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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

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:

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

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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The 8 s the solution of equation StartFraction x Over 8 EndFraction = 1 i.e., x/8 = 1. So, the correct option is D).

To determine for which equations 8 is a solution, we can simply substitute 8 for x in each equation and see if the equation holds true.

Substituting x = 8 in the given equations, we get

x + 6 = 8 + 6 = 14 (not equal to 8)

x + 2 = 8 + 2 = 10 (not equal to 8)

x - 4 = 8 - 4 = 4 (not equal to 8)

x - 2 = 8 - 2 = 6 (not equal to 8)

2x = 2(8) = 16 (not equal to 8)

3x = 3(8) = 24 (not equal to 8)

x/2 = 8/2 = 4 (not equal to 8)

x/8 = 8/8 = 1 (equal to 8)

Therefore, only one equation x/8 = 1 has 8 as a solution.

Mathematically, we can evaluate this equation as follows

x/8 = 1

Multiplying both sides by 8

x = 8 * 1

x = 8

Since we have substituted x=8 and obtained the same value on both sides of the equation, the equation holds true for x=8. So, the correct answer is D).

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Answer:

  5.1%

Step-by-step explanation:

You want the rate of inflation if the price of a Honda Civic increase from $2000 in 1972 to $25000 in 2023.

The rate of inflation can be computed from ...

  r = (p1/p0)^(1/t) -1

  r = (25000/2000)^(1/51) -1 ≈ 0.05077 ≈ 5.1%

The rate of inflation is about 5.1%.

__

Additional comment

The question refers to "today," but we don't know exactly what is intended by that. The year at the time of this writing has been used. The required answer may vary, depending on the intended number of years.

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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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Answer:

Step-by-step explanation:

Since the two bottles are similar, we know that they have the same shape, but the larger bottle is scaled up by a certain factor compared to the smaller bottle. Let's denote this scaling factor by k.

The volume of the smaller bottle is 500 ml, so we can set up the following proportion between the volumes of the two bottles:

volume of larger bottle / volume of smaller bottle = k³

Since the scaling factor applies to all three dimensions of the bottle, we need to use k³ instead of just k. We want to solve for the volume of the larger bottle, so we can rearrange the proportion to isolate the volume of the larger bottle:

volume of larger bottle = (k³) * volume of smaller bottle

We don't know the value of k, but we do know that the bottles are similar, which means that corresponding dimensions are proportional. In particular, the ratio of corresponding lengths is k, the ratio of corresponding widths is k, and the ratio of corresponding heights is k. Therefore, we have:

k (corresponding length) = k (corresponding width) = k (corresponding height)

We also know that the smaller bottle has a volume of 500 ml, which is equivalent to 0.5 liters. We can use this information to solve for k:

0.5 liters = (1/1000) cubic meters = (k³) * (1/1000) cubic meters

Simplifying, we get:

k³ = 500/1000 = 1/2

Taking the cube root of both sides, we get:

k = (1/2)^(1/3)

Now we can substitute this value of k into the formula we derived earlier to find the volume of the larger bottle:

volume of larger bottle = ((1/2)^(1/3))³ * 500 ml

Simplifying, we get:

volume of larger bottle = (1/2) * 500 ml = 250 ml

Therefore, the larger bottle can hold 250 ml of water.

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

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]

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

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 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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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: 1/3

Step-by-step explanation:

9÷(9+18/9)

 9/27

=1/3

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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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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a. The approximate value for the standard error of the mean is 0.22.

b. The approximate 90% bootstrap percentile confidence interval for the true average adult height in the population is [67.55, 68.81] inches, with a one-sentence interpretation being that we are 90% confident that the true average adult height in the population lies between 67.55 and 68.81 inches.

c. The approximate 90% bootstrap SE confidence interval for the true average adult height in the population is [67.67, 68.69] inches, with a one-sentence interpretation being that if we were to take many samples from the same population, then 90% of the intervals calculated using this method would contain the true average adult height in the population.

For a: To find an approximate value for the standard error of the mean, we can use the standard deviation of the bootstrap sampling distribution. From the histogram, we can estimate that the standard deviation is about 0.22, which gives us an approximate value for the standard error of the mean.

For b: To find an approximate 90% bootstrap percentile confidence interval for the true average adult height in the population, we can use the 5th and 95th percentiles of the bootstrap sampling distribution. From the histogram, we can estimate that the 5th and 95th percentiles are about 67.55 and 68.81 inches, respectively. Therefore, the approximate 90% bootstrap percentile confidence interval is [67.55, 68.81] inches. We can interpret this interval as saying that we are 90% confident that the true average adult height in the population lies between 67.55 and 68.81 inches.

For c: To find an approximate 90% bootstrap SE confidence interval for the true average adult height in the population, we can use the mean of the bootstrap sampling distribution plus or minus 1.645 times the standard error of the mean. From part (a), we estimated the standard error of the mean to be about 0.22. From the histogram, we can estimate that the mean of the bootstrap sampling distribution is about 68.18 inches. Therefore, the approximate 90% bootstrap SE confidence interval is [67.67, 68.69] inches. We can interpret this interval as saying that if we were to take many samples from the same population, then 90% of the intervals calculated using this method would contain the true average adult height in the population.

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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).

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:

[tex]f(x)=3x^2+12x+9[/tex]

Step-by-step explanation:

Recall that the factored form of a quadratic is:

[tex]f(x)=a(x-r_{1} )(x-r_{2})[/tex]

Where r1 and r2 are the roots of the quadratic.

As shown in the image, the x-intercepts are (-3, 0) and (-1, 0).

Since these are the values of x when y=0, they are the roots of the quadratic equation. Let's plug them in. We get:

[tex]f(x)=a(x-(-3)(x-(-1)=\\f(x)=a(x+3)(x+1)=\\f(x)=a(x^2+4x+3)[/tex]

We are given that the point (-2, -3) also belongs to the graph. This means that when x=-2, y=-3. Let's plug in those points and solve for a:

[tex]f(x)=a(x+3)(x+1)=\\-3=a(-2+3)(-2+1)=\\-3=a(1)(-1)=\\-3=-a=\\3=a[/tex]

Now, let's go back to the equation:

[tex]f(x)=a(x^2+4x+3)[/tex]

and substitute a with 3, then solve.

[tex]f(x)=a(x^2+4x+3)=\\f(x)=3(x^2+4x+3)=\\f(x)=3x^2+12x+9[/tex]

Thus, the equation of this function is [tex]f(x)=3x^2+12x+9[/tex]

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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The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.

Then the expected value of the number of heads can be evaluated by multiplying each probability with its  corresponding number of heads and suming them.
For the given case, we possess five coins with different probabilities of getting heads when flipped.
Therefore, getting heads for each coin in context of probability are 0.1, 0.2, 0.3, 0.4 and 0.5

Now, the expected value of the number of heads is
Expected value = [tex](0.1 * 1) + (0.2 * 1) + (0.3 * 1) + (0.4 * 1) + (0.5 * 1)[/tex]
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5
=1.5
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.

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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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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:

Step-by-step explanation:

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 probability that a random sample of 40 adult caucasian women have a mean height greater than 64.0 inches is approximately 0.1569 or 15.69% (rounded to four decimal places).

We can use the central limit theorem to approximate the distribution of the sample mean as normal, with mean μ = 63.6 inches and standard deviation σ/√n = 2.5 inches/√40 = 0.3953 inches.

Thus, we need to find the probability that a normally distributed random variable with mean μ = 63.6 inches and standard deviation σ/√n = 0.3953 inches is greater than 64.0 inches.

Using the z-score formula, we can standardize the value of 64.0 inches to get:

z = (64.0 - 63.6) / 0.3953 = 1.011

From the standard normal distribution table, the probability of a z-score greater than 1.011 is 0.1569.

The central limit theorem is a statistical concept that describes the behavior of the means of a large number of independent random variables. It states that when the sample size is large enough, the distribution of the means will be approximately normal, even if the underlying variables are not normally distributed.

Specifically, the theorem states that as the sample size increases, the mean of the sample means approaches the population mean and the standard deviation of the sample means are close to the population standard deviation when the sample size is squared. This theorem is important because it allows us to make statistical inferences about a population based on a sample. For example, we can use it to estimate the mean and variance of a population, or to calculate confidence intervals and hypothesis tests.

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Complete Question:-

Assume that the heights of adult caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. if 40 women are randomly​ selected, find the probability that they have a mean height greater than 64.0 inches. round to four decimal places.

The total area of the given figure is 34 square meter.

The figure can be divided into two triangles and one rectangle. The triangle at one end is 3 m long and 4 m high, while the triangle at the other end has a base of 4 m and a height of 3 m. The rectangle in between has a length and width of 4 m.

The total area of the triangles is 1/2 ×Base×Height= 1/2×3×4 + 1/2×4×3

= 18 m²

The total area of the rectangles is 4 × 4 = 16 m²

The total area of the figure is 18 + 16 = 34 m²

Therefore, the total area of the given figure is 34 square meter.

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