1.) Identify the similar triangles in each figure. Explain why they are similar and use the given information to find x and y.

2.) The area of a rectangle is 108 cm2. The ratio of the width to the length is 3:4. Find the length and the width.

Answer: Is a plane figure with at least 3 straight sides and angles, and typically five or more sides.

Step-by-step explanation:

the slope of the graph is 3 and the y-intercept is -27. This means that the graph crosses the y-axis at the point (0,-27).

Answer:

y = -3x - 27

Step-by-step explanation:

9x - 3y = 81

-3y = 9x + 81

-3y/3 = 9x/3 + 81/3

-y = 3x + 27

y = -3x - 27

The x-coordinate of the x-intercept of line k is -5/2.

Since this point lies on the x-axis, its y-coordinate is 0.

Given that the line has a y-intercept at the point (0, p), where p is a positive constant. This means that when x = 0, y = p.

As we know that the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope is the negative of the fraction 2p/5, so the equation of line k is y = -2p/5 x + p.

Substitute y = 0 into the equation and solve for x:

0 = -2p/5 x + p

Subtract p from both sides and then multiply by 5/(-2p):

-2p/5 x = -p

x = (-p)(5/2p)

x = -5/2

Therefore, the x-coordinate of the x-intercept of line k is -5/2.

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The percentage daily value for protein for a serving of miso soup is around 16%.

The percentage daily value will be calculated by the formula -

Percentage daily value = mass of protein in miso soup/ amount of daily requirement of protein × 100

Assuming the daily value of protein to be 50 gram based on the question. Keep the values in formula -

Percentage daily value = [tex] \frac{8}{50} \times 100[/tex]

Cancelling zero and performing multiplication and division

Percentage daily value is 16%.

Hence, the daily value of protein in miso soup is 16%.

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Budgeting for a household and a business both require setting financial goals, prioritizing expenses, and tracking income and expenses

Given that;

To find budgeting for a household be similar to budgeting for a business.

Since, Budgeting for a household and a business both require setting financial goals, prioritizing expenses, and tracking income and expenses.

Here,  In both cases, it's important to consider fixed and variable expenses, such as rent or mortgage payments, bills, food costs, and employee salaries.

And, Additionally, creating a contingency plan for unexpected expenses is essential for both households and businesses.

Hence, The main difference is that businesses may have more complex financial structures with investors or loans to consider, while households typically have simpler financial structures.

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Answer:   = 8[tex]\pi[/tex]

Step-by-step explanation:

The length of AB is 12, which is the diameter, so

r=6

You need to find the angle of BOD. It is on the bottom half.  Also, AOC is the same angle

180-20 =160  now divide by 2

<BOD=80

In order to find area you multiply the fractional portion by the area

A(BOD) = [tex]\frac{80}{360} \pi r^{2}[/tex]

            =[tex]\frac{8}{36} \pi 6^{2}[/tex]                I reduced by 10 and the 36's cancel out

            = 8[tex]\pi[/tex]

A: y = 248.2 * (0.9896)^t

B: 169.6

a) To find an exponential model for this data, we can use the formula:

y = ab^t

where y is the age-adjusted death rate per 100,000 Americans from heart disease, a is the initial death rate, b is the growth factor, and t is the number of years since 1998.

We are given two data points:

(0, 248.2) for 1998

(6, 213.2) for 2004

Let's plug in the first data point to find 'a':

248.2 = a * b^0

Since any number raised to the power of 0 is 1, we have:

a = 248.2

Now let's plug in the second data point and 'a' to find 'b':

213.2 = 248.2 * b^6

To find 'b', we'll first divide both sides by 248.2:

213.2 / 248.2 = b^6

0.859033 = b^6

Now take the sixth root of both sides to solve for 'b':

b = (0.859033)^(1/6)

b ≈ 0.9896

Our exponential model is:

y = 248.2 * (0.9896)^t

b) To estimate the death rate in 2025, we need to find the value of 't' for 2025:

t = 2025 - 1998 = 27

Now, we can plug 't' into our exponential model:

y = 248.2 * (0.9896)^27

y ≈ 169.6

Assuming the model remains accurate, the estimated age-adjusted death rate per 100,000 Americans from heart disease in 2025 is approximately 169.6 (rounded to the nearest tenth).

In the provided problem, the sampling mean  for a random sample of 35 employees from a population of hourly workers in South Carolina with an average hourly wage of $17.52 and a standard deviation of $6.00 per hour is being sought after.

Even if the underlying population is not normally distributed, the central limit theorem predicts that with a high sample size, the sampling distribution of the means will be about normally distributed.

In this case, since the sample size is large enough (n=35), we can assume that the sampling distribution of the means will be approximately normally distributed with a mean of $17.52 and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.

In summary, a small survey of 35 employees from the Carolina group of hourly workers yielded a mean of $17.5 as determined by the  testing distribution of means.

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An algebraic expression to represent the absolute difference is |d - 24|.

The algebraic expression to represent the absolute difference between varying values of the depth of the hole (d), and the ideal depth of the hole (24 inches), also known as the margin of error, is:

|d - 24|

The vertical bars denote the absolute value, which gives the magnitude of the difference between d and 24, regardless of whether d is greater than or less than 24. The resulting value represents the distance between the actual depth of the hole and the ideal depth of 24 inches. This margin of error is an important concept in various fields, such as engineering, construction, and manufacturing, as it helps to determine the accuracy and precision of measurements and designs.

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Answer:

17

Step-by-step explanation:

5(20+...)=100+85

Let x =...

[Put 5 as a factor in the second unit]

5(20+x)=5(20+17)

Compare number

5=5, 20=20, x=17

So X=17

Answer:

The answer for the Area of the shape is

1357in²

Step-by-step explanation:

cut the shape into rectangle and another rectangle

then,Area of the shape =Area of small rectangle +Area of big Rectangle)

A=L×B+L×B

A=25×1015×75

A=250+1125

A=1357in²

Answer: 1/3

Step-by-step explanation:

9÷(9+18/9)

 9/27

=1/3

Answer:

The difference is meaningful because the means are separated by about 3 MADs.

Answer: 4

Step-by-step explanation:

It creates a right triangle.  

one leg is 3

the hypotenuse is 5  (the key here is to know that the radius is 5 and can be moved anywhere

the last leg is BC which is what you are looking for

so use pythagorean

c²=a²+b²

5²=3²+BC²

25-9=BC²

BC=√16

BC=4

The binary number 1011011 is equal to the denary number 91.

1011011two is converted to  denary by writing the numbers and assigning powers of 2 from zero to the number of digits available. For the problem, we have zero to six. then multiply out and add

= 1 x 64 + 0 x 32 + 1 x 16 + 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1

this results to

= 64 + 0 + 16 + 8 + 0 + 2 + 1

then the addition is equal to

= 91.

hence, the binary number 1011011 is equal to the denary number 91.

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3 + 6 + 1 + 4 or 2 + 3 + 4 + 5

Step-by-step explanation:

3 + 6 + 1 + 4 or 2 + 3 + 4 + 5

Using the frequency table provided, the mean number of games to complete a randomly selected championship from among those considered in the table is 4.333 games. The standard deviation of Y is 0.655 games.

The first team to four victories in a competition wins the title. The table provides the game lengths for the championship matches.

Let X be the total number of games required to win a championship, and let Y represent the total number of games required to win a championship chosen at random from those taken into account in the table.

Using the frequency table provided, the mean number of games to complete a randomly selected championship from among those considered in the table is 4.333 games. The standard deviation of Y is 0.655 games.

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The bracket should be placed 40 inches away from the vertex (0,0) looking at the equation y=1/160x^2 models a solar cooker.

The equation with a vertex is : y = ax²

We know that the focus of a parabola is normally at the point (h, k + p), where (h, k) is the vertex of the  parabola  and 'p' is the distance between the vertex and the focus.  

Since the vertex at the origin is  (0,0), the parabolic equation then becomes;

y = (1/4p)x²

1/4p = 1/160

4p = 160

p = 160 ÷ 4

p = 40

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Answer:

Step-by-step explanation:

AUB and AnB for the set A and B is  { } ( empty set)

To find A U B, we need to combine all the elements of A and B and remove duplicates:

A U B = {2, 3, 4, 5, 7, 8}

To find A n B, we need to find the elements that are common to both A and B:

A n B = {} (since there are no elements common to both sets A and B)

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Answer: The linear function representing the total cost of the patio is:

f(x) = 13x + 832

Step-by-step explanation:

The total cost of the patio consists of the original quote and the additional cost for expanding it by x square feet. Since the cost of expanding the patio is given in dollars per square foot, this relationship is linear. We can write a linear function in the form f(x) = mx + b, where:

In this case, the slope m is $13 per square foot, and the y-intercept b is the original quote of $832. So the linear function representing the total cost of the patio is:

f(x) = 13x + 832

Answer:

No, this is not a solution.

Step-by-step explanation:

To solve this you have to substitute 16 into the inequality w - 12 < 4.

Subtracting 12 from 16 gives you 4 which is equal to 4 not less than. So 16 is not a solution to this problem.

The total number of  positive even integers that satisfied the inequality 4x - 15 ≤ 125 is equal to 17.

The inequality is equal to,

4x - 15 ≤ 125

Adding 15 to both sides, we get,

⇒ 4x ≤ 140

Dividing both sides by 4, we get,

⇒x ≤ 35

Since we are looking for positive even integers,

Find the number of even integers less than or equal to 35.

The even integers less than or equal to 35 are,

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34

There are 17 even integers less than or equal to 35 that satisfy the inequality 4x - 15 ≤ 125.

Therefore, there are 17 positive even integers which satisfy the given inequality .

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Step-by-step explanation:

We can use the formula for continuously compounded interest to find the balance in Amadou's account after 20 years:

A = Pe^(rt)

where A is the balance, P is the initial investment, e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years. Plugging in the values given, we get:

A = 760e^(0.81*20)

A ≈ $91,012.43

Now we can use the formula for annually compounded interest to find the balance in Mia's account after 20 years:

A = P(1 + r)^t

Plugging in the values given, we get:

A = 760(1 + 0.83)^20

A ≈ $33,883.24

Finally, we can subtract Mia's balance from Amadou's balance to find the difference:

$91,012.43 - $33,883.24 ≈ $57,129.19

So Amadou would have about $57,129 more in his account than Mia after 20 years.

The factorized form of the given quadratic equation is:

y = -1*(x + 3)*(x + 1)

To factorize it we need to find the two zeros of the quadratic equation below.

y = -(x + 2)² + 1

The two zeros are when:

x + 2 = 1

x = 1 - 2 = -1

and:

x + 2 = -1

x = -1 - 2 = -3

And we can see that the leading coefficient is a = -1

Then the factorized form of the quadratic equation is:

y = -1*(x + 3)*(x + 1)

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Statement b) 'The spread of the data is the same for both towns' and c) 'The interquartile range is less for Town A than Town B' are true.

a) The median is greater for town A:

To find the median, we need to arrange the data in order:

Town A: 0, 0, 0, 1, 2, 2, 3, 4, 5, 10

Town B: 2, 2, 4, 4, 5, 6, 8, 9, 12

The median for town A is 2 and the median for town B is 5. Therefore, statement (a) is false.

b) The spread of the data is the same for both towns:

To compare the spread of the data, we can look at the range, which is the difference between the largest and smallest values.

Town A: Range = 10 - 0 = 10

Town B: Range = 12 - 2 = 10

Both towns have the same range, so statement (b) is true.

c) The interquartile range is less for Town A than Town B:

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). To find the quartiles, we need to arrange the data in order:

Town A: 0, 0, 0, 1, 2, 2, 3, 4, 5, 10

Q1 = 0.5, Q3 = 4

Town B: 2, 2, 4, 4, 5, 6, 8, 9, 12

Q1 = 2.5, Q3 = 9

The IQR for town A is 3.5 (4 - 0.5) and the IQR for town B is 6.5 (9 - 2.5). Therefore, statement (c) is true.

d) The modes are the best representation of the data for both towns:

The mode is the value that occurs most frequently in the data.

Town A: The mode is 0, which occurs three times.

Town B: There are two modes, 2 and 4, which each occur twice.

While the modes are a useful summary of the data, they may not be the best representation in this case since there are only ten data points for each town. Therefore, statement (d) is false.

e) The mean number of inches of snow per day was twice as much as in Town B as in Town A:

To compare the means, we need to calculate them for each town:

Town A: Mean = (2+0+5+4+2+10+1+3+0+0)/10 = 2.7

Town B: Mean = (4+4+9+8+12+2+2+2+6+5)/10 = 5.2

The mean for town B is approximately 1.9 times greater than the mean for town A, but not twice as much. Therefore, statement (e) is false.

Correct Question :

Two friends both claim that their towns received more snow during January. They picked ten random days in the month and listed the number of inches of snow that fell on those days in each of their towns.

Town A: 2, 0, 5, 4, 2, 10, 1, 3, 0, 0

Town B: 4, 4, 9, 8, 12, 2, 2, 2, 6, 5

Choose all true statements :-

a) The median is greater for town A

b) The spread of the data is the same for both towns

c) The interquartile range is less for Town A than Town B

d) The modes are the best representation of the data for both town

e) The mean number of inches of snow per day was twice as much as in Town B as in Town A

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The surface area of the square pyramid is 40.86 in²

The formula of surface area of square pyramid is given as;

S.A = a² + 2a√(a²/4 + h²)

h = height of the pyramid

a = side length of the base

However, we don't know the height of the pyramid, but we can apply Pythagorean theorem.

x² = y² + z²

6² = h² + 2²

NB: Half the length of the base is the length of one of the legs of the triangle.

h² = 36 - 4

h = √32

Substituting the value of h into the formula of surface area of the square pyramid;

S.A = 4² + 2(4)√(4²/4) + √32)

S.A = 40.86 in²

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The vectors v1 and v2 are linearly independent if and only if the only solution to the equation a1v1 + a2v2 = 0 is a1 = a2 = 0.

In this case, we have
a1(1, c) + a2(-1, 2c) = (a1 - a2, ac + 2ac)
Setting this equal to (0,0), we get the system of equations
a1 - a2 = 0
ac + 2ac = 0
Simplifying the second equation, we get
3ac = 0
So either c = 0 or a = 0.
If c = 0, then the two vectors become (1,0) and (-1,0), which are linearly independent.
If c ≠ 0, then a1 = a2 = 0 implies that the vectors are linearly independent.
Therefore, the vectors are linearly independent for c ≠ 0, and linearly dependent for c = 0.
Answer: DNE, 0

To find all values of c for which the vectors v1 = (1, c) and v2 = (-1, 2c) are linearly independent, follow these steps:
1. First, recall that two vectors are linearly independent if one cannot be represented as a scalar multiple of the other.
2. Assume that there is a scalar k such that v1 = k * v2.
3. We can write this assumption as (1, c) = k * (-1, 2c).
4. Expanding the equation, we get (1, c) = (-k, 2ck).
5. Now, compare the corresponding components of the two vectors:
  1 = -k
  c = 2ck
6. From the first equation, we find that k = -1.
7. Substitute k = -1 into the second equation:
  c = 2c(-1)
  c = -2c
8. To solve for c, we can write the equation as:
  c + 2c = 0
  3c = 0
  c = 0
Therefore, the vectors v1 = (1, c) and v2 = (-1, 2c) are linearly independent when c ≠ 0.

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