The functions S(t) = 1.0841t + 17.392 models the amount of money, S, in billions of dollars, the United States government spent on science, space, and technology for the time period 1999-2009, where t is the number of years since 1999.
a. Write the constraints for the variable t using set-builder notation.

b. Determine the value of S(7)

c. Interpret the value of S(7) in context

d. Name the key feature that is found when solving S(t) = 0. Then, label the key feature on the graph of S(t) = 1.084t + 17.392.

e. determine if the value for S(t) = 0 is reasonable for the context. Explain why or why not.

4,034.06 ,5,965.94 are confidence interval for the population average wages at the factory.

What is confidence interval estimation?

Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

                                              If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty.  Another term for probability in statistics is confidence.

The formula for confidence interval estimation is:

μ = M ± Z(sM)

where:

M = sample mean

Z = Z statistic determined by confidence level

sM = standard error = √(s2/n)

M = 50000

Z = 2.58

sM = √(30002/64) = 375

μ = M ± Z(sM)

μ = 50000 ± 2.58*375

μ = 50000 ± 965.94

μ = 4,034.06 ,5,965.94

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Answer:I hope this helpful mark me brainlist if correct then no if wrong

Step-by-step explanation:

P times 3 =-0.0027

Use the commutative property to reorder the terms

3p=-0.0027

Divide both sides of the equation by 3

p=-0.009 or p=-9/1000

Answer:

Below

Step-by-step explanation:

2.42 x 10^4  = 24200

 24200

+ 23580

 47 780    or   4.778 x 10^4

Answer:

ANS:- 15.9

Step-by-step explanation:

5814/365 = 15.9

The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x² + x + __ = (_____)²

Now,

Since, The expression is,

⇒ x² + x + __ = (_____)²

Hence, We can add the number to form the complete square as;

⇒ x² + x + 1/4 = x² + x + (1/2)²

                     = ( x + 1/2)²

Thus, The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

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We can estimate the number of adult partons at 2187 by solving equations.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

A function is an equation that has only one answer for y for every possible value of x.

When utilizing a function, each input of a specific type receives exactly one output.

A function is commonly referred to as f(x) or g instead of y. (x).

Because f(2) instructs us to do so, we should figure out the value of our function when x is equal to 2.

So, the total number of adults present was thus:

Let a be an adult, and b and c be kids.

Ticket totals:

a + c = 5200

c = (5200-a)

Total amount:

7.50a + 4.50c = 29961

In the first equation, swap out c with (5200-a).

7.5a + 4.5(5200-a) = 29961

7.5a + 23400 - 4.5a = 29961

7.5a - 4.5a = 29961 - 23400

3a = 6561

a = 6561/3

a = 2187

Therefore, we can estimate the number of adult partons at 2187 by solving equations.

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Answer:

c= 1.5t, c=t+0.5t and c=(1+0.5)t

Step-by-step explanation:

Given that, Clare scored 50% more points than Tyler, c is the number of points that Clare scored and t is the number of points that Tyler scored,According to question,c = 150% of tc = 1.5tHence, the correct options are c = 1.5t, c = t+0.5t and c = (1+0.5)t

Answer:

x> -10

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf 157.1 \ units^2}[/tex]

Step-by-step explanation:

Diameter = 20

Radius = Diameter/2 = 20/2 = 10

[tex]\displaystyle =\frac{\pi r^2}{2} \\\\r = 10\\\\= \frac{\pi (10)^2}{2} \\\\= \frac{100 \pi}{2} \\\\= \frac{314.2}{2} \\\\= 157.1 \ units^2\\\\\rule[225]{225}{2}[/tex]

In 2000, the population of the state was 23.1 million, After 13 years , the population of the state reach 28.3 million.

What is population?

The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a given area is depicted by this indicator. The annual changes in population brought on by births, deaths, and net migration are measured as growth rates.

Given:

[tex]A = 23.1e^0^.^0^1^5^2^t[/tex] models the population of US

where A is in million

t is years after 2000.

(a) We have to find the population in 2000.

In 2000, t = 0

Plug t = 0 in the above equation

[tex]A(0) = 23.1e^0^.^0^1^5^2^(^0^)\\A = 23.1[/tex]

Hence, in 2000 the population is 23.1 million.

(b) To find when the population of the state reach 28.3 million.

Plug A = 28.3 in above equation and solve for t.

[tex]28.3 = 23.1e^0^.^0^1^5^2^t\\e^0.0152t = \frac{28.3}{23.1} \\t*ln(0.0152) = ln( \frac{28.3}{23.1})\\t = 13.35718\\t = 13[/tex]

Hence, after 13 years the population of the state reach 28.3 million.

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Answer:

m∠A = 60

m∠D = 60

Step-by-step explanation:

∆ABC and ∆DEF are congruent triangles

So,

m∠A = m∠D

x + 30 = 2x

2x - x = 30

x = 30

So,

m∠A = x + 30 = 30 + 30 = 60

m∠D = 2x = 2(30) = 60

Thus, m∠A and m∠D are 60°

Answer:

Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40

Marie is $10 000 richer

Step-by-step explanation:

Albert

(a) $1000 at 1.2 % compounded monthly

A = P (1 + r/n )^nt

A = 1000(1 + 0.001)¹²⁰ = $1127.43

(b) $500 losing 2%

0.98 × 500 = $490

(c) $500 compounded continuously at 0.8%

A = Pe^rt

  = 500e^0.008 * 10

 =  $541.64

(d) Balance

Total = 1127.43 + 490.00+ 541.64 = $2159.07

Marie

(a) 1500 at 1.4 % compounded quarterly

A = 1500(1 + 0.0035)⁴⁰ = $1724.99

(b) $500 gaining 4 %

1.04 × 500 = $520.00

(c) Balance

Total = 1724.99 + 520.00 = $2244.99

Hans

$2000 compounded continuously at 0.9 %

A = 2000e^0.009 * 10

  = $ 2188.35

Max

(a) $1000 decreasing exponentially at 0.5 % annually

A = 1000(1 - 0.005)¹⁰= $951.11

(b) $1000 at 1.8 % compounded biannually

A = 1000(1 + 0.009)²⁰ = $1196.29

(c) Balance

Total = 951.11 + 1196.29 = $2147.40

Marie is $10,000 richer at the end of the competition.

Hope this helps!!! :)

The total weight of the water in a filled tank will be equal to 16,336 Pounds.

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given data in the question,

Radius, r = 10/2 = 5 ft.

Use the equation of the volume of a sphere,

V = 4/3πr³

We only require half of it then,

V =  2/3πr³

V = 261.8 ft³

So, the total weight will be,

W = 261.8 × 62.4

W = 16,336 Pounds.

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Answer:

a. [tex]1 * 10^{-10}[/tex]

Explanation:

A converted to standard notation is the same number.

Answer:

6790 km

Step-by-step explanation:

move the decimal 3 places to the right.

For the function in the given case the constraint on domain can be written as  x ≥ 182. The correct option is (a).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

Suppose the amount of money spent be x.

And, the number of food items be y.

Now, as per the question the function can be written as follows,

y = x/182

As the number of food items can only be positive integers, the values of x must be the multiples of 182.

Thus, the expression for the domain can be written as x ≥ 182.

Hence, the constraint on the domain is given as x ≥ 182.

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The expected value of this game will be 1,784.75.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

In a lottery game, a player picks six numbers from 1 to 28. Assuming the player matches each of the six numbers, they win 50,000 bucks. In any case, they lose $1.

Then the probability of winning (p) and losing (q) is given as,

p = 1 / 28

q = 27 / 28

Then the expected value is given as,

E(x) = 50,000 (1 / 28) - 1 (27 / 28)

E(x) = 1785.714 - 0.964

E(x) = 1,784.75

The expected value of this game will be 1,784.75.

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Answer:

the width of the rectangle is -5/3 inches.

Step-by-step explanation:

To find the perimeter of the rectangle, we add together the lengths of all four sides. Since the rectangle is 5 inches long and 2x inches wide, the perimeter is given by:

Perimeter = 5 + 2x + 5 + 2x = 10 + 4x

To find the area of the rectangle, we multiply the length by the width. The area is given by:

Area = 5 * 2x = 10x

Setting the perimeter equal to the area, we have:

10 + 4x = 10x

Subtracting 10 from both sides, we have:

4x = 10x - 10

Combining like terms, we have:

-6x = -10

Dividing both sides by -6, we have:

x = 10 / -6

Simplifying, we have:

x = -5/3

Answer: To find the value of m in the equation W = 1/2 * m * v^2, you need to know the values of W and v. The variable m represents the mass of the object, and W represents the kinetic energy of the object. The equation states that the kinetic energy of an object is equal to 1/2 of its mass multiplied by its velocity squared.

If you are given the values of W and v, you can solve for m by rearranging the equation as follows:

m = 2 * W / v^2

Plugging in the values of W and v will give you the value of m.

For example, if W = 100 joules and v = 10 meters per second, the equation would be:

m = 2 * 100 joules / 10 m/s^2 = 20 kilograms

This is the mass of the object.

[tex]m=\frac{2W}{v^{2} }[/tex].

[tex]W=\frac{1}{2} mv^{2}[/tex]

[tex]\frac{W}{\frac{1}{2} v^{2} }=m\\ \\[/tex]

[tex]m=\frac{W}{\frac{1}{2} v^{2} }\\ \\m=\frac{2W}{v^{2} }[/tex].

Answer:

Step-by-step explanation:

Let x be the number.

The square of the number is x2

Increased by twice the number means add 2x.

So your equation is :

X2 +2x = 48.

Can you take it from here?

The asked number is 12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, When the square of a certain number is added to the number, the result is the same as when 48 is added to three times the number.

Let the number be x,

x²+x = 48X3 + x

x² = 144

x = 12

Hence, The asked number is 12.

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Answer:

y=2x+8

Step-by-step explanation:

-6x+3y=24

-6x+6x+3y=24+6x  ==> isolate the y variable

3y=6x+24  ==> simplify

(3y=6x+24)/3

y=2x+8  <== y=mx+b  <== slope intercept form

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The point which satisfies equation is (-2,4)

What is circle?

A circle could be a form consisting of all purposes during a plane that are at a given distance from a given point, the centre.

Main body:

The center of circle formula is also known as the general equation of a circle. In a circle, if the coordinates of the center are (h,k), r is the radius, and (x,y) is any point on the circle, then the center of circle formula is given below:

Formula of circle =

(x - h)² + (y - k)² = r²

According to question:

center of circle = (2,1)

diameter of circle = 10 units

radius = 5 units

equation of circle ⇒

(x - 2)² + (y - 1)² = 25

for a point to lie on circle , it need to satisfy the equation of circle:

A) (1,-3)

⇒(1 - 2)² + (3 - 1)²

⇒(-1)² +2²

⇒5

so it does not lie on circle.

B) (-2,4)

⇒(-2 - 2)² + (4 - 1)²

⇒-4²+3²

⇒ 25

so, it satisfies the equation.

hence, the point which satisfies equation is (-2,4)

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Hello,

I hope you and your family are doing well!

Let's call Sydney's age x and Devaughn's age y. We know that y = 3x and x + y = 116.

Substituting the first equation into the second equation gives:

3x + x = 116

4x = 116

x = 29

So Sydney's age is 29.

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Happy Holidays!

The type of the function for the given graph f(x) on the right is odd function.

An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.

The link between varying amounts and other variables was the foundational idea behind functions. The effect of time on a planet's position serves as an example of this. The infinitesimal calculus was used to develop the concept in the past, beginning at the end of the 17th century and continuing through the 19th century.

An odd function's graph possesses rotational symmetry with respect to the origin, which means that it doesn't change after being rotated by 180 degrees around the origin.

Therefore, The type of the function for the given graph f(x) on the right is odd function.

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The expression that is equivalent to  ∛ 5 * [tex]\sqrt[5]{4}[/tex] is [tex]5^{1/3}*4^{2/5}[/tex]

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.

This equation represents exponents in fraction form and the basics for the calculation is from

x^(b/n)

[tex]\sqrt[n]{x}^{b}[/tex]

Rewriting the expression is done as below

∛ 5

= [tex]5^{1/3}[/tex]

and

[tex]\sqrt[5]{4}[/tex]

[tex]= 4^{2/5}[/tex]

combining both gives

∛ 5 * [tex]\sqrt[5]{4}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex] is the equivalent expression

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The confidence interval of this confidence level as calculate from the given data is 3.68 and 99% respectively.

Number of random sample (n)=28

Sample Standard deviation (S)=19.52

Confidence interval = 439.23 -  460.77 =  21.54

t = s/root of n

=19.52 /5.29

=3.68

v = n -1 = 27

now, confidence level

= 1 - alpha

= 99%

Confidence Interval, put simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.

The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.

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The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.

We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.

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Answer:

Step-by-step explanation:

1) x - 1 = 2x - 2

-x = -1

x = 1

2) 4x = x + 3

3x = 3

x = 1

3) x + 1 = x + 1

infinite solutions (parallel lines)

For graphing, just look at the y-intercept, in the equation y = mx + b.

b is the y-intercept, so, for you plot the y-intercpet on the y-axis. You look at m, which is the slope. For positive, you go up how many ever it says in the numerator and then to the right how many ever it says in the denominator. For a negative you do the same thing except you go down and then to the right, or up and to the left. For positive there is only up and then to the right. I hope this answers your question.

The time needed for the account value to reach 11200 dollars is approximately 15.9 years.

Simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

( A/P - 1 ) = rt

t = ( A/P - 1 ) / r

t = ( $11200/$5400 - 1 ) / 6.75%

t = ( $11200/$5400 - 1 ) / 6.75/100

t = ( 56/27 - 1 ) / 0.0675

t = ( 29/27 ) / 0.0675

t = 15.9 years.

Therefore, the required time to reach the accrued amount is 15.9 years.

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Answer:

203 dollars

Step-by-step explanation:

100 percent = 145

10 percent = 14.5

30 percent = 43.5

43.5 + 14.5 + 145 = 203