3. Reasoning In Example 2, what happens to the
value of the dependent variable, a, the amount
still owed, when the value of the independent
variable, w, the number of weeks Ethan pays $5,
is increased by 1?

Answer:

no

Step-by-step explanation:

using Pythagorean theorem:

[tex]26^{2} +42^{2}=50^{2}[/tex]

676+1764=2500

2440=2500

2440<2500

Answer:no

Yes, this relation is a function and here the domain and range are:

domain = {3,6,2,-7} and range ={0,-2,-1,0}

Domain and Range:

The domain and scope of a function are part of the function. The domain is the set of all input values ​​of a function, and the range is the possible outputs given by the function. Field → Function → Sequence. If there is a function f : A → B such that each element of set A corresponds to an element of set B, then A is the field and B is the codomain. The graph of an element "a" under a relation R is given by "b", where (a,b) ∈ R.

The scope of the function is the set of images. The domain and range of a function are usually expressed as:

Domain(f) = {x ∈ R: State} and range(f)={f(x): x ∈ domain(f)}

According to the Question:

The given function is:

{(3,0),(6,-2),(2,-1),(-7,0)}

It is a function as every input has a single output.

So, 3,6,2,-7 are the elements of the domain of the given relation.

Here domain = {3,6,2,-7} and range ={0,-2,-1,0}

Therefore, this relation is a function.

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suppose we should solve the following equation:

[tex]s = \frac{13}{2} (12 + 75)[/tex]

which equals 565.5

Answer: 20:21 or 20 to 21

Step-by-step explanation:

Answer:

If 20 out of 21 students want pancakes, then only 1 student wants waffles.

The ratio of the number of students who want waffles to the total number of students is therefore:

1 waffle student : 21 total students

or simplified as:

1 : 21

So the ratio is 1 to 21

The equation that shows how the amount of money Dalton gets in a week, y, depends on the number of times he walks the dog, x is y = 5 + x

Given that

Weekly allowance = $5

Amount earned for walking the dog = $1

The above means that

Total money = Weekly allowance  + Amount earned for walking the dog  * Number of times

So, we have

y = 5 + 1 * x

Evaluate

y = 5 + x

Hence, the equation is y = 5 + x

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The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store, with both stores having the same price.

The difference between the two terms is that "difference" refers to the way in which two or more things are not the same, whereas "difference" is more of a comparison between two or more things.

The difference between the lowest price in store 1 and the lowest price in store 2 is the difference between the first digit of each store's key. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1.

The difference between the highest prices in store 1 and store 2 is the difference between the last digit of each store's key. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0.

The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1. This difference is reflected in the lowest prices of each store, with store 1 having a lower price than store 2.

The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0. This difference is reflected in the highest prices of each store, with both stores having the same price.

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The ratio of Ali's score to Ben's score to Clare's score in its simplest form is  1 : 3.5 : 7

Given data:

Claire's score = 7 * Ali's score

Ben's score = 0.5 * Claire's score

How to solve for the ratio of Ali's score to Ben's score to Clare's score

let Ali's score = x

let Ben's score = y

let Claire's score = z

z = 7 * x = 7x

z = 7x

y = 0.5 * z = 1/2 * z = z / 2

plugging the value of z gives

y = 7x / 2

writing the ratios in terms of x gives

Ali : Ben : Claire

x : y : z

x : 7x/2 : 7x

Reducing the terms by dividing through by x

1 : 7/2 : 7

OR

1 : 3.5 : 7

clearing the fraction gives

2 : 7 : 14

Therefore, the ratio of Ali's score to Ben's score to Clare's score in its simplest form is  1 : 3.5 : 7

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To the nearest tenth, the length of each side of the equilateral triangle is roughly [tex]10(\sqrt{(3) - 1)[/tex].

An equilateral triangle has the following three characteristics: identical lengths on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure.

All of the triangle's sides are equal in length since it is equilateral. Call this length "s" for short.

The distance from vertex A to side x, measured in altitude, is equal to the length of side x. Call the intersection of the altitude and side x "P" for short.

The length of AP is [tex](s/2) * \sqrt{}[/tex] because we know that the altitude from vertex A creates a triangle with sides of 30-60-90. (3).

Since side BP is half the length of side AB, we also know that its length is (s/2).

As a result, x's length equals the product of AP and BP:

x = AP + BP

= (s/2) * [tex]\sqrt{(3) + (s/2)[/tex]

= [tex](s/2)(\sqrt{(3) + 1)[/tex]

We are told that x equals 10. We may put the formula we discovered for x equal to 10 and do the following calculation to find s:

[tex](s/2)(\sqrt{(3) + 1)[/tex] = 10

The result of multiplying both sides by two is:

[tex]s(\sqrt{(3) + 1) = 20[/tex]

When you divide both sides by [tex](\sqrt{(3) + 1)[/tex], you get:

[tex]s = 20/(\sqrt{3) + 1)[/tex]

The result of multiplying the numerator and denominator by the conjugate of [tex](\sqrt{(3) + 1), (\sqrt{(3) - 1)[/tex], is as follows:

s = [tex]20(\sqrt{3) - 1)/(3 - 1)[/tex]

= [tex]10(\sqrt{(3) - 1[/tex]

As a result, to the nearest tenth, the length of each side of the equilateral triangle is about [tex]10(\sqrt{(3) - 1[/tex].

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When the polynomial p(x)=-x^5-2x^3+4x-3, then the value of p(-1) is 3

The Remainder Theorem is a fundamental concept in algebra that relates the value of a polynomial at a certain point to the remainder of the polynomial's division by a linear factor.

The remainder theorem states that when a polynomial p(x) is divided by (x - a), the remainder is equal to p(a).

In this case, we are asked to find p(-1) when p(x) = -x^5 - 2x^3 + 4x - 3.

To use the remainder theorem, we need to divide p(x) by (x - (-1)), which is the same as (x + 1).

We can perform polynomial long division to find the quotient and remainder

The remainder is -x + 2, which means that p(-1) = -(-1) + 2 = 3.

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z = 110°

mEB = 90°

mCE = 74°
I’m not sure about x or y but I think these are right.

Answer: 32

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 is the base and 5 is the exponent, so we have to multiply 2 5 times.

2*2*2*2*2=32

The probability that Mark selects a car key or door key from the key ring is 0.3 or 30%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory provides a framework for understanding random events and the laws of chance, and it is an important tool for modeling and simulating complex systems.

Calculating the probability that he selects a car key or door key :

In this context, we are asked to find the probability of Mark selecting a car key or door key from the key ring. To calculate this probability, we need to first determine the total number of keys on the key ring and then count the number of car keys and door keys.

Total number of keys = 10

Number of car keys = 2

Number of door keys = 1

The probability of selecting a car key or door key can be found by adding the probability of selecting a car key to the probability of selecting a door key. Since there is only one door key and two car keys, the probability of selecting a car key is higher, and we can simplify the calculation by finding the probability of selecting a car key and then adding the probability of selecting a door key that hasn't already been selected.

Probability of selecting a car key = 2/10 = 0.2

Probability of selecting a door key = 1/9 (since one key has already been selected) = 0.1111...

Therefore, the probability of Mark selecting a car key or door key from the key ring is 0.2 + 0.1111... ≈ 0.3 or 30%.

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The area of the given parallelogram is A- 33(1/2) ft² using the base and height of the parallelogram. the correct answer is (c).

A quadrilateral with two sets of analogous edges is appertained to as a parallelogram. In a parallelogram, the opposing edges are of equal length, and the opposing angles are of equal size. also, the internal angles that are supplementary to the transversal on the same side. 360 ° is the sum of all internal angles. A parallelepiped is a three- dimensional shape with parallelogram- shaped sides. The base( one of the analogous lines) and height( the distance from top to bottom) of the parallelogram determine its area. A parallelogram's border is determined by the lengths of its four edges. The characteristics of a parallelogram are participated by the shapes of a square and cell. What's area? The size of a section on a face is determined by its area. face area refers to the area of an open face or the border of a three- dimensional object, whereas the area of an area area plane region or area  area plane area refers to the area of a shape or planar lamella.

The area of a parallelogram is given by

[tex]base*height.base=8(1/3)ft[/tex]

height=4ft

[tex]Area=b*h =(25/3)*4 =100/3 = 33[/tex]

[tex][base]\frac{1}{3}[(hieght)] ft^{2}[/tex]

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[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o }{3} \right) +i \sin\left( \cfrac{ 219^o }{3} \right)\right]\implies \boxed{4[\cos(73^o)+i\sin(73^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 579^o }{3} \right) +i \sin\left( \cfrac{ 579^o }{3} \right)\right]\implies \boxed{4[\cos(193^o)+i\sin(193^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=2}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 939^o }{3} \right) +i \sin\left( \cfrac{ 939^o }{3} \right)\right]\implies \boxed{4[\cos(313^o)+i\sin(313^o)]}[/tex]

a. The account balance is $1000 when opened.

b. $1,060 is the balance after 1 year.

c. 42.98 years as per compound interest.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on the accumulated interest from previous periods. This means that interest is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.

In the given question,

a. When the account is opened, t = 0. Therefore, the balance is:

1 × e(0.06 × 0) = 1 × e⁰ = 1

The account balance is $1,000 when it is opened.

b. After 1 year, t = 1. Therefore, the balance is:

1 × e(0.06 × 1) ≈ 1.06

The account balance is approximately $1,060 after 1 year.

c. After 2 years, t = 2. Therefore, the balance is:

1 × e(0.06 × 2) ≈ 1.123

The account balance is approximately $1,123 after 2 years.

Diego's statement is not accurate. The expression In 5 represents the natural logarithm of 5, which is approximately 1.609. It does not represent the time, in years, when the account will have 5 thousand dollars.

To find the time when the account will have a balance of $5,000, we need to solve the equation:

1 × e(0.06t) = 5

Dividing both sides by 1:

e(0.06t) = 5

Taking the natural logarithm of both sides:

ln(e(0.06t)) = ln(5)

0.06t = ln(5)

t = ln(5) / 0.06 ≈ 11.55

Therefore, the account will have a balance of $5,000 after approximately 11.55 years.

We can use the same equation as in part 2 to find out if the account balance will reach $1,000,000. We need to solve the equation:

1 × e(0.06t) = 1000

Dividing both sides by 1:

e(0.06t) = 1000

Taking the natural logarithm of both sides:

ln(e(0.06t)) = ln(1000)

0.06t = ln(1000)

t = ln(1000) / 0.06 ≈ 42.98

Therefore, the account balance will reach $1,000,000 after approximately 42.98 years.

Whether or not this will make you a millionaire by the time you reach retirement depends on when you plan to retire and how much money you need for retirement. If you plan to retire in less than 43 years or you need more than $1,000,000 for retirement, then this account alone will not make you a millionaire.

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The Perimeter of the parallelogram whose vertices are given by the coordinates (3 ,6), (-5, 6), (6, -1), (-2, -1) is: 16 + 2√(58)

To find the perimeter of the parallelogram, we need to find the distance between each pair of adjacent vertices and add them up.

First, let's find the distance between (3, 6) and (-5, 6). This is simply the difference between their x-coordinates, which is 3 - (-5) = 8.

Next, let's find the distance between (-5, 6) and (-2, -1). To do this, we need to find the difference between their x-coordinates and their y-coordinates, and then use the Pythagorean theorem. The difference in x-coordinates is -5 - (-2) = -3, and the difference in y-coordinates is 6 - (-1) = 7. So the distance between these two points is √((-3)^2 + 7^2) = √(58).

We can use the same method to find the distance between (6, -1) and (3, 6), which is also √(58).

Finally, we need to find the distance between (6, -1) and (-2, -1), which is simply the difference between their x-coordinates, which is 6 - (-2) = 8.

Adding up all these distances, we get 8 + √(58) + √(58) + 8 = 16 + 2√(58).

So the exact perimeter of the parallelogram is 16 + 2√(58)

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Answer:No

Step-by-step explanation:

Because each X is an input, this means that Y is obviously the output.

In order for a set of data, there must ALWAYS be one output for every input, no more, no less. Because this particular set of data has multiple Y values with respect to different X values, this is not a function. Your correct answer is "No, because for each input there is not exactly one output."

Answer:

Step-by-step explanation:

To find the equation of a line when you have two points, you can use the point-slope formula. Here's how to do it:

1. Find the slope of the line using the two points:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, 3) and (x2, y2) = (5, 3)

slope = (3 - 3) / (5 - 0) = 0/5 = 0

2. Use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the points on the line. Using (0, 3) as the point, we get:

y - 3 = 0(x - 0) or y = 3

So the equation of the line is y = 3, a horizontal line passing through y = 3.

The domain of this equation is all real numbers, since x can take on any value and y will always be 3.

The range of this equation is a single value, y = 3, since the line is horizontal and every point on the line has the same y value of 3.

Answer:

17.8

Step-by-step explanation:

a^2+b^2=c^2

To find the distance between Tallahassee and Miami we need to find the distance from...

(10,17) and (10,3)

as well as (10,3) and (21,3)

The distance from the point (10,17) to (10,3) is the difference in y or 17-3, which gives you 14

The distance from the point (10,3) to (21,3) is the difference in x or 21-10, which gives you 11

Now you can plug in the values in the pythagorean theorem like so:

14^2+11^2=c^2

196+121=c^2

317=c^2

Square root both sides

The sqrt of 317 is approximately 17.804, rounding to 17.8 to the nearest tenths place.

The probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes is 0.33 or 33%.

Uniform distribution is a probability distribution where all outcomes are equally likely. In this case, the time it takes to wash dishes is uniformly distributed between 8 and 17 minutes. This means that any time between 8 and 17 minutes is equally likely to occur.

To find the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes, we need to find the area under the curve of the uniform distribution function between 12 and 15 minutes.

Since the distribution is uniform, the area under the curve between 12 and 15 minutes is simply the width of the interval divided by the total width of the distribution. Mathematically, we can express this as:

P(12 ≤ X ≤ 15) = (15 - 12) / (17 - 8)

P(12 ≤ X ≤ 15) = 3 / 9

P(12 ≤ X ≤ 15) = 0.33 or 33%.

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Answer: the team amassed 88i points total, by shooting t two-point baskets and u 1-point free throws.

t+u = 53

total is:  2t + u = 88.

Step-by-step explanation:

hope i makes sense

Point A is three units left and three units up from the origin, so its coordinates are (-3, 3). Therefore, the correct answer is option 2) (-3, 3).

The topic of coordinate geometry involves the use of the Cartesian plane, also known as the coordinate plane or xy-plane, to graph and analyze relationships between points, lines, and shapes. The plane consists of two perpendicular number lines called the x-axis and the y-axis.

The origin, denoted by the point (0, 0), is the point where the two axes intersect. Points on the plane are represented by ordered pairs of numbers (x, y), where x is the distance from the y-axis and y is the distance from the x-axis. Lines on the plane can be represented by their slope and y-intercept, while shapes like circles, rectangles, and triangles can be graphed and analyzed using their respective formulas.

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Answer: (−3, −3)

Step-by-step explanation:

Given that the perimeter of the square base is 32 cm, The surface area of the square pyramid is 304 cm².

The surface area of a square pyramid can be calculated using the formula: SA = B + (1/2)Pl, where B is the area of the base, P is the perimeter of the base, l is the slant height, and SA is the total surface area.

Given that the perimeter of the square base is 32 cm, we can divide it by 4 to find the length of each side: 32 cm / 4 = 8 cm.

Now, we can calculate the area of the base by squaring the length of a side: B = (8 cm)² = 64 cm²

Using the given slant height of 15 cm, we can plug in the values into the formula for SA: SA = 64 cm² + (1/2)(32 cm)(15 cm) = 64 cm² + 240 cm² = 304 cm².

Therefore, the surface area of the square pyramid is 304 cm².

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Answer:

379.94

Step-by-step explanation:

Area of a circle given radius is really easy! The equation for area of a cicle is pi x r^2. So just plug in. Assuming pi is 3.14 your equation would be

3.14x11^2. 11 squared is 121. Then multiply by 3.14 and thats your answer.

Answer: 63.8

Step-by-step explanation:

Area of the solid composite shape with triangle and rectangle is =832cm².

The area of a composite shape can be determined by adding or subtracting its component pieces.

Hence, we can use two formulas:

Area of Composite Shape + Area of Composite Shape + Area of Basic Shape A (additive)

Basic Shape Area A, Basic Shape Area B, and Composite Shape Area (subtractive)

In the figure,

Dimensions of the triangle are height, h = 16cm and base, b = 12cm.

Area = 1/2 ×b ×h

= 1/2 × 16× 12

=96cm²

There are two triangles, so the total area = 96+ 96 = 192cm².

Now area of the rectangle = length × width

= 20 × 32

= 640cm².

Total area of the solid= 192 + 640 = 832cm².

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The relationship between the mean and median depends on the shape of the distribution of the data, therefore correct options are

(a) The mean is approximately the same as the median

(b) The mean is greater than the median

(c)  The mean is less than the median.

The relationship between the mean and the median depends on the shape of the distribution of the data. In a symmetric distribution, the mean and median will be approximately the same. In a skewed distribution, the mean will be pulled in the direction of the skew, and the median will be a better representation of the "typical" value.

If the distribution is symmetrical (i.e., evenly distributed around the center), the mean and median will be approximately the same.

If the distribution is positively skewed (i.e., has a long tail on the right side), the mean will be greater than the median.

If the distribution is negatively skewed (i.e., has a long tail on the left side), the mean will be less than the median.

Therefore, correct options are

(a) The mean is approximately the same as the median

(b) The mean is greater than the median

(c)  The mean is less than the median.

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4 feet.

The length of the rope from the ground to the top of the tent is 4 feet.

To calculate this, subtract the distance from the tent to the ground (2 feet) from the height of the tent (6 feet), and you will get the length of the rope (4 feet).

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