Annual U.S. imports from a certain country in the years 1996 through 2003 can be approximated by
I(t) = t^2 + 3.7t + 50 (1 leq t leq 9)
billion dollars, where t represents time in years since 1995. Annual U.S. exports to this country in the same years can be approximated by
E(t) = 0.3t^2-1.4t + 16 (0 leq t leq 10)
billion dollars.
Assuming the trends shown in the above models continue indefinitely, numerically estimate the following. (If you need to use infinite or -infinite, enter INFINITY or -INFINITY, respectively. If an answer does not exist, enter DNE.)
lim t tends to +infinite and
lim t tends to +infinite E(t)/I(t) lim t tends to +infinite E(t)= lim t tends to +infinite E(t)/I(t)=
Interpret your answers.
A. In the long term, U.S. exports to the country will fall without bound and be 0.3 times U.S. imports from the country.
B. In the long term, U.S. exports to the country will rise without bound and be 0.3 times U.S. imports from the country.
C. In the long term, U.S. imports from the country will rise without bound and be 0.3 times U.S. exports to the country.
D. In the long term, U.S. imports from the country will fall without bound and be 0.3 times U.S. exports to the country.
Comment on the results.
A. In the real world, imports and exports can rise without bound. Thus, the given models can be extrapolated far into the future.
B. In the real world, imports and exports can fall without bound. Thus, the given models can be extrapolated far into the future.
C. In the real world, imports and exports do not change, they always stay fixed. Thus, the given models should not be extrapolated far into the future.
D. In the real world, imports and exports cannot rise without bound. Thus, the given models should not be extrapolated far into the future.

Explanation

Given that at a school fair, a person can go on up to 10 rides. The description best represents the number of rides a person can go on would be that the person can try out rides from 0 to 10. This will give;

Answer: Any value less than or equal to 10

$330 in a cookie jar

$29 additional

On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )

A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.

public static double solve(double a, double b, double c, boolean flag)

{     double d = Math.sqrt(b*b - 4*a*c);     if(flag)

{         return (-b + d) / (2*a);     }

else {         return (-b - d) / (2*a);     } }

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Answer: The probability of choosing an ace or a club is 16.

Step-by-step explanation:

The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept. We can use the given slope and point to solve for the y-intercept and write the equation in slope-intercept form.

Given: Slope (m) = -2 and point (-2, -3)

Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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Answer:

,,,,,

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Answer:4

2+2=4 if I have two apples and pick up two more I now have 4 total

Answer:

\(\displaystyle d = 5\sqrt{2}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

Point (-2, 1)

Point (5, 0)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

Solution given:

(x1,y1)=(-2,1)

(x2,y2)=(5,0)

distance=?

we have

distance=\( \sqrt{(x2-x1) ²+(y2-y1) ²}\)

d=\( \sqrt{(5+2)²+(0-1) ²}\)

d=\( \sqrt{50}\)

d=\( 5\sqrt{2}\)units

\( 5\sqrt{2}\)units I travelled.

Answer:

2.43 cu ft

Step-by-step explanation:

mark me brainliest!!

Step-by-step explanation:

4(2x-1) ,x=5

4(2(5)-1)

4(10-1)

4(9)

36

hope it's helpful ❤❤❤❤❤❤

THANK YOU.

#

Answer:

36

Step-by-step explanation:

when you plug 5 into this equation you get 36!

The box plots provide visual representations of the distribution of salaries at two companies, Company A and Company B. To compare the ranges and medians of the data sets, we examine the characteristics of each box plot.

The range of a data set represents the difference between the maximum and minimum values. Looking at the box plots, we can determine that the range of Company A's salaries is larger than the range of Company B's salaries.

This can be inferred by observing the lengths of the whiskers, where the whiskers in Company A's box plot extend further in both the upper and lower directions compared to Company B's box plot.

The median of a data set represents the middle value when the data is arranged in ascending or descending order. Comparing the medians of the two box plots, we can determine that the median of Company A's salaries is higher than the median of Company B's salaries.

This is evident by comparing the positions of the medians within the boxes. In Company A's box plot, the median is closer to the upper quartile, indicating a higher median salary, while in Company B's box plot, the median is closer to the lower quartile, suggesting a lower median salary.

In summary, the range of salaries at Company A is larger than that of Company B, indicating a wider spread of salary values. Additionally, the median salary at Company A is higher than the median salary at Company B, suggesting a higher central tendency or midpoint in the distribution of salaries.

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Answer: No

Step-by-step explanation:

m∠BCD = 31.57° (approx). Hence, the answer of the angle is 31.57 degrees.

In the given diagram, BD is extended through point D to point E, m∠CDE = (9x - 12)°, m∠BCD = (2x + 3)°, and m∠DBC = (3x + 5)°. We need to find m∠BCD.

       We know that m∠BCD = (2x + 3)°

       Substituting x = 92/7, we get:

       m∠BCD = (2 × 92/7 + 3)° = (184/7 + 3)° = 221/7°

       Therefore, m∠BCD = 31.57° (approx). Hence, the answer is 31.57.

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2/3

5/7

24 pack is cheaper

Both the costs are equal.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, target sells a pack of 24 pencils for $3.60 and a pack of 50 pencils for $7.00

Finding the unit rates for each;

1) 24 pencils for $3.60

For $1 ≈ 7 pencils

2) 50 pencils for $7.00

For $1 ≈ 7 pencils

Since, both unit rates are equal.

Hence, both are equal.

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Answer:

\(x^{2}\)-6x=-58

Step-by-step explanation:

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

In the fifth year, Mariah's balance will be higher than Colton's. Therefore, option C is the correct.

The given function is f(t)=400(1.15)t.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, from the table

(0, 500), (1, 550), (2, 600), (3, 650) and (4, 700)

The equations for the given points is y=500+50t

Put t=0, 1, 2, 3, 4 in f(t)=400(1.15)t

When t=0, f(0)=$0

When t=1,

f(1)=400×1.15×1

= $460

When t=2,

f(2)=400×1.15×2

= $920

When t=3,

f(3)=400×1.15×3

= $1380

When t=4,

f(4)=400×1.15×4

= $1840

Fifth year:

Balance in Mariah account is

f(t)=400(1.15)t

⇒ f(5)=400×1.15×5

= $2300

Balance in Colton account is

y=500+50t

⇒ y=500+50(5)

= $750

In the fifth year, Mariah's balance will be higher than Colton's. Therefore, option C is the correct.

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The solutions to the nearest tenth are x = -0.1 and x = 1.3

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

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

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Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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Answer:

20-12=8 the answer is 8 I did the math

Answer:

8 is right

Step-by-step explanation:

because 20-12=8

Answer:

Reject the Null ;

0.928

Step-by-step explanation:

Given the data: 2, 4, 3, 5, 1, 1, 4

Sample mean = (2 + 4 + 3 + 5 + 1 + 1 + 4) / 7 = 2.857

Standard deviation, s = 1.57 ( using calculator)

The hypothesis :

H0 : μ = 1.4

H1 : μ ≠ 1.4

Since sample size is small, use T test

Test statistic :

Tstatistic = (x - μ) / s/sqrt(n)

Tstatistic = (2.857 - 1.4) / 1.57/sqrt(7)

Tstatistic = 1.457 / 0.593 = 2.455

Two tailed test at α = 0.05

Tcritical at df = 7-1 = 6 ; α = 0.05 = 2.447

Tstatistic > Tcritical ; reject the null

Since ;

2.455 > 2.447 ; we reject the null ;

There is significam evidence that Number of complaints has changed.

Effect size ;

d = (x - μ) / s

d = (2.857 - 1.4) / 1.57

d = 1.457 / 1.57

d = 0.928

Answer: The car was not speeding. It went 27.6 mi/h.

Step-by-step explanation: The equation v=2/5L is given where v is measured in mi/h. L is measured in ft. Since we have the value 69 for L, we sub it into the equation. We end up getting 27.6 mi/h after evaluating.

The fraction of the area of the tray occupied by the blondies is 1/9.

To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.

Let's calculate the area of each individual blondie:

The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.

Now, let's calculate the area occupied by the blondies in each row:

Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.

So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.

Next, let's determine the area occupied by the brownies:

The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.

Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.

Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.

Now, let's calculate the total area of the tray:

Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:

Total area of the tray - Area occupied by the brownies = Area occupied by the blondies

648 square inches - 576 square inches = 72 square inches.

So, the fraction of the area of the tray occupied by the blondies is:

Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:

72 square inches / 648 square inches = 1/9.

Therefore, the blondies' percentage of the tray's surface area is 1/9.

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False, since the hypothenuse is the squared root of the sum of both sides squared. Actually, the hypothenuse is alwas the largest side.