13. Write 7% as a decimal

The continuous growth rate of a function is given by its derivative.

So, taking the derivative of f(x) with respect to x, we get:

f'(x) = 0.07e^(0.07x)

Therefore, the continuous growth rate of the function is 1.07.

Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.

It functions by dividing distance by speed. The time can also be calculated by dividing the distance traveled by the speed. You can determine the third input if you know the first two. For instance, we may get the speed as 120 x 2 = 60 miles per hour if a car travels 120 miles in two hours.

The equation of the line of best fit is:

y = -1.4x + 117.8

where x is the age in years and y is the typing speed in words per minute. To find the expected typing speed of a 17-year-old student, we can substitute x = 17 into the equation:

y = -1.4(17) + 117.8

y = -23.8 + 117.8

y = 94

Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.

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So the area of one tile is 50 square inches. Therefore, the length of the triangle's base is 20 inches.

Area is a measure of the amount of space inside a two-dimensional (2D) shape or figure. It is usually measured in square units, such as square meters (m²) or square centimeters (cm²). The area of a shape is calculated by multiplying the length of one side or dimension of the shape by the length of another side or dimension. The resulting value represents the total number of square units that are contained within the shape.Area is an important concept in mathematics and is used in various fields, such as geometry, physics, and engineering. It helps in measuring and comparing the sizes of shapes and figures, and in determining how much material is needed to cover or fill a certain area.

Here,

The area of a parallelogram can be calculated as the product of its base and height. In the case of the given tile, the base and height are 10 inches and 5 inches respectively. Therefore, the area of one tile is:

Area of tile = Base x Height

Area of tile = 10 in x 5 in

Area of tile = 50 square inches

If the two tiles have the same area, then we can assume that the area of the triangle tile is also equal to 50 square inches (the area of one parallelogram tile that we calculated in the previous question).

The formula for the area of a triangle is:

Area of triangle = (1/2) x Base x Height

where the base is one of the sides of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.

In this case, we know that the area of the triangle is 50 square inches and the height is 5 inches, so we can solve for the base as follows:

Area of triangle = (1/2) x Base x Height

50 = (1/2) x Base x 5

Base = (2 x 50) / 5

Base = 20

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Complete question:

An artist is using tiles in the shape of a parallelogram to make a mosaic. The tiles are in the shape of parallelogram with height as 5 inch and length as 10 inch. What is the area of one tile? if the two tiles have the same area, what is the length of the triangles base?

Keith pays about 80% of the price of a new SUV for the used SUV.

To find what percent of the price of a new SUV Keith pays for a used SUV, we need to divide the price of the used SUV by the price of the new SUV and then multiply by 100 to express the answer as a percentage:

used SUV price / new SUV price * 100%

Substituting the given values, we get:

$20,000 / $25,000 * 100% ≈ 80%

So Keith pays about 80% of the price of a new SUV for the used SUV. Rounded to the nearest whole number, this would be 80%.

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Answer:

8) Area of triangle ABC is 60

   Area of triangle XYZ is 540

9) The ratio is 1:9

10) (use Pythagorean theorem)

     BC is 12 [tex]\sqrt{13^{2}-5^{2} } =12[/tex]

     YZ=39 (the legs are the same because it is an Isosceles triangle)

11) the ratio is 1:3

Step-by-step explanation:

Solving the given radical equation [tex]\sqrt{(4x+5)} = x-4[/tex] ,  the solution set is {11}

To solve the radical equation, we need to isolate the radical on one side of the equation and then square both sides to eliminate the radical. We can then solve for x and check our proposed solutions. Here are the steps:

Step 1: Isolate the radical on one side of the equation:
[tex]\sqrt{(4x+5)} = x-4[/tex]

Step 2: Square both sides of the equation to eliminate the radical:
[tex](\sqrt{(4x+5))^2} = (x-4)^2\\4x+5 = x^2-8x+16[/tex]

Step 3: Rearrange the equation and solve for x:
[tex]x^2-12x+11 = 0\\(x-11)(x-1) = 0[/tex]

Step 4: Solve for x:
[tex]x-11 = 0 , x-1 = 0\\x = 11 , x = 1[/tex]

Step 5: Check the proposed solutions by plugging them back into the original equation:
[tex]\sqrt{(4(11)+5)} = 11-4\\\sqrt{49 } = 7[/tex]
7 = 7 (True)

[tex]\sqrt{(4(1)+5) } = 1-4\\\sqrt{9} = -3[/tex]
3 = -3 (False)

Therefore, the solution set is {11}.

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The first equation describing the given conditions is x - y = 2, as the difference between the two outputs of a firm is 2. The second equation is 8x = 10y, as eight times the larger quantity is 10 times the smaller quantity. The system of equations can be written as:

x - y = 2
8x = 10y

To solve the system, we can use the substitution method. First, we can solve for x in the first equation:

x = y + 2

Then, we can substitute this expression for x into the second equation:

8(y + 2) = 10y

Distributing the 8 gives:

8y + 16 = 10y

Subtracting 8y from both sides gives:

16 = 2y

Dividing by 2 gives:

y = 8

Finally, we can substitute this value of y back into the first equation to find x:

x = 8 + 2 = 10

So the two output levels are x = 10 and y = 8.

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The possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1 .

The polynomial 6x4 - 11x3 + 8x2 - 33x - 30 has 4 possible rational roots. To find them, use the Rational Root Theorem.

This theorem states that any rational roots of a polynomial must be in the form a/b, where a is a factor of the constant term and b is a factor of the leading coefficient.

In this case, the constant term is -30, so the possible factors are -1, -2, -3, -5, -6, -10, -15, -30. The leading coefficient is 6, so the possible factors are 1, 2, 3, 6.

Therefore, the possible rational roots are -1/6, -1/3, -1/2, -1, 1/6, 1/3, 1/2, 1.

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The probability of winning on the first try is 0.000003426 .

P(MUF) = P(M) + P(F) - P(M and F) = 73/293 + 79/293 - 14/293 = 138/293

P(B) = 80/293

P(E/S) = P(E and S)/P(S) = 20/293 / 78/293 = 20/78 = 10/39

P(ENS) = P(E and S and N) = 0 (since there is no N category in the table)

P(MUJUH) = P(M and J and H) = 0 (since there is no intersection of all three categories in the table)

P(SEUM) = P(SE and M) = 10/293

P(F/B) = P(F and B)/P(B)

=> 16/293 / 80/293

=> 16/80

=> 1/5

P(AUB) = P(A) + P(B) - P(A and B)

=> .4 + .35 - (.4 * .35)

=> .595
If order matters, the probability is

(5/30) * (4/29) * (3/28) * (2/27) * (1/26) * 5!

=> 0.00002056

The probability of winning on the first try is

(5/30) * (4/29) * (3/28) * (2/27) * (1/26)

=> 0.000003426

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Micah can use the <div> tag.

What is Tag?

A tag is given as the label that has been attached to someone or something in order to add identification to the particular thing. The tag in the HTML or any other language has been used for the conversion of the HTML document into web pages. The tags are braced in the < >.

Micah can use the <div> tag to divide a block of content on a web page and set it apart with different formatting.

The <div> tag is a container tag that is used to group and separate HTML elements on a web page.

Micah can give the <div> tag a class or an ID attribute and use CSS to apply different formatting to the content within that tag.

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The probability that the distance between them is more than the radius of the circle is given as follows:

0.5 = 50%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the circle, we have that the radius is the distance between any point on the circumference of the circle, and the center.

The largest distance is the diameter, which is the distance between two points on the circumference of the circle, passing through the center.

The diameter is twice the radius, hence the probability is given as follows:

p = r/2r

p = 1/2

p = 0.5 = 50%.

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To decode the words 0011, 0101, 0110 and 1111, we can find the corresponding codeword in the standard array. The codewords for 0011, 0101, 0110 and 1111 are 0011, 0101, 0110 and 1111, respectively.

To construct a standard array for this code, we can start by finding the generator polynomial of the code. This can be done by multiplying the generator matrix with its transpose and finding the resultant matrix. This results in the generator polynomial: 110101001.

To construct the standard array, we first construct a parity check matrix, which is the transpose of the generator matrix: 0101 1001 1100 1000.

From the parity check matrix, we can then construct the standard array. The standard array consists of all the possible codewords given the generator polynomial and the parity check matrix. It can be constructed by multiplying the generator matrix with all possible vectors of length 3.

The standard array of the code is:
0011  0101  0110  1001  1010  1100  1101  1111

To decode the words 0011, 0101, 0110 and 1111, we can find the corresponding codeword in the standard array. The codewords for 0011, 0101, 0110 and 1111 are 0011, 0101, 0110 and 1111, respectively.

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Answer:

[tex] = 3kd + 2d + 5r + 6kr[/tex]

Step-by-step explanation:

[tex]7dk + 6kr + 4d + 8r - 4 kd - 2 d - 3r \\ = 3kd + 2d + 5r + 6kr[/tex]

Answer:

Step-by-step explanation:

The days where it is illuminated is Day 13= 50% and Day 26=100%

Linear model:

Here A simple approach should be considered for linear model that begins at Day 1. In the case when the illumination is increased by 4% every day, so after 11 more days (after Day 2) it reaches 50%. In 13 more days, illumination reaches 100%.

Therefore, we can conclude that The days where it is illuminated is Day 13= 50% and Day 26=100%

The first experiment is not a binomial experiment because it does not meet the criteria of a binomial experiment. The criteria of a binomial experiment are:

1. The experiment consists of a fixed number of trials, n.
2. Each trial has only two possible outcomes: success or failure.
3. The trials are independent of each other.
4. The probability of success, p, remains constant for each trial.

In the first experiment, the trials are not independent of each other because the marbles are selected without replacement. This means that the probability of success changes with each trial. Therefore, it is not a binomial experiment.

The second experiment is a binomial experiment because it meets the criteria. There are a fixed number of trials (100), each trial has only two possible outcomes (steel penny or not steel penny), the trials are independent of each other (one penny is selected and then replaced), and the probability of success remains constant (1% for each trial). Therefore, p = 0.01 and n = 100.

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Answer: it can change the amount of force that you can apply on an object.

Step-by-step explanation:

Answer:

Simple machine makes work go faster

Step-by-step explanation:

If you replace human Labour with simple machine, work is completed faster. It increases output

Answer:

First, we need to calculate the total cost of Lisa's and Tracy's lunches before tax and tip.

Lisa's lunch = $6

Tracy's lunch = $7

Total before tax and tip = $6 + $7 = $13

Now we need to add the 5% sales tax:

$13 x 0.05 = $0.65

Total after tax = $13 + $0.65 = $13.65

Finally, we need to add the 15% tip:

$13.65 x 0.15 = $2.05

Total bill = $13.65 + $2.05 = $15.70

Therefore, the total bill, including tax and tip, is $15.70.

Answer:

Step-by-step explanation:

6 + 7 = 13

Now for the sales tax and tip, we need to add 15 and 5 together which is 20. So now we need to multiply 13 times the decimal equivalent of 20%. So, 0.20 x 13 = 2.6

2.6 + 13 = 15.6

The answer is 15.6

In answering the question above, the solution is Yet it's obvious that this function isn't the right response. As a result, the question or the possible answers might be wrong.

Mathematicians investigate the relationships between numbers, equations, and related structures, as well as the locations of forms and possible placements for these items. A set of inputs and their corresponding outputs are referred to as a "function" in this context. If each input results in a single, unique output, the relationship between the inputs and outputs is known as a function. Each function has its own domain, codomain, or scope. A common way to denote functions is with the letter f. (x). is an x for entry. One-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

We must work out the equation c(n)/n = 1.3, where c(n)/n is the average cost per part, in order to get the value of n. When we replace the provided cost function, we obtain:

103n/n = 1.3

By condensing, we obtain: 103 = 1.3n.

The result of dividing both sides by 1.3 is: n 79.23

In order for the typical part to cost $1.3 million, around 79 pieces must be produced. The closest option is (d) 10 pieces because this isn't one of the available options. Yet it's obvious that this isn't the right response. As a result, the question or the possible answers might be wrong.

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The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Ordered pair (0, 3), (1, 48) and many more lies on the graph of the function.

What are Functions?

A function in math is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. It can be represented using an equation, graph, or table of values.

The exponential function [tex]f(x) = 3(4)^(2x)[/tex] can be evaluated for any value of x to get the corresponding value of y. To find ordered pairs that lie on the graph of this function, we can substitute different values of x into the function and calculate the corresponding values of y.

For example, if we substitute x = 0 into the function, we get:

[tex]f(0) = 3(4)^(2(0)) = 3(4)^0 = 3(1) = 3[/tex]

So the ordered pair (0, 3) lies on the graph of the function.

Similarly, if we substitute x = 1 into the function, we get:

[tex]f(1) = 3(4)^(2(1)) = 3(4)^2 = 3(16) = 48[/tex]

So the ordered pair (1, 48) also lies on the graph of the function.

We can repeat this process for other values of x to find more ordered pairs that lie on the graph of the function.

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The answer is 49

To evaluate the given expression, we will use the special product formula for the square of a binomial:

(a+b)^(2)=a^(2)+2ab+b^(2)

In this case, we have:

52^(2)=(5+2)^(2)=5^(2)+2(5)(2)+2^(2)=25+20+4=49

Therefore, the answer is:

52^(2)=49

So, using the special products of algebraic expressions, we can evaluate the given expression to be 49.

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Part A) Estimated Populations of Cities A and B are given.

Part B)  City A's estimated population is increasing at a faster rate than City B's estimated population for each decade.

Part C) the estimated population of City A first exceeds the estimated population of City B at the start of the 4th decade (t = 3)

Part D) The models may not realistically predict population growth over very long time scales, as they do not take into account other factors  

Part A:

Estimated Populations of Cities A and B

Decades Since 1980  City A (in thousands)          City B (in thousands)

0                                       15                                           16

1                                  19.5                                   16.4

2                                  25.2                                   17.8

3                                  32.7                                   19.2

4                                  42.4                                    20.6

Part B:

Population Increases from the previous Decade for Cities A and B

Decades Since 1980 City A (in hundreds)           City B (in hundreds)

0                                         -                                                   -

1                                       450                                              40

2                                       570                                               140

3                                       750                                               140

4                                       970                                               140

Interpretation:

From the table, we can see that City A's estimated population is increasing at a faster rate than City B's estimated population for each decade. This indicates that City A is growing more rapidly than City B, and may continue to do so in the future.

Part C:

To find the start of the decade when the estimated population of City A first exceeds the estimated population of City B, we need to solve the equation:

15[tex](1.03)^t[/tex] > 0.4t + 16

where t is the number of decades since 1980.

One way to solve this is to use a graphing calculator to graph both functions and find their intersection point. Alternatively, we can use trial and error to test different values of t until we find the smallest one that satisfies the inequality.

Using a graphing calculator, we find that the estimated population of City A first exceeds the estimated population of City B at the start of the 4th decade (t = 3), when the estimated population of City A is approximately 32.7 thousand people, and the estimated population of City B is approximately 19.2 thousand people.

Part D:

The models may not realistically predict population growth over very long time scales, as they do not take into account factors such as changes in birth and death rates, migration patterns, and economic or environmental changes that may affect population growth. Additionally, the models assume that population growth will continue to follow a linear or exponential pattern, which may not be accurate in the long term. Therefore, while the models can provide useful estimates for short- to medium-term population trends, they should be used with caution when making long-term projections.

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The correct question should be:

The estimated population, in thousands of people, of city A can be modeled by the function SO) = 15(1.03), where is the number of decades (10-year period) since 1980 The estimated population, in thousands of people, of the city can be modeled by the function (1)-0.41 +16, where is the number of decades since 1980

Part A)     Complete this table, showing both estimated population values, rounded to the nearest tenth for each city based on the number of decades since 1980 Estimated Populations of Cities A and B City Decades Since 1980 City B (thousands of people) (thousands of people) 0 . 2 3 4

Part B)      Using the table in Part A, complete this table showing population increases, in hundreds of people, cach decade Population Increases from previous Decade for Cities A and B Decades Since 1980, Increase of City A Increase of City B (hundreds of people), (hundreds of people), fin)-(-1) g) -R-1) 2 3 4 Interpret the differences in the increases of the estimated populations of the two cities based on the functions that model cach city's population. Provide evidence to support your answer

Part C)    At the start of which decade will the estimated population of city A first exceed the estimated population of city B? What will be the estimated populations of each city at the start of that decade? Provide evidence to support your answers.

Part D)   Based on the behavior of the functions, do the models realistically predict population growth over very long time scales? Provide evidence to support your answer.

It is possible for each of the six quadratic equations to have at least one real root.

This is because the discriminant of a quadratic equation determines the nature of its roots. The discriminant is given by the formula: D = b² - 4ac.

If D > 0, the equation has two distinct real roots.
If D = 0, the equation has one real root (a double root).
If D < 0, the equation has no real roots (two complex roots).

In each of the six equations, the coefficients a, b, and c are non-zero real numbers. This means that the discriminant can be positive, zero, or negative, depending on the values of a, b, and c. Therefore, it is possible for each of the six equations to have at least one real root.

For example, consider the equation ax² + bx + c = 0. If b² > 4ac, then the equation has two distinct real roots. If b² = 4ac, then the equation has one real root (a double root). If b² < 4ac, then the equation has no real roots (two complex roots).

Similarly, the other five equations can also have at least one real root, depending on the values of the coefficients a, b, and c.

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sin(30°) = ½

Sin(30°) have the value of √1/2 which gives ½

The probability of at least one part being defective is 21 or more when 14 parts are produced. So, the correct answer is D: 14.

Let X be the number of defective parts among n parts produced. Since each part can either be defective or non-defective, X follows a binomial distribution with parameters n and p, where p = 0.05.

We want to find the smallest value of n such that P(X ≥ 1) ≥ 0.21. We can use the complement rule to rewrite this as P(X < 1) ≤ 0.79.

P(X < 1) = P(X = 0) = (1 - p)^n

= (0.95)^n

We need to find n such that (0.95)^n ≤ 0.79. Taking logarithms of both sides, we get:

n log(0.95) ≤ log(0.79)

n ≥ log(0.79) / log(0.95)

n ≥ 13.65

Since we need n to be an integer, we round up to the nearest integer and get n = 14.

Therefore, the answer is option D: 14.

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Answer:

3(4x + 7) - (8x - 7)

Step-by-step explanation:

Answer:

x = 16

AB = 25

BC = 15

AC = 20

Step-by-step explanation:

I have marked the vertices to explain

There are three right triangles that can be seen in the picture

Δ ABC with legs BC and AC and hypotenuse AB

ΔACD with legs AD and CD and hypotenuse AC

ΔBCD with legs CD and BD and hypotenuse BC

We will using the Pythagorean formula in all three triangles:
hypotenuse² = sum of squares of legs

------------------------------------------------------------------------------------------

(1) Let's first find missing side BC

In right triangle ΔBCD ,
BC² = CD² + BD²

We have CD = 12, BD = 9
BC² = 12² + 9²
= 144 + 81

= 225

BC = √225 = 15

--------------------------------------------------------------------------------------------------
(2) Now let's focus on ΔABC

AB is the hypotenuse
AC and BC are the legs

AB² = AC² + BC²

or

AC² = AB² - BC²

Since AB = AD + BD = x + 9 and BC = 15

AC² = (x + 9)² - 15²

(x + 9)² = x² + 2 · 9 · x + 9² = x² + 18x + 81

15² = 225

AC² =  x² + 18x + 81 -225

AC² =  x² + 18x - 144                  (1)

-----------------------------------------------------------------------------------------------

(3) Now let's turn our attention to ΔACD with legs AD and CD  and hypotenuse AC

AC² = AD² + CD²

With AD = x and CD = 12,

AC² = x² + 12²

AC² = x² + 144                               (2)

------------------------------------------------------------------------------------------------

Equations (1) and (2) have the same left side, AC²
So the expressions on the right side must be equal

Therefore:

x² + 18x - 144     =  x² + 144

x² terms cancel out from left and right sides giving

18x - 144 =  144

Add 144 on both sides:
18x - 144 + 144 = 144 + 144

18x = 288

x = 288/18 = 16

Plugging this into equation (2) AC² = x² + 144 gives
AC² = 16² + 144

AC² = 256 + 144

AC² = 400

AC = √400

or

AC = 20

Since AB is the third unknown side and AB = x + 9 we get
AB = 16 + 9 = 25

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer