5 lily pads are found in a pond. Thirty days later, there are 16 lily pads. Find the exponential growth
model, L(t) = Aekt for the lily pad colony. Enter your answers as expressions or numbers rounded to four
decimal places.
A =
k=

The number of extra tables that you need to double the original seating capacity will be 7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The seating capacity y for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need.

If the no extra table is there. Then the value of 'y' will be

y = 8 (0) + 56

y = 56

Then the number of extra tables do you need to double the original seating capacity will be

8x + 56 = 2 × 56

8x = 56

x = 7

Then the number of extra tables that you need to double the original seating capacity will be 7.

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a. The annual base premium when Danielle cecils driver rating factor is 1.60 and her car is in age group is $709.

b. The annual premium is $1134.40

It should be noted that the annual premium simply refers to the amount of premium that's paid yearly by the entity. The insurance company has premium payment options for the clients.

The annual base premium will be:

= Liability premium + Collision premium + Comprehensive premium

= $383 + $240 + $86

= $709

The annual premium will be:

= Annual base premium × Driver rating factor

= $709 × 1.60

= $1134.40

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According to the solving Probability the value are as follows.

a) P(Blue)= 0/10

b) P(Red)= 5/10

c) P(Red or Yellow)= 9/10

The definition of probability is "How likely something is to happen."

Probability is indeed a number ranging from 0 to 1 that expresses the likelihood that an event will take place as specified.

First, 0 P(E) 1 (where P(E) specifies the probability of an event E) and second, the sum of the probabilities of any collection of mutually and exclusive exhaustive occurrences equals 1 are the two characteristics that define a probability.

We have a Bag of marbles has 4 yellow, 5 red, and 1 purple.

Total balls in a bag= 4+5+1=10 balls.

Something that is IMPOSSIBLE to happen.

P(Blue)= 0/10

Something that is EQUALLY LIKELY to happen.

P(Red)= 5/10

Something that is LIKELY to happen.

P(Red or Yellow)= 9/10

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The total amount accumulated after 2 years is $3704. 0

The formula for calculating compound interest is expressed as;

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

Where;

Now, let's substitute the values into the formula, we have;

A = $3500 ( 1 + 0. 03 / 0. 25) ^(0.25× 2)

Find the exponent

A = $3500 ( 1 + 0. 03 / 0. 25) ^0.5

A =  $3500( 1+ 0. 12)^0. 5

Expand the bracket

A = $3500 (1. 12)^0. 5

A = $3500(1. 05)

multiply the values

A = $3704. 0

Hence, the value is $3704. 0

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The solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is -5ax⁶(2ax⁴ + 7x²). The solution of the expression will be done as,

E =  -5ax⁶(2ax⁴ + 7x²)

E = -10a²x¹⁰-35ax⁸.

Therefore, the solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.

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Answer:

  78°

Step-by-step explanation:

You want the measure of base angle x in an isosceles triangle with a.pex angle 24°.

The two base angles of an isosceles triangle are congruent. The sum of all angles is 180°, so we have ...

  24° +2x = 180°

  12° +x = 90° . . . . . . divide by 2

  x = 78° . . . . . . . subtract 12°

The measure of angle x is 78°.

The explicit form of the arithmetic sequence is

5, 13, 21, 29, .....

What is arithmetic sequence?

A sequence of numbers is said to be in arithmetic progression if the difference between the consecutive terms of the series are same

If the first term is a, common difference is d, then nth term of the sequence is given by

[tex]a_n = a + (n-1)d[/tex]

The recursive form of the given arithmetic series is

[tex]a_n = a_{n-1} + 8[/tex]

First term [tex]a_1 = 5[/tex]

[tex]a_2 = a_1 + 8\\a_2 = 5 + 8\\a_2 = 13[/tex]

[tex]a_3 = a_2 + 8\\a_3 = 13 + 8\\a_3 = 21[/tex]

[tex]a_4 = a_3 + 8\\a_4 = 21+8\\a_4 = 29[/tex]

So the explicit form of the arithmetic sequence is

5, 13, 21, 29, .....

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The standard score (z-score) of the given sample mean is equal to 7.11

A standard score is also referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the standard score of a given sample mean can be calculated by using this formula:

[tex]Z=\frac{\bar{x}\;-\;\mu}{ \frac{\delta}{n} }[/tex]

Where:

Where:

Substituting the given parameters into the formula, we have;

Standard score, z = (30 - 31)/(9/64)

Standard score, z = -1/0.140625

Standard score, z = 7.11

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The expression that represents the age of randy's brother is

2x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Randy age = 8 years old

Randy's brother age = 2 x 8 = 16

Randy's sister age = 8 - 3 = 5

The expression that represents the age of randy's brother.

Let the age of Randy = x.

=  2x

= 2x

= 2 x 8

= 16 years old.

Thus,

The expression that represents the age of randy's brother is

2x.

Where x is the age of Randy.

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Answer:

Step-by-step explanation:

ZT=YT

x+3=3x-11

x-3x=-11-3

-2x=-14

x=-14/-2=7

YT=3×7-11=21-11=10

YT=10

Answer:

[tex]16x {}^{3} + 1[/tex]

Step-by-step explanation:

We need to differentiate the following function,

[tex]\longrightarrow f(x) = 4x^4 + x [/tex]

Let ,

[tex]\longrightarrow y = f(x) [/tex]

So that ,

[tex]\longrightarrow y = 4x^4+x [/tex]

Differentiating both sides wrt x ,

[tex]\longrightarrow \dfrac{dy}{dx}= \dfrac{d(4x^4+x)}{dx}\\[/tex]

[tex]\longrightarrow\dfrac{dy}{dx}= \dfrac{d(4x^4)}{dx}+\dfrac{dx}{dx}\\ [/tex]

[tex]\longrightarrow \dfrac{dy}{dx} = 4(4)x^{4-1} + 1 \\ [/tex]

[tex]\longrightarrow \underline{\underline{ \dfrac{dy}{dx}= 16x^3 +1}}[/tex]

The probability that the part is between 10.8 and 12.8 cm is 0.0669.

What is a normal distribution?

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is symmetric around the mean.

Here, we have

Mean = 16.3cm

Standard deviation = 2.5cm

We have to find the probability that the part is between 10.8 and 12.8 cm

Now,

we know that z = (x−μ)/σ

putting values in the normal distribution formula, we get

P( 10.8 < x < 12.8) = P( (10.8 - 16.3)/2.5 < z < (12.8 - 16.3)/2.5)

                            = P ( -2.2 < z < -1.4)

P( 10.8 < x < 12.8) = 0.0669, by normal distribution table

Hence, the probability that the part is between 10.8 and 12.8 cm is 0.0669.

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20 amount of 30% salt solution

How to find the salt solution percentage?

Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.

Let x be the amount of 30% salt solution

Then, 60-x = amount of 15% salt solution

Salt content of the first solution + salt content of second solution = salt content of the mixture

∴ 0.30x + 0.15(60-x) = 0.20*60

  0.30x + 9 - 0.15x = 12

             0.15x = 3

                   x = 20

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The inequality as per the question is x ≥ 9 and y > 3 and the diagram according to this is attached below.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given information in the question.,

x ≥ 9 and,

y > 3

The equation is,

650 x + 1400 y ≤ 1

[tex]\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1[/tex]

x/23.07 + y/10.71 ≤ 1

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Step-by-step explanation:

use formula

[tex](x - y) {2} = x {}^{2} - 2xy + y {}^{2} [/tex]

The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

Given that,

The equation is 3x-8y=39.

We have to find the x- intercept and y- intercept of the equation.

We know that,

x/a + y/b = 1 is the intercept form of the line's equation. One of the key types of line equations is this one. In this equation, the sign of the intercepts also enables us to determine where the line is in relation to the coordinate axes.

To find the x- intercept of the equation.

We have to take y as 0.

3x-8(0)=39

3x=39

x=39/3

x=13

To find the y- intercept of the equation.

We have to take x as 0.

3(0)-8y=39

-8y=39

x=-39/8

Therefore, The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

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Step-by-step explanation:

Jim has 65 coins in his pocket. All of the coins are nickels and dimes. If the total value of his coins is $5.10, how many nickels or dimes does he have?

nickels = n

dimes = d

We use:

d + n = 65

0.10d + 0.05n = 5.10

solve for d:

d + n = 65

d + n - n = 65 - n

d = 65 - n

substitute in for the second equation: d = 65 - n

0.10(65 - n) + 0.05n = 5.10

6.5 - 0.10n + 0.05n = 5.10

6.5 - 0.05n = 5.10

6.5 - 0.05n - 6.5 = 5.10 - 6.5

- 0.05n= -1.4

n = 28

so there are 28 nickels

Now, solve for d: when n = 28

d + n = 65

d + 28 = 65

d = 37

so there are 37 dimes

Jim has 28 nickels and 37 dimes in his pocket. which is determined by the substitution method.

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

Let the number of nickels would be n

Let the number of dimes would be d

As per the given question,

d + n = 65  ....(i)

0.10d + 0.05n = 5.10  ....(ii)

From equation (i),

d + n = 65

d + n - n = 65 - n

d = 65 - n

Substitute in for the equation(ii): d = 65 - n

0.10(65 - n) + 0.05n = 5.10

6.5 - 0.10n + 0.05n = 5.10

6.5 - 0.05n = 5.10

6.5 - 0.05n - 6.5 = 5.10 - 6.5

- 0.05n = -1.4

n = 28

This means there are 28 nickels

Substitute the value of n = 28 in the equation (i),

d + n = 65

d + 28 = 65

d = 37

So there are 37 dimes

Thus, Jim has 28 nickels and 37 dimes in his pocket.

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We have to label a graph with the following points: (1,3), (4,2), (0,5), and (5,1).

All the points (and only those points) which lie on the graph of the function satisfy its equation. Thus, if a point is on te graph of a function, then it must also satisfy the function.

To plot the graph with the points follow all the steps given below;

Points are (1,3) , (4,2) , (0,5),and (5,1).

Step1 The coordinate of the graph are; (1,3) , (4,2) , (0,5),and (5,1).

Step2 Plot the coordinate 1 on the x-axis and 3 on the y-axis.

Step3 Plot coordinate 4 on the x-axis and 2 on the y-axis.

Step4  Plot the coordinate 0 on the x-axis and 5 on the y-axis.

Step5 Plot the coordinate 5 on the x-axis and 1 on the y-axis.

Step6 Then Draw a line with the help of the scale and meet all the points.

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1. The completion of the inventory table is as follows:

                                   Units  Unit Cost    Total Cost

Jan. 1  Beg. Inventory     8       $6.00                 $48

Apr. 11 Purchases         24       $11.00              $264

May 17 Purchases        30      $14.00              $420

Dec. 5 Purchases         19      $16.00              $304

2. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:

                                      LIFO           FIFO         Weighted-Average

Ending inventory          $704          $845                $767.40

Cost of goods sold       $332          $191                $268.60

FIFO (First-in, First-out) is based on the assumption that the physical flow of goods sold depends on the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.

LIFO:

Ending inventory = $704 ($48 + $264 + 28 x $14)

Cost of goods sold = $332 ($1,036 - $704)

FIFO:

Ending inventory = $845 (11 x $11 + 30 x $14 + 19 x $16)

Cost of goods sold = $191 ($1,036 - $845)

Weighted Average:

Ending inventory = $767.40 (60 x $12.79)

Cost of goods sold = $268.60 (21 x $12.79)

                                   Units  Unit Cost    Total Cost

Beg. Inventory Jan. 1     8       $6.00                 $48

Apr. 11 Purchases         24      $11.00              $264

May 17 Purchases        30     $14.00              $420

Dec. 5 Purchases         19     $16.00              $304

Total                              81                           $1,036

Units sold                      21

Ending inventory         60

Average cost per unit = $12.79 ($1,036/81)

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The instantaneous rate of change of monthly output with respect to the number of workers is equal to 184.

The instantaneous rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity at a particular instant.

In Mathematics, the instantaneous rate of change can be calculated by taking the derivate of the function with respect to an independent variable. This ultimately implies that, the instantaneous rate of change is equivalent to the change in the derivative value at a particular instant.

Taking the derivate of the given function, we have:

Q(x) = 15,000 + 2x²

Q'(x) = d/dx(15,000) + d/dx(2x²)

Q'(x) = 0 + 2x(2)

Q'(x) = 4x.

At x = 46, we have:

Q'(x) = 4(46)

Q'(x) = 184.

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Complete Question:

The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 ≤ x ≤ 60), where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).

Q'(46) =

Answer: D because 8 1/5 is smaller than 8 1/3

Answer:

so now i think you can find the slope of the sides.the product of slopes of two perpendicular lines is - so now you can also find the slopes of the altitude. i will do one side for you and you do the remaining the slope of side BC is (2-0)/(9-0) = 2/9 so the slope of the altitude passing through A will be -9/2

Step-by-step explanation:

so i think it would be side AC

Answer:

Side BC

Step-by-step explanation:

Let's calculate the slopes of the sides of triangle ABC:

Slope of side AB = (2 - 0) / (9 - 16) = 2 / (-7) = -2/7

Slope of side BC = (0 - 2) / (2 - 9) = -2 / (-7) = 2/7

Slope of side CA = (0 - 0) / (2 - 16) = 0 / (-14) = 0

Among the three sides, only side BC has a slope of 2/7, which is the negative reciprocal of the given slope of -2/7.

Therefore, side BC represents the altitude of triangle ABC with a slope of -2/7.

A 95% confidence interval for the proportion who believe immigration is a good thing is; CI = (0.4173, 0.7173)

The formula for the confidence interval of proportions is;

CI = p ± z√(p(1 - p)/n)

where;

p is sample proportion

z is z-score at confidence level

n is sample size

We are given;

Number of success; x = 631

Sample size; n = 1095

Thus;

sample proportion; p = x/n = 631/1095 = 0.5763

The z-score at 95% confidence level is 1.96. Thus;

CI = 0.5673 ± 1.96√(0.5673(1 - 0.5673)/1095)

CI = 0.5673 ± 0.015

CI = (0.5673 - 0.15), (0.5673 + 0.15)

CI = (0.4173, 0.7173)

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Abdiel's total if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount is $27.46

The correct answer option is option B

Amount of total after discount = 12% × $24.30

= 0.12 ×24.30

= $2.916

Amount of abdiel's tip = 25% × $24.40

= 0.25 × 24.30

= $6.075

Abdiel's total after discount before tip = (Amount of abdiel's tip + Abdiel's subtotal) - Amount of total after discount

= (6.075 + 24.30) - $2.916

= $30.375 - $2.916

= $27.459

Approximately,

$27.46

Therefore, the total amount Abdiel paid after discount before tip is $27.46

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The partial fraction form of the given fraction [x+5/(x-7)(x-5)] is

[A/(x-7)+B/(x-5)].

So, the fraction is:

We know that:

Use the same identity to get the partial fraction of the given fraction as follows:

Therefore, the partial fraction form of the given fraction [x+5/(x-7)(x-5)] is [A/(x-7) + B/(x-5)].

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Answer:

(10 + 8) - (7 * 2) = x, 4 pounds of birdseed left

Step-by-step explanation:

      For the first part of our equation, we will find the total amount of pounds of seeds among the bags (addition).

      For the next part, we will find out how much of the bird seed is used (subtraction).

      Then, it will equal whatever is left.

(10 + 8) - (7 * 2) = x, x = pounds of bird seed left

      Now, we will solve.

(10 + 8) - (7 * 2) = x

(18) - (14) = x

x = 4 pounds of birdseed left

A number line is a simple graph with numerical increments spaced evenly. The numbers on the line determine how the number on the line can be answered. The number's application is determined by the question to which it corresponds, such as when plotting a point.

A number line is a horizontal line with evenly spaced numerical increments. The numbers on the line will determine how to answer the number on the line. The number's use is determined by the question that goes with it, such as plotting a point.

The number line is a straight line with divisions at equal intervals, similar to a scale. You can choose any point as "0," and all positive numbers will be to the right of the "0," and all negative numbers will be to the left of the "0." Q.

Therefore,

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The critical values of the chi statistic are; χ²R = 8.643 and χ²L = 42.796

The confidence interval estimate of σ is; 0.20 < σ < 0.45

We are given the following data;

Sample size; n = 23

Degree of freedom; df = n - 1 = 23 - 1 = 22

Confidence level; α - level = 99%

Sample standard deviation; s = 0.25 mg

For χ²R;

The significance level is; 1 - (1 - 0.99)/2= 0.995

The degree of freedom is; df = 22

From critical value tables, we know that; χ²R = 8.643

For χ²L ;

The significance level is; (1 - 0.99)/2 = 0.005

The degree of freedom is; df = 22

From critical value tables, we know that; χ²L = 42.796

The confidence interval estimate of σ is;

s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]

Plugging in the relevant values gives;

0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)

0.2008 < σ < 0.4467

0.20 < σ < 0.45

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