the value of a building is currently 281000. if the value increase by 4.5%, what will the new be value

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

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.

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

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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Answer:

Step-by-step explanation:

The probability of the spinner landing on blue is 1/4, since there are 4 equally likely outcomes.

The probability of rolling an even number on a fair 6-sided die is 3/6 or 1/2, since there are 3 even numbers (2, 4, 6) out of 6 possible outcomes.

To find the probability of both events happening together (landing on blue and rolling an even number), we multiply their probabilities:

P(blue and even) = P(blue) x P(even)

= 1/4 x 1/2

= 1/8

Therefore, the probability of the spinner landing on blue and rolling an even number is 1/8.

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:

[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]

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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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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The slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.

Hence the correct option is (G).

Here in the given graph we can see that H, P, K are on the same line that is the points H, P, K are collinear.

We know that in Cartesian Coordinate Plane, the slope of one line is unique.

Slope = (Change in y coordinate)/(Change in x coordinate)

We can see that the coordinates are:

H = (-12, 10)

K = (-4, 5)

P = (4, 0)

So the slope of HK = (10 - 5)/(-12 - (-4)) = 5/(-8) = -5/8

Slope of PK = (5 - 0)/(-4 - 4) = 5/(-8) = -5/8

Hence the slope of HK is equal to the slope of PK because the ratio in the change in the y values of the endpoints to the change in x values of the endpoints is the same for HK as it is for PK.

So the correct option will be (G).

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The question is incomplete. The complete question will be -

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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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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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:

18.75 or 1.87

Step-by-step explanation:

If its 124n=2325, n is 18.75

If its 124n=232, n is 1.87

The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.

The MAD indicates that the men's score spread is marginally less than the women's score spread.

The difference between a dataset's largest and lowest values is known as the range.

The range for the men's scores is: 75 - 65 = 10.

The range for the women's scores is 80 - 69 = 11.

The spread of the women's scores is therefore somewhat larger than the spread of the men's scores based on the range.

The average distance between each data point and the dataset's mean is measured by the mean absolute deviation (MAD).

Find the mean first before calculating the MAD for the men's scores:

(65 + 68 + 70 + 72 + 73 + 75) / 6 = 70.5

The MAD indicates that the men's score spread is marginally less than the women's score spread.

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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.

The amount of 8% liquid polymer to make 55 gallons of a 0.5% polymer solution is around 3.4 gallons.

The relationship between concentration and volume will be used to find the volume of liquid polymer. The formula to be used is -

[tex] C_{i}[/tex] [tex] V_{i}[/tex] = [tex] C_{o}[/tex] [tex] V_{o}[/tex], where [tex] C_{i}[/tex] and [tex] C_{o}[/tex] are initial and final concentration and [tex] V_{i}[/tex] and [tex] V_{o}[/tex] are initial and final volume.

Keep the values in formula -

[tex] C_{i}[/tex] × 8% = 55 × 0.5%

Rearranging the equation

[tex] C_{i}[/tex] = 55 × 0.5%/0.8%

Performing multiplication and division on Right Hand Side of the equation

[tex] C_{i}[/tex] = 3.4375 gallons

Hence, the volume of liquid polymer is around 3.4 gallons.

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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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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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The value of [tex]5x^{2} - 27[/tex] ÷ y - (9 + 13) when x = 10 and y = 9 is 2501

BODMAS is an acronym and it standsB = BracketO = OrderD = DivisionM = MultiplicationA = AdditionS = Subtraction

How to determine this

[tex]5x^2 - 27 /y - (9 + 13)[/tex]

Where x = 10y = 9By substituting the values

[tex]5(10)^2 - 27 / y - (9 + 13)[/tex]

By removing bracket [tex]50^2 - 27 / 9 - 9 + 13[/tex]

Order, by finding the square root of 502500

- 27 / 9 - 9 + 13

By dividing

2500 - 27/9 - 9 + 132500 - 3 - 9 + 13

By addition

2500 + 13 - 3 - 92513 - 3 - 9

By subtraction

2513 - 12= 2501

Therefore, the value of the expression is 2501

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Answer:

Step-by-step explanation:

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 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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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.

Step-by-step explanation:

To find the slope of the line, we need to select any two points on the line and then use the slope formula:

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

Let's choose the points (-2, 6) and (2, -6) on the line. Then, we can calculate the slope as:

slope = (-6 - 6) / (2 - (-2))

slope = -12 / 4

slope = -3

Therefore, the slope of the line is -3.

To solve for x in the equation -2cosx+2cos2x=0, we can use the trigonometric identity cos2x = 2cos^2x - 1 to rewrite the equation as:

-2cosx + 4cos^2x - 2 = 0

Next, we can rearrange the terms and factor out a 2 to obtain:

2cos^2x - cosx - 1 = 0

This is now a quadratic equation in terms of cosx. We can solve for cosx using the quadratic formula:

cosx = [1 ± sqrt(1 - 4(2)(-1))] / (2(2))

cosx = [1 ± sqrt(9)] / 4

cosx = (1/2) or (-1/2)

Now, we need to find the values of x that correspond to these values of cosx. We can use inverse trigonometric functions to do this:

cosx = 1/2 => x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.

cosx = -1/2 => x = 2π/3 + 2πn or x = 4π/3 + 2πn, where n is an integer.

Therefore, the solutions for x are:

x = π/3 + 2πn, x = 2π/3 + 2πn, x = 4π/3 + 2πn, x = 5π/3 + 2πn, where n is an integer.

The average distance walked is  5 + 4/11 miles.

By using the graph we can see that:

So there are a total of:

5 + 9 + 3 + 5 = 22 girls.

And the average distance walked is:

A = (5*4 + 9*5 + 3*6 + 5*7)/22

A = 118/22 = 110/22 + 8/22 = 5 + 8/22 = 5 + 4/11

So the correct option is the first one.

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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

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).