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Answer: In the figure above, clearly the line L is perpendicular to x-axis and passing through the value 'c' on x- axis. So, the equation of a line perpendicular to x axis is x = c

a. To find the average rate of growth between each pair of years, we can use the formula: (end value - start value) / (end year - start year).

2004 to 2006: (12,440 - 8,574) / (2006 - 2004) = 3,866 / 2 = 1,933 locations/year

2006 to 2007: (15,006 - 12,440) / (2007 - 2006) = 2,566 / 1 = 2,566 locations/year

2005 to 2006: (12,440 - 10,238) / (2006 - 2005) = 2,202 / 1 = 2,202 locations/year

b. To estimate the instantaneous rate of growth in 2006, we can take the average of the last two rates of change from part (a).

(2,566 + 2,202) / 2 = 2,384 locations/year

c. To estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through (2005, 10,238) and (2007, 15,006), we can use the formula:

(15,006 - 10,238) / (2007 - 2005) = 4,768 / 2 = 2,384 locations/year

d. To estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through (2006, 12,440) and (2008, 16,676), we can use the formula:

(16,676 - 12,440) / (2008 - 2006) = 4,236 / 2 = 2,118 locations/year

e. Comparing the growth rates from part (c) and (d), we can see that the growth rate in 2007 is less than the growth rate in 2006. So we can conclude that 2. The rate of growth is decreasing.

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a)The set of integers between 1 and 50, divisible by 8 are given as.

S={ 8,16,24,32,40,48}

b ) Hence, the set {-5,1}

c) The list of set of outcomes when a coin is tossed until a tail or three heads appear will be.

S={T,HT,HHT,HHH}

d) S={Europe, Asia, Australia, North America, South America, Africa, Antarctica.}

a) We have to find a list of integers between 1 and 50, divisible by 8.

Keep in mind that the S is the event that represents the sample space. The set of integers between 1 and 50, divisible by 8 are given as.

S={ 8,16,24,32,40,48}

b)  We need to list the set S= {[tex]x| x^2+4x-5=0}[/tex]}

[tex]x^2+4x-5=0\\\\x^2+5x-x-5=0\\x(x+5)-(x+5)==\\(x+5)(x-1)=0\\\\x=-5 , x=1[/tex]

Hence, the set {-5,1}

c) c) We have to find a list of the set of outcomes when a coin is tossed until a tail or three heads appear.

Let T denote the event that tail appeared.

Let H denote the event that head appeared.

The list of set of outcomes when a coin is tossed until a tail or three heads appear will be.

S={T,HT,HHT,HHH}

d) We need to list the set

S={x ∣ x is a continent}.

There are 7 continents:

S={Europe, Asia, Australia, North America, South America, Africa, Antarctica.}

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​

By performing a change of units, we will see that the caterer should purchase 107.8 lb

First, let's find how many kilograms are needed. We know that the recipe recomends using 0.7kg per person, and there are 70 guests, so an estimate of the mass needed is:

M = 70*0.7kg = 49 kg

Now weneedto do a change of units, we know that:

1 kg =  2.2 lb

Then we can rewrite:

49 kg = 49*(2.2 lb) = 107.8 lb

The caterer should purchase 107.8 pounds

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Answer:

20

Step-by-step explanation:

1/5 = 20/100

Reducing the completion average  time for Jobs J and K by one day will shorten the overall project completion time by one day, allowing the project to finish one day early.

In order to finish the project one day early, the completion time for Jobs J and K should be reduced by one day. This is because these two jobs are part of the three critical paths of the project. By reducing the completion time for these two jobs by one day, the entire project will be completed one day early. This is because the critical paths are the paths that will determine the overall project completion time. By reducing the completion time for these two jobs, the overall project completion time will be shortened. This will allow the project to be finished one day earlier than expected.

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The object that is about 15 cm is pencil.

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.

Given:

Measurement = 15 cm

As, the average length for the pencil varies from 7 cm - 17 cm.

and, average length for the desk is 120 cm.

and, the average length for the paper is 30.3 x 40.6cm.

and, the average length for the clip is 4 cm.

and, the average length for the television is 40 cm.

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Answer:

2/n+2

Step-by-step explanation:

Answer:

206

Step-by-step explanation:

cube volume = 5*5*5 +3*3*3 = 125+81 = 206

Answer:

(x^2 - 7)(4x - 3)

Step-by-step explanation:

first, we split the expression by grouping the first two terms in parentheses and the last two terms in parentheses. this gives us:

[tex](4x^{3}-3x^{2})(-28x+21)[/tex]

next, we factor out the GCF of each group. this gives us:

[tex]x^{2}(4x-3)-7(4x-3)[/tex]

finally, all you have to do is take each factored-out term and put them together into a group/expression. the leftover expression from both groups is the same value, so you get:

[tex](x^{2}-7)(4x-3)[/tex]

hope this helped, good luck!

Using properties of triangles, Correct options are A,B and D. AE = EB, EG || AC and AC = 2 EG.

A triangle has three sides, three angles, and three vertices, which are its characteristics.

A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.

Any two triangle sides can add up to a length that is longer than the third side.

A triangle's total angles are always 180 degrees.

A triangle's outside angles are always a sum of 360 degrees.

The total of the parallel interior and exterior angles is additional.

From the given figure,

As E is the mid point of BA,

So, BE = EA

As it is clearly seen that EG is parallel to AC = EG||AC

Further,

As, EG is intersecting AB and BC at mid points,

⇒ AC = 2EG

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A truth table deconstructs a logic function by outlining all possible outcomes the function might achieve.

A truth table offers a way to map out the potential truth values in an expression and predict their results. The table has a row for each conceivable combination of truth values and a column for each variable in the expression. There is also a column that displays the results of each set of values.

For propositional logic formulations, this tool builds truth tables. There are numerous formats available for entering logical operators. As an illustration, the propositional formula p q r could be represented as p / q -> r, p and q => not r, or p && q ->!r. You can enter the connectives and as T and F.

P Q (Q ∧ P)

F F F

F T F

T F F

T T T

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There is a difference in average systolic blood pressure between smokers and non-smokers.

To evaluate if average systolic blood pressure differs by smoking status, we need to calculate the mean systolic blood pressure for both smokers and non-smokers. We can calculate the mean systolic blood pressure for smokers by taking the sum of systolic blood pressure values for all smokers in the sample, divided by the number of smokers in the sample. This formula can be written as:

Mean Systolic Blood Pressure for Smokers = (Sum of Systolic Blood Pressure Values for all Smokers) / (Number of Smokers)

Similarly, we can calculate the mean systolic blood pressure for non-smokers by taking the sum of systolic blood pressure values for all non-smokers in the sample, divided by the number of non-smokers in the sample. This formula can be written as:

Mean Systolic Blood Pressure for Non-Smokers = (Sum of Systolic Blood Pressure Values for all Non-Smokers) / (Number of Non-Smokers)

Once we have calculated the mean systolic blood pressure for both smokers and non-smokers, we can compare the two means to evaluate if there is a difference in average systolic blood pressure between smokers and non-smokers.

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Answer:

42

Step-by-step explanation:

determinant of matrix

= 5(2) - 8(-4)

= 10 - (-32)

= 10 + 32

= 42

Answer:

32

Step-by-step explanation:

the determinant of matrix

[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] = ad - bc

then

[tex]\left[\begin{array}{ccc}5&-4\\8&2\\\end{array}\right][/tex]

= (5 × 2) - (- 4 × 8) = 10 - (- 32) = 10 + 32 = 42

Answer: Anything that has the same two numbers

Step-by-step explanation:

You don't have a picture, so I'm basing this off of what I know. A number over another number that is the same is equivalent to one.

The chance of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000 is 0.0003%.

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The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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The equation which represents the graph function is g ( x ) = f ( x - 3 ) + 3

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = x³   be equation (1)

Now , the graph of the function f ( x ) is plotted with the exponent value meeting closely at ( 0 , 0 )

And , the function which describes the function g ( x ) is given by

g ( x ) = f ( x - 3 ) + 3

Hence , the function is g ( x ) = f ( x - 3 ) + 3

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The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.

Original cylinder: The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.

Scaled cylinder 1: The first scaled cylinder has a scale factor of 2, so its radius is 2 * 2 = 4 units and its height is 13 * 2 = 26 units. Its volume is given by: V = πr²h = π * 4² * 26 = 672π cubic units.

Scaled cylinder 2: The second scaled cylinder has a scale factor of 3, so its radius is 2 * 3 = 6 units and its height is 13 * 3 = 39 units. Its volume is given by: V = πr²h = π * 6² * 39 = 1764π cubic units.

Scaled cylinder 3: The third scaled cylinder has a scale factor of 4, so its radius is 2 * 4 = 8 units and its height is 13 * 4 = 52 units. Its volume is given by: V = πr²h = π * 8² * 52 = 3072π cubic units.

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Answer:

20,45 kg,

Step-by-step explanation:

45  Lb * (1 kg / 2,2 Lb) + (12 Austrália * (1 kg / 35 ,2 Austrália)) = 20,45 kg

Um resposta é 20,45 kg.

The amount of juice for 30% orange juice is 22 liters,

and the amount of juice for 5% orange juice is 3 liters mixed together in order to get 25 Liters.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given One canned juice drink is 30% orange juice, another is 5% orange juice,

Let x and y be the amount of 30% and 5% orange juice respectively,

according to condition

0.30x + 0.05y = 0.27(25) .........(1)

x + y = 25.........(2)

Multiply the second equation by -0.05,

0.30x + 0.05y = 0.27(25)

-0.05x - 0.05y = -0.05(25)

Add equation to eliminate y,

0.30x - 0.05x + 0.05y - 0.05y = 0.27(25) - 0.05(25)

Solve for y,

0.25x = 5.5

x = 5.5/.25

x = 22

substitute value of x in equation,

x + y = 25

(22) + y = 25

y = 25 - 22

y = 3

Hence the amount of 30% orange juice is 22 liters and the amount of 5% orange juice is 3 liters.

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the fourth one. I know it is correct, you may look it up on the desmos graphing calculator if you have suspicion it is not.

The solution to the system of equations is 6x – 2y = -14 with x = -4 and y = -5

4x – 3y = -31

To find x or method, you must first make one of the words the same so that they may cancel out.

To determine the x terms, we will make the y terms the same in this example.

To do so, multiply the first equation by three, yielding:

18x – 6y = - 42

And multiply the second equation by two to get:

8x – 6y = - 62

Now that we have the y terms, you may cancel them out.

You now have the following two equations:

18x = -42

8x = -62

The next step is to combine them, since the preceding – and – form a +.

This implies that you are left with one equation

26x = -104

Now divide by 26 on each side to get:

x = -4

As you have x, you substitute it into one of the ORIGINAL equations.

6x – 2y = -14

Substitute x in:

6(-4) – 2y = -14

-24 – 2y = -14

Add 24 on each side to get:

-2y = 10

y = -5

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Answer:

42=3.5x+2y

Step-by-step explanation:

3.5 is the cost of the cakes and 2 is the cost of the oreos. 42 is how much Francis can spend

On evaluating the fraction 3 3/4 the cost of 3 3/4 kg of sugar is $30.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The cost of 1 kg of sugar is = $ 80

The amount of sugar is given in fractional form - 3 3/4 kg

The equation for cost of 3 3/4 kg sugar is -

Cost = 3 3/4 × 8

Solve the fractional part first -

Cost = 15/4 × 8

Simplify the equation -

Cost = 15/4 × 8

Cost = 120/4

Cost = 30

Therefore, the cost value is obtained as $ 30.

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If the cost of 1 kg of sugar is $8, what is the price of 3 3/4 kg?

The required value of exponential function for the given values of x are 1.43, 1 , 0.7.

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. ​

We have,

f(x) = [tex](0.7)^{x}[/tex]

So, at x = -1

f(x) = (0.7)^-1

f(x) = 1.43

At x = 0

f(x) = (0.7)^0

f(x) = 1

At x = 1

f(x) = (0.7)^1

f(x) = (0.7)

Thus, required value of function are 1.43, 1, 0.7

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Answer:

Step-by-step explanation:

In a​ right-skewed distribution, which of the following is​ true? The mean tends to be greater than the median.