Landon Invested 110 In An Account With An Interest Rate Of 4.1 How Much Would Be There After 5 Years (2024)

B) The values of x and y in the figure are x=30 and y=150 respectively, with x and y corresponding to specific angles formed by the transversal line q intersecting parallel lines l, m, n, and p.

Based on the given information in the figure, we can see that:

L II n {Then lines are the alternate are equal}

x=30°

x=30

n II p

y+30=180°

y=150°

y=150

angles 1 and 2 are corresponding angles and are congruent (since lines l and q are transversals of parallel lines l and m respectively),

therefore: 1 = x

angles 2 and 3 are alternate interior angles and are congruent (since lines q and n are transversals of parallel lines m and n respectively), therefore: 2 = yangles 3 and 4 are corresponding angles and are congruent (since lines n and q are transversals of parallel lines n and p respectively), therefore: 3 = y

Therefore, we can conclude that x = 30 and y = 150, so the answer is B) x=30, y=150.

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The complete question is :

In the figure shown, line q is a transversal of parallel lines l,m,n, and p what are the values of x and y?

Given equation: y = √25 - x^2

The domain of this equation is all real values of x such that √25 - x^2 is defined.

Step 1: Write the equation in terms of x only so that we can identify the domain:

y = √25 - x^2

=> x^2 = √25 - y

=> x = √(√25 - y)

Step 2: Since "√25-y" must be greater than or equal to 0 for the equation to be defined, we can set the inequality to find the domain for x as:

√25 - y ≥ 0

=> -y ≥ -√25

=> y ≤ √25

Therefore, the domain for the equation y = √25 - x^2 is all real values of x such that y is less than or equal to √25. Represented in the standard form of intervals, this can be written as:

Domain: x ∈ (-∞, +∞) and y ∈ [0, √25]

The surface area is 228 in²

The number of cans is 30

How to determine the surface area

The formula for calculating the surface area of a rectangular prism is expressed as;

Surface area = 2(lw + wh + hl)

Substitute the values, we have;

Surface area = 2(36 + 36 + 36)

Add the values

Surface area = 2(108)

Surface area = 216in²

Area of a triangle = 1/2 × 6 × 4

Multiply the values

Area = 12 in²

Total = 228 in²

Surface area of the figure;

2(lw + lh + hw)

2(132 + 180 + 165)

2(477)

954ft²

If 1 can = 32ft²

x = 954ft²

x = 30 cans

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Primero, debemos determinar el número de personas que escucharon tanto salsa como bachata. Para hacer esto, podemos restar el número de personas que escucharon solo salsa y el número de personas que escucharon solo bachata del número total de personas que fueron encuestadas:

2500 encuestados - 2100 que escucharon salsa - 1500 que escucharon bachata + 350 que no escucharon ningún ritmo = 250 encuestados que escucharon ambos ritmos

Por lo tanto, de los 2500 encuestados, 250 escucharon tanto salsa como bachata, 1850 escucharon solo salsa, 1250 escucharon solo bachata, y 350 no escucharon ningún ritmo.

Para calcular la probabilidad de que una persona elegida al azar haya escuchado salsa y/o bachata, podemos sumar las probabilidades de que haya escuchado solo salsa, solo bachata o ambos:

Probabilidad de haber escuchado solo salsa = 1850/2500 = 0.74

Probabilidad de haber escuchado solo bachata = 1250/2500 = 0.5

Probabilidad de haber escuchado tanto salsa como bachata = 250/2500 = 0.1

Por lo tanto, la probabilidad de que una persona elegida al azar haya escuchado salsa y/o bachata es:

0.74 + 0.5 - 0.1 = 1.14 - 0.1 = 1.04

Final answer:

The probability that a randomly selected person listens to both salsa and bachata is 86%.

Explanation:

The problem asks for the probability that a randomly selected person from the surveyed population listens to both salsa and bachata. To solve this, we need to find the number of people who listen to both salsa and bachata and divide it by the total number of surveyed people.

From the given information, we know that 2,100 people listen to salsa, 1,500 people listen to bachata, and 350 people do not listen to either. To find the number of people who listen to both, we subtract the number of people who do not listen to any rhythm from the total number of surveyed people, giving us [tex]2,500 - 350 = 2,150.[/tex]

Therefore, the probability that a randomly selected person listens to both salsa and bachata is 2,150 / 2,500 = 0.86, or 86%.

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Answer:

A = 2.18m, B = 1.94m

Step-by-step explanation:

first of all, convert 240mm to metres. 240mm = 0.24m.

now, A is 0.24m longer than B.

that is, A = B + 0.24

B = A - 0.24.

A + B = 4.12

A + (A - 0.24) = 4.12

2A - 0.24 = 4.12

2A = 4.12 + 0.24 = 4.36

A = 2.18.

B = A - 0.24 = 2.18 - 0.24 = 1.94.

so, A = 2.18m and B = 1.94m

1. The percentage of maize flour is given as 16.7 %

2. The common ratio of the GP is r = 1.5.

How to solve for the common ratio

1. We have to set up equation

60x + 90(1 - x) = 85

60x + 90 - 90x = 85

now we have to solve for the value of x

-30x = -5

x = 5 / 30

x = 0.167

Hence percentage of maize flour is given as 16.7 %

2. a + ar = 20 (1)

ar + ar^2 = 30 (2)

We can rearrange equation (1) to get an expression for a:

a = 20 / (1 + r)

Now, we can substitute a into equation (2) to get an equation only in terms of r:

[tex]20r / (1 + r) + 20r^2 / (1 + r) = 30\\20r + 20r^2 = 30(1 + r)\\20r + 20r^2 = 30 + 30r\\20r^2 - 10r - 30 = 0\\2r^2 - r - 3 = 0[/tex]

Solving this quadratic equation, we get:

We have two solutions, r = 1.5 and r = -1. But since the GP is increasing, we discard the negative solution. Therefore, the common ratio of the GP is r = 1.5.

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Answer:

The answer is down below

Step-by-step explanation:

a)done

b)anticlockwise

(-3,-7)

The derivative of the function f(x)= csch⁻¹(x²) is -2/x√1+x⁴

The given function is f(x)= csch⁻¹(x²)

We have to find the derivation of the hyperbolic function

d/dx f(x)= d/dx csch⁻¹(x²)

f(x)=csch⁻¹(x²)

We know that the derivative csch⁻¹x is -1/|x|√1+x²

Differentiate and apply the chain rule

=-1/|x²|√1+x⁴ d/dx (x²)

We know that d/dx (x²) = 2x as d/dx (xⁿ)=nxⁿ⁻¹

Apply these on the above function

= 2x/x²√1+x⁴

= -2/x√1+x⁴

Hence, the derivative of the function f(x)= csch⁻¹(x²) is -2/x√1+x⁴

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Answer:

[tex]\text{A.} \quad \dfrac{-2}{x\sqrt{x^4+1}}[/tex]

Step-by-step explanation:

Given inverse hyperbolic function:

[tex]f(x)=\text{csc\:h}^{-1}(x^2)[/tex]

To find the derivative of the function, we can use the chain rule:

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]

[tex]\textsf{Let}\;\;y = \text{csch}^{-1}(u)\;\; \textsf{where}\;\;u=x^2.[/tex]

Differentiate the two parts separately.

Differentiate u with respect to x:

[tex]u = x^2 \implies \dfrac{\text{d}u}{\text{d}x}=x[/tex]

Use the following derivative of hyperbolic functions to differentiate y with respect to u:

[tex]\boxed{\dfrac{\text{d}}{\text{d}x}\left(\text{csch}^{-1}x\right)=\dfrac{-1}{|x|\sqrt{x^2+1}}, \quad x \neq 0}[/tex]

Therefore:

[tex]y = \text{csch}^{-1}(u)\implies \dfrac{\text{d}y}{\text{d}u}=\dfrac{-1}{|u|\sqrt{u^2+1}}[/tex]

Put everything into the chain rule formula:

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}\\\\&=\dfrac{-1}{|u|\sqrt{u^2+1}} \times 2x\\\\&=\dfrac{-2x}{|u|\sqrt{u^2+1}} \\\\&=\dfrac{-2x}{|x^2|\sqrt{(x^2)^2+1}} \\\\&=\dfrac{-2x}{|x^2|\sqrt{x^4+1}}\\\\&=\dfrac{-2x}{|x^2|\sqrt{(x^2)^2+1}} \\\\&=\dfrac{-2}{x\sqrt{x^4+1}}\end{aligned}[/tex]

Therefore, the derivative of the given inverse hyperbolic function is:

[tex]\boxed{-\dfrac{2}{x\sqrt{x^4+1}}}[/tex]

The measurements of angles ∠3 and ∠4 are both 50°.

We have,

∠3 = 6x + 2

∠4 = 8x - 14

Now,

∠3 and ∠4 are alternate angles.

This means,

∠3 = ∠4

6x + 2 = 8x - 14

2 + 14 = 8x - 6x

2x = 16

x = 8

Now,

Substitute x = 8,

∠3 = 6x + 2 = 6 x 8 + 2 = 48 + 2 = 50°

∠4 = 8x - 14 = 8 x 8 - 14 = 64 - 14 = 50°

Thus,

The measurements of angles ∠3 and ∠4 are both 50°.

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Answer: To find out whether Maya hiked more than 3 kilometers in all, we need to add the lengths of the two trails and compare the sum to 3 kilometers.

The length of the first trail is 1 and 1-third kilometers, which can be written as:

1 + 1/3 = 4/3 kilometers

The length of the second trail is 1 and 2-fifths kilometers, which can be written as:

1 + 2/5 = 7/5 kilometers

Adding these two lengths, we get:

4/3 + 7/5 = (20/15) + (21/15) = 41/15 kilometers

To compare this to 3 kilometers, we need to convert 3 kilometers to the same unit as the sum of the two trail lengths, which is kilometers. We can write 3 kilometers as:

3 = 45/15 kilometers

Now we can compare the two values:

41/15 kilometers < 45/15 kilometers

Since the sum of the two trail lengths is less than 3 kilometers, Maya did not hike more than 3 kilometers in all.

Answer is x=23

Have a nice day

Answer:

The division of 319 by 12391, divided by 21, equals 0.00122592818. This is the answer to the calculation given.

Step-by-step explanation:

Answer:

The answer is 319/260211 or 0.001225

Step-by-step explanation:

319/12391/21=319÷12391/

=319/12391×21

=319/260211=0.001225

The variables are fluid ounces = dependent and cost = independent

The linear function that relates y to x is y = x/32The graph is attachedThe cost of 32 fluid ounces of brewed coffee is $2

Which variable is independent? dependent?

Given that

The table shows the cost y (in dollars) of x fluid ounces of brewed coffee

This means that

fluid ounces = dependent cost = independent

The linear function that relates y to x

From the table of values, we can see that

The fluid ounces is divided by 16 to get the cost

So, the linear function is

y = x/16

The slope means that the cost per fluid ounce is $1/16

The graph of the function is attached

The cost of 32 fluid ounces of brewed coffee

This means that

x = 32

So, we have

Cost = 32/16

Evaluate

Cost = 2

Hence, the cost of 32 fluid ounces of brewed coffee is $2

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The first five terms of the arithmetic sequence are 5, 8, 11, 14, and 17.

We have,

In an arithmetic sequence, each term is obtained by adding a fixed constant, called the common difference (d), to the previous term.

To find the common difference, we can use the formula:

a_n = a_1 + (n-1)*d

where a_n is the nth term of the sequence, a_1 is the first term, and n is the position of the term in the sequence.

Using the given information, we can write two equations:

a_2 = a_1 + d = 8

a_6 = a_1 + 5d = 15

Solving these equations simultaneously.

a_1 = 5

d = 3

Now, we can use the formula for the nth term to find the first five terms of the sequence:

a_1 = 5

a_2 = a_1 + d = 5 + 3 = 8

a_3 = a_2 + d = 8 + 3 = 11

a_4 = a_3 + d = 11 + 3 = 14

a_5 = a_4 + d = 14 + 3 = 17

Therefore,

The first five terms of the arithmetic sequence are 5, 8, 11, 14, and 17.

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(a) The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

We know that the width is 86m and the perimeter is 366m. Substituting these values into the formula, we get:

366 = 2l + 2(86)

Simplifying the right side, we get:

366 = 2l + 172

Subtracting 172 from both sides, we get:

194 = 2l

Dividing both sides by 2, we get:

l = 97

Therefore, the length of the rectangular field is 97m.

(b) The formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.

We know that the length is 96cm and the area is 7200cm^2. Substituting these values into the formula, we get:

7200 = 96w

Dividing both sides by 96, we get:

75 = w

Therefore, the width of the rectangular painting is 75cm.

probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 40%.probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 20%.

Using the table provided, we can find the probabilities requested in the question.

The table gives the probabilities of different types of orphaned pets in six cities. We will focus on the row for Austin, which tells us the probabilities for orphaned pets in animal shelters in Austin.

To find the probability that a randomly selected orphan pet in an animal shelter in Austin is a dog, we need to look at the second column of the row for Austin, which gives the probability of a dog. Let's assume this probability is 0.4, or 40%. This means that out of all the orphaned pets in animal shelters in Austin, 40% of them are dogs. Therefore, the probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 40%.

To find the probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua, we need to use conditional probability. Let's assume that the probability of a Chihuahua given that the pet is a dog in Austin is 0.2, or 20%.

This means that out of all the dogs in animal shelters in Austin, 20% of them are Chihuahuas. Therefore, the probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 20%.

It is important to note that the actual values for the probabilities may be different depending on the specific table provided in the question. However, the general approach to finding the probabilities will remain the same. By understanding the concepts of probability and practicing with different examples, we can become more skilled at analyzing and interpreting data.

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When a whole number greater than 1 has a negative integer exponent, the value of the expression is greater than zero but less than one.

How to deal with a negative exponent?

The standard format of an exponential expression is given as follows:

[tex]a^b[/tex]

In which:

a is the base.b is the exponent.

When we have a negative exponent, the equivalent expression with a positive exponent is obtained inverting the base.

If we have a positive base greater than one to a negative exponent, we invert the base, meaning that it is less than one with a positive exponent, hence the value of the expression is greater than zero but less than one.

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The difference in miles between the students who live closest and furthest away is 2 miles

The difference between the students who live closest and furthest away

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

The line plot

On the line plot, we have

Furthest = 7

Closest = 5

Using the above as a guide, we have the following:

Difference = Furthest - Closest

So, we have

Difference = 7 - 5

Evaluate

Difference = 2

Hence, the difference is 2

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a. The table beside the graph should be completed as follows;

"The coordinate of the vertex is (-3, -4).""The equation of the axis of symmetry is x = -3."The minimum value is -4.The y-intercept is (0, 4)."The x-intercepts are (-5, 0) and (-1, 0)."

b. The table beside the graph should be completed as follows;

"The coordinate of the vertex is (1, 9).""The equation of the axis of symmetry is x = 1."The maximum value is 9.The y-intercept is (0, 8)."The x-intercepts are (-2, 0) and (4, 0)."

How to interpret the graph and complete the table?

Based on the diagram, we can logically deduce that the graph of the first quadratic function is an upward parabola because the coefficient of x² has a positive value. Also, the value of "a" is greater than zero (0) with the x-intercept (roots) being (-5, 0) and (-1, 0) while the y-intercept is (0, 4).

Additionally, the vertex is given by the ordered pair (-3, -4) and it has a minimum value of -4.

Part b.

Based on the diagram, we can logically deduce that the graph of the second quadratic function is a downward parabola because the coefficient of x² has a negative value. Also, the value of "a" is less than zero (0) with the x-intercept (roots) being (-2, 0) and (4, 0) while the y-intercept is (0, 8).

In conclusion, the vertex is given by the ordered pair (1, 9) and it has a maximum value of 9.

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The vertical change from Point A to Point B is 1 unit.

The horizontal change from Point A to Point B is 2 units.

The rate of change (slope) is the vertical change divided by the horizontal change, which is 1/2 or 0.5.

We have,

Vertical change from Point A to Point B:

Point A is at (2, 1) and point B is at (4, 2).

The vertical change is the difference in the y-coordinates, which is 2 - 1 = 1.

Horizontal change from Point A to Point B:

Point A is at (2, 1), and point B is at (4, 2).

The horizontal change is the difference in the x-coordinates, which is 4 - 2 = 2.

Rate of change on the graph:

The rate of change is the slope of the line, which is the vertical change divided by the horizontal change.

From point A to point B, we have a vertical change of 1 and a horizontal change of 2.

The slope is 1/2, which can be written as 0.5 as a decimal rounded to the nearest tenth.

Thus,

The vertical change from Point A to Point B is 1 unit.

The horizontal change from Point A to Point B is 2 units.

The rate of change (slope) is the vertical change divided by the horizontal change, which is 1/2 or 0.5.

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The value of the number X is 72.

Given that,

For a number X, the number X is four times as great as another number which is two less than twenty.

There is another number, let's call it Y.

X is four times as great as Y.

X = 4Y

Y is number which is two less than twenty.

Y = 20 - 2 = 18

So, the value of X is,

X= 4 × 18 = 72

Hence the number X is 20.

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The probability that at least 20 will last that long is given as follows:

0.5 = 50%.

How to obtain probabilities using the normal distribution?

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].

The parameters for the binomial distribution are given as follows:

n = 30, p = 0.65.

Hence the mean and the standard deviation are given as follows:

[tex]\mu = 30 \times 0.65 = 19.5[/tex][tex]\sigma = \sqrt{30 \times 0.65 \times 0.35} = 2.61[/tex]

Using continuity correction, the probability that at least 20 will last that long is one subtracted by the p-value of Z when X = 19.5, hence:

Z = (19.5 - 19.5)/2.61

Z = 0

Z = 0 has a p-value of 0.5

1 - 0.5 = 0.5.

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The Ratio of the number of students who went to the aquarium to the number of students who went to the zoo is 19:12.

The ratio of the number of students who went to the aquarium to the number of students who went to the zoo, we need to determine the number of students who went to each place.

Given that there are 31 students in total and 12 students went to the zoo, we can find the number of students who went to the aquarium by subtracting the number of students who went to the zoo from the total number of students:

Number of students who went to the aquarium = Total number of students - Number of students who went to the zoo

= 31 - 12

= 19

Therefore, 19 students went to the aquarium.

The ratio of the number of students who went to the aquarium to the number of students who went to the zoo can be expressed as:

Number of students who went to the aquarium : Number of students who went to the zoo

Substituting the values, we have:

19 : 12

This ratio cannot be simplified any further because 19 and 12 do not have a common factor other than 1.

Therefore, the ratio of the number of students who went to the aquarium to the number of students who went to the zoo is 19:12.

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The critical point for the function f(x) = (2x + 1) eˣ is

A -3/2

What are critical points

On a graph critical points refer to the locations where the derivative of a function is either zero or undefined. these points can provide important information about the behavior of the function and can indicate where the function may have maximum or minimum values or points of inflection.

Examining the graph attached, the minimum point which is the critical point is -3/2 this is equivalent to -1.5.

Having coordinates (-1.5, -0.446), the x coordinate is -1.5.

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The linear function of the table are A and C.

How to find the table that is a linear function?

If the rate of the change in the input to the change in the output is the same for every point in the table, then the table represents a linear function.

A linear function can be represented as follows:

y = mx + b

where

m= slopeb = y-intercept

Therefore, the tables that are linear function are as follows:

Therefore, the linear function are A and C.

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Answer:

1/343

Step-by-step explanation:

(1/7)³ = 1³/7³ = 1/343

Answer:

E) 16 inches by 22 inches

a. One potential source of bias in the study published by the Canadian Medical Association Journal is that it is a the selection bias.

b. . One potential source of bias in the claim is that the diet supplement is a selection bias.

What is the potential source of bias?

Limiting the study to certain healthcare systems or populations may give an inaccurate portrayal of doctor visits across nations. The study's bias could affect views and limit generalizability.

The bias in the diet supplement claim: If participants were selected for success or high motivation, it could overestimate supplement effectiveness.

Claiming it works for disciplined people ignores other contributing factors. The claim's bias may affect views of the study's validity and applicability. The chosen participants and basic weight loss process may raise doubts about its reliability.

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The percent of apartment residents who pay from $600 to $749 per month is 94%.

We can see from our given bar graph that 25 residents pay from $600 to $649, 44 residents pay from $650 to $699 and 25 residents pay from $700 to $749.

So, total residents who pay 4600- $749

= 25+ 44 + 25

= 94

and, total residents in apartment

= 100

So, the percent of apartment residents who pay from $600 to $749 per month

= 94/ 100 x 100

= 94%

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