The following scenario represents a proportional relationship.

John's last paycheck was $450 for 40 hours of work.

What is the constant of proportionality?

Enter your answer in the box.

By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.

The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.

We have the inequality:

-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49

We can rewrite this inequality as:

-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1

Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.

As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:

-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1

0 ≤ lim f(x) ≤ 1

Therefοre, by the squeeze theοrem, we have:

lim f(x) = 0 as x apprοaches -5.

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The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The distributive property is given as:

a(b + c) = ab + ac

3(20 + 16) = 3(20) + 3(16) = 60 + 48 = 108

Also:

4(13 + 14) = 4(13) + 4(14) = 52 + 56 = 108

The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108

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The value of the expression -x³ + 3x² - x + 20 when x = -1 is 23.

Given the expression in the question;

-x³ + 3x² - x + 20

To determine the value of the expression,

First, we substitute -1 for x in the expression:

-( -1 )³ + 3( -1 )² − ( -1 )) + 20

Next, we simplify each term using the order of operations (also known as PEMDAS):

-( -1 )³ = -( -1 ) = 1

(recall that the exponent is evaluated first, then the negative sign is applied)

3( -1 )² = 3(1) = 3

(recall that the exponent is evaluated first)

-( -1 ) = 1

(recall that subtracting a negative is the same as adding a positive)

Now, putting these simplified terms back into the original expression, we get:

1 + 3 + 1 + 20

Finally, we add these terms together to get the final answer:

23

Therefore, the value of the expression is 23.

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The answer of the given question based on the triangle which is  sequences of transformations of △ABC exhibit the congruence between the two triangles the answer is given below,

Congruent triangles are two or more triangles that have  same shape and size. In other words, they have same angles and  same side lengths.

The congruence between the two triangles can be exhibited by the following two sequences of transformations:

a) a rotation of 180° about the origin and a translation of 1 unit left

c) a rotation of 180° about the origin and a translation of 1 unit right

Option b) and option e) involve a translation and a reflection that do not preserve orientation, so they do not result in a congruent triangle.

Option d) involves two reflections, which do not commute, so the order matters. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit right, followed by a reflection across the line x = -1, which does not result in a congruent triangle.

Option f) is similar to option d) in that it involves two reflections that do not commute. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit left, followed by a reflection across the line x = 1, which also does not result in a congruent triangle.

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The inverse functions and the domains and ranges of the inverse functions can be presented as follows;

A. The inverse function of f(x) is; [tex]f^{-1}(x) = \frac{3-x}{7\cdot x}[/tex]

B. f(g(x)) = [tex]\frac{3}{7\times \frac{(3-x)}{7\cdot x} + 1}[/tex] = x

C. The inverse function reverses the effect of the function. The inverse function is therefore;

x [tex]{}[/tex]      y

10[tex]{}[/tex]     5

6[tex]{}[/tex]      8

5[tex]{}[/tex]      9

4[tex]{}[/tex]      13

2) Domain; 10, 6, 5, 4

Range; 5, 8, 9, 13

An inverse function maps the output, or y-value of a function to the input value or x-value of the function.

2. A. f(x) = 3/(7·x + 1)

The inverse function can be found as follows;

Let f(x) = y

y = 3/(7·x + 1)

(7·x + 1) = 3/y

7·x = (3/y) - 1 = (3 - y)/y

x = (3 - y)/(7·y)

Plugging in x = f⁻¹(x), and y = x, to get;

B. g(x) = (3 - x)/(7·x)

f(x) = 3/(7·x + 1)

f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = 3/(((3 - x)/(x)) + 1) = 3/(3/x - 1 + 1)

3/((3/x - 1 + 1) = 3/(3/x) = 3 × x/3 = x

Therefore; f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = x

C. The inverse of the function is the function that produces the input of the function from the function's output, therefore, the inverse of the function can be presented as follows;

x [tex]{}[/tex]     y

10[tex]{}[/tex]    5

6[tex]{}[/tex]     8

5[tex]{}[/tex]     9

4[tex]{}[/tex]     13

2) The domain is the set of the possible inputs of the function, and the range is the set of the possible outputs of the function.

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Answer: i think the answer is A

Step-by-step explanation:i think bc i is a quadratic function

Answer: D

Step-by-step explanation:

A and B don't make sense, since the maximum value > 0, and the function is more negative than positive. C and D are our remaining answers. C would be incorrect, since if X reaches \infinity , the function isn't infinite. The only way to make C correct, is a sudden spike in the function to infinity. So, the only correct answer is D.

Hope this helps (please respond if I'm wrong)

Answer:

The answer is (f.g)(x) = 12x^2 - 9.

Step-by-step explanation:

To find (f.g)(x), we need to apply the composition of functions formula, which is:

(f.g)(x) = f(g(x))

First, we need to find g(x):

g(x) = 3x^2

Now, we need to plug g(x) into f(x) in place of x:

f(g(x)) = 4(g(x)) - 9

= 4(3x^2) - 9

= 12x^2 - 9

Therefore, (f.g)(x) = 12x^2 - 9.

Hope this helps, I'm sorry if it doesn't! If you need more help, ask me! :]

[tex]\dfrac{x^{2} + 10x + 21}{x + 7} = \dfrac{(x+3)(x+7)}{x + 7} = \bf x + 3[/tex]

___

[tex]x^{2} + 10x + 21 = x^{2} + 3x + 7x + 21 = x(x+3)+7(x+3) = (x+3)(x+7)\\[/tex]

The equation would be y = 0.50x + 10.00, and we have drawn the graph for the same.

What is the graph of the equation?

The graph of an equation is a visual representation of the set of all solutions (points) that satisfy the equation.

To find the equation of the line, we use the slope-intercept form of a linear equation, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

In this case, we are given the slope of the line (0.50) and the y-intercept (10.00), so we can simply substitute these values into the equation:

y = 0.50x + 10.00

This gives us the equation of the line in slope-intercept form. We can use this equation to find the cost of a cab ride for any distance x (in miles) by substituting the value of x into the equation and solving for y (the fare).

Now let's draw the graph of the equation y = 0.50x + 10.00, we get

Hence, the equation would be y = 0.50x + 10.00, and we have drawn the graph for the same.

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The width of the patio, given the area of the pool and the patio, can be found to be 19. 59 ft

The area of the pool is said to be equal to the area of the patio which means that to find the width of the patio, you need to find the area of the pool which is :

= 16 ft x 24 ft

= 384 ft ²

The patio is such that the width is the same on every side which makes it a square shaped patio. The width of the patio is therefore:

Width = √ Area of square patio

= √ 384

= 19. 59 ft

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Answer:

In question 3 a triangle can be formed however in question 4 it can't be formed

Step-by-step explanation:

there is a theorem that states that two sides of a triangle when added up should be greater than the third one which isn't true in question 4 as

12+9=21 so its equal to the third side but not greater hence a triangle can't be formed

Answer:

We can use the distance formula to find the distance between the center of the circle (2, -3) and the point (-1, -6), which should be equal to the radius of the circle.

Step-by-step explanation:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Distance = √[(-1 - 2)² + (-6 - (-3))²]

Distance = √[(-3)² + (-3)²]

Distance = √(18)

So the radius of the circle is equal to √(18) or approximately 4.24.

Answer:

It is not clear what is meant by "a log can Kate use to fill remaining 1/3 meters." However, if we assume that Kate has a gap of 1/3 meters that she needs to fill, she could use a log that is 1/3 meters long to fill the gap. Alternatively, she could use any other object that is 1/3 meters long to fill the gap.

According to the solving Triangle The Value of X in the given figure is 20°

Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees which is called interior angles.

The three angles are given as ∠1=84°, ∠2=41°, ∠3=2x+15°.

Adding three angles

84° + 41° + 2x + 15° = 180° (sum of interior angle is 180°)

140° + 2x = 180°

2x = 180°-140°

2x = 40°

x = 20°

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Answer:

To find the price of 3 tons of concrete, we need to first figure out how much Trey paid per ton of concrete.

Since Trey paid 42 dollars for 2/3 ton of concrete, we can set up a proportion:

2/3 ton = 42 dollars

1 ton = x dollars

To solve for x, we can cross-multiply:

(2/3) * x = 42 * 1

2x = 126

x = 63

So, Trey paid 63 dollars per ton of concrete.

To find the price of 3 tons of concrete, we can multiply the cost per ton by the number of tons:

3 tons * $63/ton = $189

Therefore, the price of 3 tons of concrete is $189.

Based on the above, the Perimeter of the triangle DEF is 43.3 units

A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, reduction, multiplication, division, exponents, and so forth.

Given the triangle DEF. Using trigonometric ratio:

sin(38) = EF / 18EF = 11.1

Also: cos(38) = DF / 18DF = 14.2

The perimeter of triangle

DEF = DE + EF + DF

= 18 + 11.1 + 14.2 = 43.3 units

Hence, the Perimeter is 43.3 units

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Answer:

See below.

Step-by-step explanation:

We're asked to prove that ΔSTV ≅ ΔTUW.

Let's begin by reviewing what was given to us.

Because we already have one side and an angle congruent, we need to prove that another angle or side is congruent.

Our goal is to find a Congruency Postulate to prove that ΔSTV ≅ ΔTUW.

As we can see in the diagram, ∠STV ≅ ∠UTV as they're vertical angles. This is possible because Line Segment SV ≅ & ║ Line Segment TW.

We are now able to prove that ΔSTV ≅ ΔTUW with the Angle-Side-Angle Triangle Congruency Postulate (ASA). We proved, and were given 2 angles, and 1 side.

Summary:

∠STV ≅ ∠UTV | Vertical Angles.

ΔSTV ≅ ΔTUW | ASA.

]Therefore , the solution of the given problem of deviation comes out to be  the confidence interval contains both positive and negative values.

Statistics uses variance as a gauge of difference. The image of that figure is used to compute the average variance between the collection and the mean. It includes those data points itself into the calculations, unlike many other real measures of variability, by comparing also every figure to the mean.

Here,

Since the population standard deviation is unknown and the sample number is less than 30, we can use a t-distribution to build the confidence interval. The confidence interval's calculation is:

=>CI =  x t /2 × (s/n).

Since we need a 99% confidence range, = 0.01 and /2 = 0.005, and (n-1) = (49-1) = 48 is the number of degrees of freedom.

We discover that t/2 = 2.678 using the t-distribution table with 48 degrees of freedom and 0.005 significance level.

When we enter the numbers, we obtain:

=> CI = 3.1 ± 2.678 * (16.5/√49) = 3.1 ± 7.34

The estimated mean net change in LDL cholesterol following treatment, according to the 99% confidence range, is (4.24, 10.44) mg/dL.

We cannot say with 99% certainty that garlic is effective at lowering cholesterol because the confidence interval contains both positive and negative values.

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Answer:

James needs 5 gallons of water.

Step-by-step explanation:

1 gallon = 8 pints

40 ÷ 8 = 5

5 gallons

Answer:

A

Step-by-step explanation:

Range referes to the smallest and largest values, so the answer you have circles is correct.

Good Job!

Answer: A) Range

Step-by-step explanation:

The range is the difference between the biggest and smallest numbers (or, in this case, folders). If Jack wants to find a notebook that will fit a small and large folder, he will need to find the range.

Note that the graphing form and vertex of each quadratic function are given as follows:


a) for f(x)=x² +6x+15, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).

b) for y= x²-4x+9 the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

c) for  f(x)= x² +8x, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).

d) for . y=x² - 4x+9, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

a. To complete the square for the quadratic function f(x)=x² +6x+15, we add and subtract the square of half of the coefficient of x, which is (6/2)² = 9:

f(x) = x² + 6x + 15

= (x² + 6x + 9) + 6

= (x + 3)² + 6

Therefore, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).

b. To complete the square for the quadratic function y= x^2-4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:

y = x^2 - 4x + 9

= (x^2 - 4x + 4) + 5

= (x - 2)² + 5

Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

c. To complete the square for the quadratic function f(x)= x² +8x, we add and subtract the square of half of the coefficient of x, which is (8/2)² = 16:

f(x) = x² + 8x

= (x² + 8x + 16) - 16

= (x + 4)² - 16

Therefore, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).

d. To complete the square for the quadratic function y=x² - 4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:

y = x² - 4x + 9

= (x² - 4x + 4) + 5

= (x - 2)² + 5

Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

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Top Career Choice: Registered Nurse

Job Description: Registered Nurses (RNs) are responsible for providing and coordinating patient care.

Personal Attributes: Compassionate, Detail-oriented, Patient, Good communication skills, Ability to work under pressure, Physical and emotional stamina

Education: A Bachelor of Science in Nursing (BSN) is the preferred degree for RNs.

Experience: RNs typically gain experience through clinical rotations during their nursing program, as well as through internships or residency programs.

Certification: RNs can earn additional certifications in specialties such as critical care, emergency nursing, or pediatric nursing.

Employment: RNs can work in a variety of settings, including hospitals, clinics, long-term care facilities, and schools.

Making a career choice opens the door to financial security. The earning potential of an occupation is a major consideration for most people when choosing a suitable career. Choosing the right profession means you will be able to have economic security, which is an important factor in our overall well-being.

Full question "Making Connections: Selecting a Career. Apply Your Knowledge" Top Career Choice, Job Description, Personal Attributes, Education, Experience, Certification, Employment, Job Outlook, Earnings, Work Environment, Related Occupations

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The Pearson correlation coefficient r for the given points is: 0.191.

We can use the formula for Pearson correlation coefficient r:

r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)²][nΣ(y²) - (Σy)²])

where n is the number of data points, Σ represents the sum, x and y are the variables, and xy, x², and y² represent the products and squares of the variables.

We can first calculate the sums and products:

n = 7

Σx = 28

Σy = 36

Σ(x²) = 140

Σ(y²) = 248

Σ(xy) = 152

Using these values, we can plug them into the formula for r:

r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)² ][nΣ(y²) - (Σy)²])

= [7(152) - (28)(36)] / sqrt([7(140) - (28)^2][7(248) - (36)²])

=  56 / 293

= 0.191

Therefore, the Pearson correlation coefficient r is 0.191.

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Answer:

38°

Step-by-step explanation:

this equal to 38° because angle EGD and angle IGJ are corresponding angles

The domain and range of given graph is Domain: (-∞, ∞) Range: (0, ∞)

What is Function ?

Function can be defined in which it relates an input to output.

The horizontal axis (x-axis) represents the input values, while the vertical axis (y-axis) represents the output values.

To identify the domain and range of this function from the graph, we can look at the values that the function takes on as well as the values that are excluded.

From the graph, we can see that the function appears to be increasing without bound as the input values increase. This means that the domain of the function is all real numbers or (-∞, ∞).

We can also see that the function appears to be taking on only positive values, and never touches or crosses the x-axis. This means that the range of the function is all positive numbers or (0, ∞).

Therefore, The domain and range of given graph is Domain: (-∞, ∞) Range: (0, ∞)

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Therefore, the likelihood of a vehicle accident just on road is 3/25. The ultimate solution is 3/25 because there is no other way to simplify this fraction.

The probability is typically defined as the proportion of favourable findings to all results inside the poll area. The formula for probability of an event is P(E) = (Number of positive occurrences) (Sample space).

If the odds against a car crash on the road are stated as "22:3", it means that for every 22 unfavorable outcomes (no car crash), there are 3 favorable outcomes (car crash).

The total number of outcomes is 22 + 3 = 25.

Therefore, the probability of a car crash on the road is:

3 favorable outcomes / 25 total outcomes = 3/25

So, the probability of a car crash on the road is 3/25. This fraction cannot be reduced further, so the final answer is 3/25.

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Answer:

Step-by-step explanation:

[tex]i=80[/tex]° (opposite angles in a cyclic quadrilateral are supplementary)

[tex]e=84[/tex]° (An exterior angle of a cyclic quadrilateral is equal to the interior

             angle at the opposite vertex.)      

The sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.

The length οf the rοad is 5/9 οf a mile.

Tο find the length οf the sectiοn that needs tο be repaved, we can multiply

the length οf the rοad by the fractiοn that represents the fractiοn οf the rοad that needs tο be repaved:

length οf sectiοn tο be repaved = (2/3) * (5/9) mile

Multiplying the numeratοrs and denοminatοrs separately, we get:

length οf sectiοn tο be repaved = (2 * 5) / (3 * 9) mile

Simplifying the fractiοn, we get:

length οf sectiοn tο be repaved = 10/27 mile

Therefοre, the sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.

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Answer:

Step-by-step explanation:

x= 20 (12) =240, Interest%= 6.4, Pv + 0, PMT= 275,temporarily skip FV,P/Y and C/Y= 12,

After 20 years, the value is $133,970.26

The simple interest value of the investment after 20 years is approximately $30,637.45

Future value (FV) is the value of an investment at a future date, based on a series of regular payments (or a lump sum) and assuming a certain interest rate over a period of time. In other words, it's the amount of money an investment will be worth after earning a certain rate of interest over a certain period of time.

Simple interest is a method of calculating interest on a loan or investment, where interest is only charged on the original principal amount. In other words, the interest is not compounded over time.

In the given question:

We can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where: FV = future value

PMT = monthly payment

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values, we have:

FV = 275 x [(1 + 0.064/12)^(12*20) - 1] / (0.064/12)

FV = 275 x (1.00533²⁴⁰ - 1) / 0.00533

FV = 275 x 111.034

FV = 30,637.45

Therefore, the value of the investment after 20 years is approximately $30,637.45.

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