5. Which of the following equations models exponential decay? Select all that apply.

y = 68000 - (0.954)^x

y = 229- (1.5)^x

y=3-(1.035)^x

y=-4-2^x

y=504200 (77)^x

Answer:

121

Step-by-step explanation:

It's a series of odd numbers. Let

\(S _{11} = 1+3+5+7+9+11+13+15+17+19+21 \)

As a rule of thumb, the sum of n numbers of odd numbers is equal to n². There're 11 numbers in this series. Hence The sum is 11² =121

Answer:

121

Step-by-step explanation:

1 + 3 + 5 + 7 + 9 + 11 +  13 + 15 + 17 + 19 + 21 is a sum of first 11 odd numbers.

   \(\sf \boxed{\text{\bf Sum of first n odd numbers = $n^2$}}\)

Here, n is the number of terms.

In this sequence, there are 11 terms.

Sum of first 11 odd numbers = 11²

                                              = 11 *11

                                              = 121

Answer:

j < 5

Step-by-step explanation:

=> 10 > j+5

Subtracting both sides by 5, we get

=> 10-5 > j

=> 5 > j

OR

=> j < 5

a. The values of Q1 = 355, Q2 = 510, Q3 = 910, range = 980 and IQR = 555.

b. The lower bound is not applicable and the upper bound is 1195. There are no outliers.

c.  The value at the 70th percentile is approximately 725.6 calories.

a. For the calories of each burger, we will find the Q1, Q2, and Q3, range, and IQR as follows -

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The median of the lower half (from 250 to 540) is the average of the two middle values: (300 + 410) / 2 = 355.

Therefore, Q1 = 355.

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The middle value is the median: Q2 = 510.

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The median of the upper half (from 670 to 1230) is the average of the two middle values: (840 + 980) / 2 = 910.

Therefore, Q3 = 910.

Range = 1230 - 250 = 980.

IQR = Q3 - Q1 = 910 - 355 = 555.

b. To calculate the outlier boundaries, we need to first calculate the lower and upper limits as follows -

Lower bound: Q1 - 1.5 x IQR

Upper bound: Q3 + 1.5 x IQR

Lower bound: 430 - 1.5 x 310 = -25

Upper bound: 740 + 1.5 x 310 = 1195

Since there are no negative values for the calories of the burgers, the lower bound is not applicable. The upper bound is 1195, which is higher than the highest value in the dataset (1090). Therefore, there are no outliers.

c. To determine the value at the 70th percentile, we need to first order the calorie values from lowest to highest as follows -

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 740, 840, 980, 1090, 1230

Next, we will calculate the percentile rank of the 70th percentile -

Percentile rank = (70/100) x (n + 1) = 10.6

Since the percentile rank is not a whole number, we need to interpolate between the 10th and 11th values in the ordered list:

10th value: 710

11th value: 740

Using linear interpolation, we get:

Value at the 70th percentile = 710 + 0.6 x (740 - 710) = 725.6

Therefore, the value at the 70th percentile is approximately 725.6 calories.

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The complete question is -

For the calories of each burger:

a. find q1, q2, q3, the range, and the IQR.

b. calculate the outlier boundaries for the data set. are there any outliers? c. determine the value at the 70th percentile.

Answer:

The space shuttle landed on Monday morning at 9:01 a.m.

I hope this helps.

The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Let the random variable & parameters be;

x1 : Number of successes from group 1

x2 : Number of successes from group 2

p1: Proportion of successes in group 1

p2: Proportion of successes in group 2

n1 : number of trial in group 1

n2: number of trial in group 2

We are given;

x1 = 260

n1 =985

x2 = 194

n2 = 842

Thus;

p1 = 260/985

p1 =0.2640

p2 = 194/842

p2 = 0.2304

Constructing a (1 - α)100% confidence interval for proportion from the formula;

(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]

plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;

(-0.0184631, 0.0855743)

Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

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A polynomial function for cars manufactured in thousands where x represents the year since 1990 according to the data in the table attached is 103x³/480 - 11x²/40 + 77x/120 + 7/10.

A polynomial function for cars manufactured in thousands where x represents the year since 1990. Let the polynomial be P(x) = Ax³ + Bx² + Cx + D, where a, b, c and d are constants. From table in 1992, when x = 2 cars manufactured is 2.6 in thousands. Thus

P(2) = 2.6

A × 2³ + B × 2² + C × 2 + D = 2.6

8A + 4B + 2C + D = 2.6                      (1)

In 1994, when x = 4, P(4) = 12.6

A × 4³ + B × 4² + C × 4 + D = 12.6

64A + 16B + 4C + D = 12.6                 (2)

Subtracting (1) from (2) we get

56A + 8B + 2C = 10

Dividing by 2 on both sides

28A + 4B + C = 5                                   (3)

In 1996, when x = 6, P(6) = 41

A × 6³ + B × 6² + C × 6 + D = 41

216A + 36B + 6C + D = 41                      (4)

Subtracting (2) from (4) we get

152A + 20B + 2C = 28.4

Dividing by 2 on both sides

76A + 10B + C = 14.2                              (5)

Subtracting (3) from (5) we get

48A + 10B = 9.2

24A + 5B = 4.6                                       (6)

In 1998, when x = 8 we get P(8) = 97.4

A × 8³ + B × 8² + C × 8 + D = 97.4

512A + 64B + 8C = 97.4                         (7)

(7) - (4) =

296A + 28B + 2C = 56.4

148A + 14B + C = 28.2                            (8)

(8) - (5) =

72A + 4B = 14                                          (9)

Solving (6) and (9) we get

A = 103/ 480, B = -11/ 40

Thus C = 77/ 120 and D = 7/10

So the polynomial is 103x³/480 - 11x²/40 + 77x/120 + 7/10

--The question is incomplete, the complete question is as follows--

"The table shows the numbers of cars manufactured by a company for selected years. Identify a polynomial function for cars manufactured in thousands where x represents the years since 1990."

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15625=295.80x is the expression for the given condition.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

Let x be the number of month to payout.

15625=295.80x

x=52.82

The expression for given condition is 15625=295.80x.

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4 is the additive inverse of -4.

              OR

The opposite of 4 is -4, or negative four.

Now, According to the question:

Opposite numbers:-

Every number has an opposite. In fact, every number has two opposites: the additive inverse and the reciprocal—or multiplicative inverse. Don't be intimidated by these technical-sounding names, though. Finding a number's opposites is actually pretty straightforward.

If a number is added to its additive inverse, the sum of both the numbers becomes zero.

For any given number, the additive inverse is a number or a value which when added to the original number results in zero.

Mathematically: a + (-a) = 0

So here, 'a' and '-a' are the additive inverses of each other.

Therefore, for 4, the additive inverse is 4 = -4

Thus, 4 is the additive inverse of -4.

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Answer:

40 degreses

Step-by-step explanation:

there is a right angle and that means it is 90 degreese then it gives you 50 degreese so you add them up and get 140 then you subtract that 140 from 180 and get 40 degreese.

Answer:

c

Step-by-step explanation:

cause it is

Answer:

always True

sometimes true

sometimes true

always true

sometimes true

always true

Step-by-step explanation:

As product of non-zero rational number and irrational number is irrational,

3x is an irrational number : always True

Take \(x=\sqrt[3]{2}\)

Here, \(x\) is an irrational number.

\(x^2=(\sqrt[3]{2})^2=2^{\frac{2}{3} }\) is also an irrational number

Now take \(x=\sqrt{2}\)

Here, \(x\) is an irrational number.

\(x^2=(\sqrt{2})^2=2\) is a rational number

So,

\(x^2\) is a rational number: sometimes true

Take \(x=\sqrt{2} \,,y=\sqrt{3}\)

Here, \(x,y\) are irrational numbers.

\(xy=\sqrt{2}\sqrt{3}=\sqrt{6}\) is also an irrational number.

Now take \(x=\sqrt{2} \,,y=\sqrt{8}\)

Here, \(x,y\) are irrational numbers.

\(xy=\sqrt{2} \sqrt{8}=\sqrt{16}=4\) is a rational number.

So,

\(xy\) is a rational number: sometimes true

As sum of a rational number and an irrational number is always irrational,

\(x+3\) is an irrational number: always true

Take \(x=\sqrt{2} \,,y=-\sqrt{2}\)

Here, \(x,y\) are irrational numbers.

\(x+y=\sqrt{2} +(-\sqrt{2})=0\) is a rational number

Now take \(x=\sqrt{2}\,,\,y=\sqrt{3}\)

Here, \(x,y\) are irrational numbers.

\(x+y=\sqrt{2}+\sqrt{3}\) is an irrational number.

So,

\(x+y\) is a rational number: sometimes true

As difference of two irrational numbers is always irrational,

\(x-y\) is an irrational number: always true

Answer:he will weigh 298lbs when he is 24 years old

Step-by-step explanation:

24-18=6  so y =6 plug this into problem (250 +(8x6))
8x6=48 (250=48)=298

The line of best fit refers to a straight line that represents the trend or relationship between two variables in a scatter plot. It is determined by minimizing the sum of the squared horizontal distances between each data point and the line.

In statistical analysis, the line of best fit, also known as the regression line, is used to approximate the relationship between two variables. It is commonly employed when dealing with scatter plots, where data points are scattered across a graph. The line of best fit is drawn in such a way that it minimizes the sum of the squared horizontal distances from each data point to the line.

The concept of minimizing the sum of squared distances arises from the least squares method, which aims to find the line that best represents the relationship between the variables. By minimizing the squared distances, the line is positioned as close as possible to the data points. This approach allows for a balance between overfitting (fitting the noise in the data) and underfitting (oversimplifying the relationship).

The line of best fit serves as a visual representation of the overall trend in the data. It provides a useful tool for making predictions or estimating values based on the relationship between the variables. The calculation of the line of best fit involves determining the slope and intercept that minimize the sum of squared distances, typically using mathematical techniques such as linear regression.

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Answer: We can use trigonometry to solve this problem. Let's call the height of the airplane H, and let's call the distance from observer X to the airplane D. Then the distance from observer Y to the airplane is L - D.

From the point of view of observer X, we can write:

tan(A) = H / D

tan(25°) = H / D

From the point of view of observer Y, we can write:

tan(B) = H / (L - D)

tan(25°) = H / (L - D)

We now have two equations with two unknowns (H and D). We can solve for one of the unknowns in terms of the other, and then substitute that expression into the other equation to eliminate one of the unknowns.

Let's solve the first equation for D:

D = H / tan(25°)

Substituting this expression for D into the second equation, we get:

tan(25°) = H / (L - H / tan(25°))

Multiplying both sides by (L - H / tan(25°)), we get:

tan(25°) (L - H / tan(25°)) = H

Expanding the left-hand side, we get:

tan(25°) L - H = H tan^2(25°)

Adding H to both sides, we get:

tan(25°) L = H (1 + tan^2(25°))

Dividing both sides by (1 + tan^2(25°)), we get:

H = (tan(25°) L) / (1 + tan^2(25°))

Now we can substitute this expression for H into the equation D = H / tan(25°) to get:

D = ((tan(25°) L) / (1 + tan^2(25°))) / tan(25°)

Simplifying, we get:

D = L / (1 + tan^2(25°))

Now that we know the distance D, we can use the equation tan(A) = H / D to find H:

tan(25°) = H / D

H = D tan(25°)

Substituting D = L / (1 + tan^2(25°)), we get:

H = (L / (1 + tan^2(25°))) tan(25°)

Plugging in the given values L = 1850 feet and A = B = 25°, we get:

H = (1850 / (1 + tan^2(25°))) tan(25°)

H ≈ 697.3 feet

Therefore, the airplane is about 697.3 feet high.

Step-by-step explanation:

Answer:

  1680

Step-by-step explanation:

To find the product of the two numbers, you can work out the values of the numbers, or you can work directly with the sum and difference figures.

__

We note that the square of a sum is ...

  (a +b)² = a² +2ab +b²

and the square of a difference is ...

  (a -b)² = a² -2ab +b²

The difference of these squares is ...

  (a +b)² -(a -b)² = (a² +2ab +b²) -(a² -2ab +b²) = 4ab

__

That is, dividing the difference of the squares of the sum and difference by 4 will give the desired product:

  P = (83² -13²)/4 = (6889 -169)/4 = 6720/4 = 1680

The product of the two numbers is 1680.

_____

Additional comment

If we factor the formula we derived, we find ...

  P = ((a +b)² -(a -b)²)/4 = ((a +b) +(a -b))/2 × ((a +b) -(a -b))/2

This simplifies to ...

  (2a)/2 × (2b)/2 = a × b

In short:

Using this fact, we find a=(83+13)/2 = 48; b=(83-13)/2 = 35, and the product is (48)(35) = 1680, as above.

The position of the apex is represented by an arrow. It is found at the fifth intercostal space, near the midclavicular line.

Right atrium=yellowLeft ventricle=grayAorta=redLeft atrium=dark greenPulmonary trunk=dark blueSuperior vena cava=purpleRight ventricle=orangeInferior vena cava=pink

Coronary sinus=light bluePulmonary arteries=brownPulmonary veins=light greenThe cardiac landmarks on the given thoracic cage are:21.

The base of the heart is represented by drawing a line between the 2nd rib and the 5th thoracic vertebra.22.

The left border of the heart is represented by drawing a line running from the 2nd intercostal space along the sternal border to the apex of the heart.23.

The right border of the heart is represented by drawing a line running from the 3rd intercostal space near the right sternal border to the 6th thoracic vertebra.24.
The inferior border of the heart is represented by drawing a line running from the 6th thoracic vertebra to the 5th intercostal space at the mid-clavicular line.25.

The position of the apex is represented by an arrow. It is found at the fifth intercostal space, near the midclavicular line.

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Therefore, the rectangle with dimensions 11 and 11 (width and length, respectively) has the minimum perimeter.

Let's denote the length of the rectangle as L. Since the area of the rectangle is given as 121, we have the equation L * w = 121.

We are looking for the rectangle with the minimum perimeter. The perimeter P can be calculated as 2L + 2w.

To write the objective function in terms of P and w, we substitute L from the area equation:

2L + 2w = 2(121/w) + 2w

Simplifying, we get:

P = 242/w + 2w

The interval of interest for the objective function P is the range of valid values for w. Since the width is less than the length, we can assume that w > 0. Also, from the area equation, we have L * w = 121, so w = 121/L. Since w > 0, L must be greater than 0. Therefore, the interval of interest is (0, ∞), meaning the width can take any positive value.

To find the dimensions that result in the minimum perimeter, we need to minimize the objective function P. Taking the derivative of P with respect to w and setting it to zero will give us the critical points. Let's differentiate:

dP/dw = -242/w^2 + 2

Setting dP/dw to zero:

-242/w^2 + 2 = 0

242/w^2 = 2

w^2 = 242/2

w^2 = 121

w = 11

Since the width cannot be negative, we discard the negative solution. Thus, the width w = 11.

Substituting this value back into the area equation, we can find the length L:

L * 11 = 121

L = 121/11

L = 11

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Answer:

305°

Step-by-step explanation:

Degree of compass, North: 0° = 360° West: 270°

35 degree north of west

»»————-♔————-««

hope it helps...

have a great day!!

The sample space of choosing 3 balls at random from a bag containing 3 reds, 5 blues, and 2 greens, without distinguishing between balls of the same color, consists of all possible combinations of the three colors.

To find the sample space, we consider all the possible outcomes of the experiment. Since we are choosing without distinguishing between balls of the same color, we can represent each ball by its color.

The sample space will consist of all possible combinations of the three colors: {RRR, RRB, RRG, RBB, RBG, BBB, BBG, BGG}.

The sample space of choosing a ball from the bag at random, replacing it, and repeating the experiment three times consists of all possible outcomes of the three independent draws.

In this experiment, each draw is independent and the ball is replaced after each draw. Therefore, each draw has the same set of possible outcomes, which is the original set of colored balls in the bag.

Since we repeat the experiment three times, the sample space will consist of all possible combinations of the three draws, where each draw can be any of the three colors: {R, B, G}.

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Answer:

I think point D.

Step-by-step explanation:

Answer:

The answer is Point G

Step-by-step explanation:

I took the test on K12

Answer:

C. Supplementary angles

Explanation:

Angles a and b are on the straight line AC.

Recall that the sum of angles on a straight line is 180 degrees.

If two angles add up to 180 degrees, they are said to be Supplementary.

Hence angles a and b are Supplementary angles.

Answer:

2/45

Step-by-step explanation:

Answer:

Option A.) 18p-5/30 is the right answer.

The conversion of a tangent line from a parametric function to a Cartesian function is based on the fact that the slope of the tangent line remains the same in both representations. This allows us to determine the Cartesian equation of the tangent line using the derivatives of the parametric equations.

When dealing with parametric equations that describe a curve, the tangent line at a specific point can be represented by the derivatives of the parametric equations. The derivatives provide information about the rate of change of the x and y coordinates with respect to a parameter.

To convert the tangent line to a Cartesian function, we consider the relationship between the parametric variables and the Cartesian coordinates. By solving the parametric equations for the parameter and substituting the resulting expressions into the original equations, we can eliminate the parameter and obtain a Cartesian equation.

Using the derivatives of the parametric equations, we can determine the slope of the tangent line. Since the tangent line has the same slope regardless of the representation, we can substitute the x and y values of the parametric equations into the equation y = mx + b, where m is the slope, and solve for the constant term b.

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The number of table in the form of mixed number will be 4 ¹/₂ tables.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

27 children sit at table of 6, fillling where possible. Then the number of table is given as,

⇒ 27 / 6

⇒ 4 ³/₆

⇒ 4 ¹/₂ tables

The number of table in the form of mixed number will be 4 ¹/₂ tables.

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All closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.

To find all closed intervals of length 1 in which a function has a unique zero, we need to look for intervals where the function changes sign exactly once. This is because if a function has a unique zero, it must change sign from positive to negative or negative to positive at that point.

Let's call the function f(x). To find these intervals, we can use the Intermediate Value Theorem. This theorem states that if a function is continuous on a closed interval [a, b] and takes on values f(a) and f(b) at the endpoints, then it must also take on every value between f(a) and f(b) somewhere on the interval.

So, to apply this theorem, we need to find values of x such that f(x) = 0. Then, we can look at the intervals between these values and see if f(x) changes sign exactly once on any of them.

Let's say we find two zeros of the function at x = a and x = b, where a < b. Then, we can consider the intervals [a, a+1] and [b-1, b] (assuming these intervals have length 1). If f(x) is positive on the interval [a, a+1] and negative on the interval [b-1, b], or vice versa, then f(x) must change sign exactly once on each of these intervals and therefore has a unique zero in each interval.

In general, to find all closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.

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Answer: it is B Slope -1/2 y-intercept 1

Answer: 0.5 = 111

Step-by-step explanation:

Answer:

Step-by-step explanation:69696969699696969696969696969699696965iu436745