

y=-300x+ 1200

Now, for y- intercept put x=0

y= 1200

and, for x- intercept put y= 0

0 = -300x +1200

x= 4

Hence, the y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

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The initial 4 gallons and the fractions of [tex]\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex] gallons of paint used on the first day indicates;

A fraction is the representation of a number in quotient form such that the value of the number is obtained by dividing the numerator by the denominator.

The amount of paint Lyle and Ming started painting the room with = 4 gallons

Amount of paint Lyle used on the first day = [tex]\dfrac{1}{2}[/tex] gallons of paint

The amount of paint Ming used on the first day =  [tex]1\frac{1}{4}[/tex] gallons of paint

Required; The amount of paint remaining after the first day of painting

The paint left after the first day of painting, V, is the difference between the amount of paint with which the painting was started and the amount used by Lyle and Ming on the first day

Therefore; [tex]V = 4 - \left(\dfrac{1}{2} + 1\dfrac{1}{4} \right) = 4 - \left(\dfrac{1}{2} +\dfrac{5}{4} \right) = 4 - \dfrac{7}{4}[/tex]

[tex]V = 4 - \dfrac{7}{4} = \dfrac{16-7}{4} = \dfrac{9}{4} = 2\dfrac{1}{4}[/tex]

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Answer:

3.09

Step-by-step explanation:

check the file attached

Answer:

100% - 80%=20%

Step-by-step explanation:

that's the answer

Yes, the two quantities have a proportional relationship because the variables x and y all have the same constant of proportionality.

Mathematically, a proportional relationship can be represented or modeled with the following mathematical expression:

y = kx

Where:

In order for the two quantities to have a proportional relationship, the variables x and y must remain in a constant ratio.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 2/3

When x = 90 and y = 60, we have:

Constant of proportionality (k) = 60/90

Constant of proportionality (k) = 2/3

When x = 120 and y = 80, we have:

Constant of proportionality (k) = 80/120

Constant of proportionality (k) = 2/3

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Answer: I would say it is 2 and 3

Step-by-step explanation:

I can't be 1 ben franklin was not the one fooling the king and France

It can't be 4 because Mesmers force did not exist.

Answer:

x=-3

Step-by-step explanation:

The values of y with respect to the points created is constant, hence the two points will have the same y values but difference their respective x values

The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1.

The probability that 2 red cards and 11 black cards are dealt is .

The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1. If for finding probability we have to select r out of n. Combination is used to select r items out of n, the formula is as follows,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Finding the probability that 2 red cards and 11 black cards are dealt,

Number of favorable outcomes will be [tex]^{26}C_2\times^{26}C_{11}[/tex].

Total number of outcomes will be [tex]^{52}C_{13}[/tex]

Now, the probability will be,

[tex]P()=\frac{^{26}C_2\times^{26}C_{11}}{^{52}C_{13}} \\\\=\frac{325\times7726160}{635013559600} \\\\=0.00395[/tex]

Therefore, the probability that 2 red cards and 11 black cards are dealt is 0.00395.

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Since random sampling is representative of the entire group, conclusions about the population can be drawn from it. Since random assignment reduces variability, conclusions about cause and effect are possible.

Random sampling is a sampling method where each sample has an equal chance of being chosen. It is the goal of a randomly chosen sample to fairly represent the entire population. A straightforward random sample might be 25 names chosen at random from a pool of 250 employees. The sample in this case is random, and the population in this case is the entire pool of 250 employees because each employee has an equal chance of being chosen.

Cause and effect can only be proven with absolute certainty through an experimental study utilizing random assignment. In a study with random assignment, for example, the experimental group receives the medication while the control group does not in order to see if the drug cures the patient.

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Based on an exponential model of the data, the predicted temperature of the water at 7 minutes is 39.7 °C using desmos graphing calculator.

Similar to how you discovered linear and quadratic models in prior chapters, exponential models can be found by fitting data to them. As you may already be aware, exponential functions take the form y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time. Based on an equation like this one, the exponential model represents the degradation failure process: Y = deterioration; T = time; A and B = parameters to be calculated using the regression approach based on historical data. An expansion within a population that happens at the same pace across time is represented by the function of exponential growth. It is reasonable to suppose that data grows exponentially as populations double or triple in size.

Graph all the points on a graph. Then from the graph, we can find that at 7 minutes the temperature is 39.7°C.

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Answer: 38.2 degrees

Step-by-step explanation:

enter into desmos

use y1 ~ abx2

then input numbers provided

(22.9178)1.07564^7

equals 38.18049

round 38.2

The null hypothesis is a statement which describe the claim of 'no difference'.

Let μ be the population mean.

Given claim : The mean age of bus drivers in Chicago is 50.2 years.

i.e. μ = 50.2

Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.

Then, the null hypothesis for the given situation is

Ηο : μ = 50.2

If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.

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The result that we get after the long division is:

3[tex]x^{2}[/tex] + 9x + 71;

What is the long-division method?

Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are often solved with. See the dividend, quotient, divisor, and remainder in the following long division.When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder. In this post, we will learn more about the long division technique, including its processes and examples.

In the given question,

The expression we have:

[tex]$3 x^3+15 x^2-17 x+6$[/tex]; and this expression is been divided with x + 6;

we get:

At first, we will divide the expression with 3[tex]x^3[/tex]; we get:

9[tex]x^{2}[/tex] -17x +6;

Now again we will divide it by 9x: we get:

71x + 6;

Now, again dividing it by 71, we get:

-70.

So, The result that we get after the long division is:

3[tex]x^{2}[/tex] + 9x + 71;

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Equation of parallel line is y = x + 5

What in math is a coordinate?

a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).

Step-by-step explanation:
If there is a constant distance between each point and the two lines never cross, they are considered to be parallel. If two lines have the same slope, they are said to be parallel.
By above statement we concluded that y = x should be same as its but we can change its intercept part
Hence Equation parallel to y = x + 6 is y = x + 5

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The length of the base edge of the given square pyramid is 3.67 feet.

What is the Surface Area?

The sum of all an item's faces makes up the surface area of a three-dimensional object. When wrapping, painting, and finally creating things to get the finest possible design, we apply the idea of surface areas of various items in real life.

What is a Square Pyramid?

Steps to Calculate the Base Edge Length of Square Pyramid

The formula for surface area of square pyramid is given by, [tex]SA=a^{2} +2a\sqrt{\frac{a^{2} }{4}+h^{2} }[/tex],    -----(1)

where [tex]a[/tex] is the length of the base edge and [tex]h[/tex] is the square pyramid height.

In the question, it is given that the surface area of the square pyramid is 96 square feet.

The height of the square pyramid is two-thirds of the base edge length.

[tex]\implies h=\frac{2a}{3}[/tex]  ------(2)

Now substituting the given values in (1), we get

[tex]96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+(\frac{2a}{3} )^{2} }\\\implies 96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+\frac{4a^{2} }{9} }[/tex]

Simplifying, we get

[tex]96=a^{2} +2a\times 0.834a^{2} \\\implies 96=a^{2} +1.668a^{3} \\\implies 1.668a^{3}+a^{2} -96=0[/tex]

Finally, we get the value of [tex]a=3.67[/tex] feet.

Therefore, the base edge length of the given square pyramid is 3.67 feet.

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Step-by-step explanation:

8x + 3x + 4 + 5y + 2

combine x terms:

11x + 4 + 5y + 2

combine numbers:

11x + 5y + 6

[Please comment if you want the answer specifically for x or y.]

Answer:

8x+3x+4+5y+2

11x+9y+2

20xy+2

=22xy

Answer: c/bd = a

Step-by-step explanation:

What we need to do is isolate a on one side of the equal side. Now, remember that multiplication and division cancel each other out, so if we divide b and d on the right side by b and d then we cancel those values and get a by itself. Now, we have to do this on the left side as well in order to keep the equation balanced. When we do this, we get c/bd = a. Keep working hard! You're doing great!

Answer:

The area of the dount is about 35.325 in²

Step-by-step explanation:

In order to find the area of a donut with a hole on the center we need to find the area of the center and the area of the circle of the donut (as if the donut was whole)

*The radius is half of the diameter or r = d/2

The area of a circle is A = n(3.14) r² or pi(3.14)× radius

From the given three options the equation y = x^2 + 6 is non - linear.

What is linear equation?

A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.

Consider, the first equation

y = 2^2

⇒ y = 4

Since, the constant equations are linear.

So, first equation is linear.

Consider, second equation

y = 2x - 5

Here, the variable x and y both having degree 1.

So, second equation is also linear.

Consider, third equation

y = x^2 + 6

Here, the variable y having degree 1, but the variable x having degree 2.

Therefore, equation (3) is non - linear.

Hence, the equation y = x^2 - 5 is non - linear.

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Answer:

Note: A percentage is always a number over 100.      (34% = [tex]\frac{34}{100}[/tex])

Cost of meal = 100%

Cost of tip = 34%

Total = 134%

134% = [tex]\frac{134}{100}[/tex]

To find the total and the tip, you must multiply it by [tex]\frac{134}{100}[/tex]

Answer:

Bill times the 0.34 percent equals the price of the tip. After you find what the tip is, you add the base price (the bill price) to the tip and you get the total number paid. However, another way you can solve (in one step) this is by adding 1.00 to the percent you are multiplying by which in this case we add 0.34 by 1.00 and this gives us 1.34. Suppose we set the bill to 4 dollars and use the normal way (2-step equation) by doing 3(0.34) which is 1.02 and 1.02 + 3 = 4.02 as our final answer / final bill. However, when we do our one-step equation, we can write this as 3x(1.34) and this is equal to 4.02.

1st Step

Bill(0.34) = tip

tip + bill = total

2nd Step (one-step equation)

Note: we are going to set the bill in this equation as $4

4(1.34) = total; Total = 4.02 ← We added 1.00 to the tip percentage in decimal form.

Answer:

14

Step-by-step explanation:

Answer:

x = -20

Step-by-step explanation:

x/4 + 8 = 3

subtract 8 from both sides:

x/4 + 8 - 8 = 3 - 8

x/4 = -5

multiply both sides by 4:

4(x/4) = 4(-5)

x = -20

Answer:

Y = 3/4x + 0

Step-by-step explanation:

Find the slope of the line = Rise/Run.

[tex]\frac{-3-6}{-4-8}[/tex]  = [tex]\frac{-9}{-12}[/tex]

= 0.75 or 3/4.

Therefore, insert into point slope form using one of the corresponding points; (8, 6) for example;

Y-6 = 3/4(x-8)

= Y-6 = 3/4x-6

and simplify the equation;

Y = 3/4x + 0 also just Y = 3/4x.  

Answer: 150*40/100=60

60+150=210.

Step-by-step explanation:

The model which model the dimensions of the bed has been attached.

Perimeter of the bed = 2(length + width)

= 2(6 + 4)

= 2(10)

= 20 feet

Area of the bed = Length × width

= 6 feet × 4 feet

= 24 square feet

Total perimeter = 14 + 10 + 10 + 6

= 40 feet

Therefore, the items listed can not all be underneath your bed because the total perimeter of the items is greater than the perimeter of your bed.

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The value of b of the equation is -9/5

Given that: line JK passes through points J(-4,-5) and K(-6,3) and if the equation of the line is written in slope-intercept form, y=mx+b

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

Using the y-y₁/y₂-y₁ = x-x₁/x₂-x₁

where (x₁, y₁) = (-4,-5) and (x₂, y₂) = (-6,3), the equation is:

y-(-5) / 3-(-5) = x-(-4)/-6-(-4)

y+5 / 3+5 = x+4 /6+4

(y+5)/8 =  (x+4)/10       cross multiply:

10(y+5) = 8(x+4)

10y + 50 = 8x + 32

10y = 8x +32 - 50

10y = 8x - 18

y = 8x/10 - 18/10

y = 4x/5 - 9/5

Comparing y = 4x/5 - 9/5 with y=mx+b

b = -9/5

Therefore, the value of b is -9/5

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