An office building worth $1 million when completed in 1997 was depreciated linearly over 50 years; that is, the book value of the building decreases at a constant rate, so that at the end of 50 years the book value is zero.
What was the book value, in dollars, of the building in 2013?
$
What will be the book value, in dollars, in 2017?
$
What will be the book value, in dollars, in 2025?
$

Answer:

I think it's 12..?

Step-by-step explanation:

Since they're supposed to be congruent and x lines up with the side on the other triangle that is 12. I think that means that x would also have to equal 12 for them to be congruent.

Answer:

x + 2x + 2x + 2 + 4x + 4 = 42

Step-by-step explanation:

Let us assume the number of orange buttons be x

So, the grey buttons be 2x

The white buttons would be 2x + 2

And the black buttons be 2(2x + 2) i.e. 4x + 4

Also the total is 42 buttons

So, the equation is

x + 2x + 2x + 2 + 4x + 4 = 42

When you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole.

It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

The top number in a fraction is referred to as the numerator, while the bottom number is referred to as the denominator.

4/5, for instance, is a fraction.

What happens to the denominator of a fraction when you divide it by a negative number is unimportant because the entire result, or quotient, is the opposite of whatever the original fraction was.

Therefore, when you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

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If cos(theta) > 0, then angle theta must be acute. This is because cosine is positive in the first and fourth quadrants, and angle theta is in the first quadrant since it is opposite the side of length a.

An acute angle is an angle that is less than 90 degrees. So, if cos(theta) > 0, then angle theta must be acute.

The side opposite angle theta is labeled as a. The sides adjacent to angle theta are labeled as b and c.

The Pythagorean theorem states that:

\(a^2 = b^2 + c^2\)

Since cos(theta) > 0, then a, b, and c must all be positive numbers. This is because cosine is only positive for positive numbers.

Therefore, if cos(theta) > 0, then angle theta must be acute and the sides of the triangle must all be positive numbers.

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Answer:

1.) Carries energy

Step-by-step explanation:

A good summary of an ATP molecule is a molecule that transfers energy between cells... meaning it carries energy from cell to cell. Furthermore, energy cannot be destroyed, and cannot be absorbed, only changed and transformed. This leaves us with two options, (1. Carries energy, and 4. None of the above). Since we already have a basic understanding of what an ATP molecule does, we can confidently determine that the correct answer is that an ATP molecule can best be described as carrying energy.

Answer:

1: b

2: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

1-D

2-B

The proportion of a normal distribution that is located in the tail when z = 1.50 is 0.0668. So, the correct option is a.

Here's how to solve the problem:

We are given that z = 1.50.

To find the proportion of a normal distribution that is located in the tail when z = 1.50, we need to use a standard normal distribution table (also known as a z-score table). The table provides the area under the standard normal distribution curve to the left of a given z-score.

Since z = 1.50 is positive, we are interested in the area in the right tail of the standard normal distribution curve. The standard normal distribution table provides the area to the left of a given z-score. Therefore, to find the area in the right tail, we subtract the area in the left tail from 1 (the total area under the curve).

Using the standard normal distribution table, we find that the area to the left of z = 1.50 is 0.9332. Therefore, the area to the right of z = 1.50 (in the right tail) is: 1 - 0.9332 = 0.0668

Thus, the proportion of a normal distribution that is located in the tail when z = 1.50 is 0.0668, which is option (a).

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A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

A function can have a "hole" if it is not defined at a certain input value. For example, consider the following function:

f(x) = 1/x

This function has a hole at x=0 because it is not defined at that value. If you try to evaluate the function at x=0, you will get an error or an undefined result.

To determine whether a function has a hole, you can consider the domain of the function, which is the set of all input values for which the function is defined. If there are any values in the domain for which the function is not defined, then the function has a hole at those values.

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Answer:

Step-by-step explanation:

The Massachusetts Body of Liberties were technically the first ever legal code system established by the colonists, and established a central court that had full rights and jurisdictions over the citizens.

Answer:

The linear equation to represent the amount of money m that Mark has earned this summer after working h hours at the grocery store is:

Step-by-step explanation:

Mark has already earned some amount x. Lets find it using the number of hours worked and the total amount after this:

This amount represents an initial value or the y-intercept of the line and the payment per hour represents the slope of same line.

We know the equation of line in slope-intercept form:

Plug in the values and variables to get the linear equation for the earned amount:

Mark's m earned this summer after working h hours at the grocery store is represented by the linear equation: m = 9.5h + 140.

Given

Earning per hour = $9.50,

Worked hours = 16,

Total earning = $292,

Mark has earned some amount initially for mowing lawns.

Linear equation of amount of money m after working h hours

Mark has already earned some amount x.

Lets find it using the number of hours worked and the total amount after this:

16 × 9.50 + x = 292

Simplifying the above equation then we get,

152 + x = 292

x = 292 - 152

x = 140

This amount represents the line's initial value or y-intercept, and the payment per hour represents the slope of the same line.

The slope-intercept equation of a line is as follows:

y = mx + b, where y is the line, m is the slope, and b is the y-intercept

To obtain the linear equation for the earned amount, enter the values and variables as follows:

∴ m = 9.5h + 140

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Answer:

3/14

Step-by-step explanation:

prob for the 1st sock=4/8=1/2

prob for the 2nd sock=3/7(there's 7 socks left now and only 3 were white since she pulled one out and didn't put it back)

so the prob of both being white is 1/2*3/7=3/14

Answer:

B. 62 un2

Step-by-step explanation:

The formula for the volume of a cylinder is given by:

Where r is the base radius and h is the height.

If the volume is 448*pi cm³ and the height is 7 cm, we have:

Therefore the radius is equal to 8 cm.

Drawing this cylinder, we have:

Answer:

An exponential decay function has the form y = a*b^(-kt) where a is the initial value, b is the base of the exponential function (in this case, 1 - the decay rate as a decimal), k is the decay rate and t is the time.

Given that the initial value is 980, the decay rate is 1% every 2 days and the time is 5 weeks. The first step is to convert the time to the same unit of time as the decay rate, in this case, days: 5 weeks * 7 days/week = 35 days.

The decay rate per day is 1/100 because 1% as a decimal is 0.01, so the decay rate per day is 0.01/2 = 0.005

Now we can plug in the values in the function:

y = 980 * (1 - 0.005)^(-0.005*35)

y = 980 * 0.995^(-17.5)

y ≈ 574.64

So, the value of the quantity after 5 weeks to the nearest hundredth is 574.64

It's worth noting that in this case, the base (1 - decay rate) is less than 1, which implies that the value of the quantity decreases over time.

Answer:

The probability that the coin lands heads up once and tails up twice is .375, or 3/8.

Step-by-step explanation:

Check the conditions for a binomial distribution problem:

We need to use combinations to determine the probability of getting one success (one head) and two failures (two tails).

The combination would be 3 choose 1:  \(p = {3 \choose 1} (.5)^1(.5)^2\).

There is one success and two failures, denoted by the superscripts above the probability p = .5.

Use a calculator to evaluate and we get:

The probability that the coin lands heads up once and tails up twice is .375, or 3/8.

The basic idea is that multiplying by 10 just moves the decimal point one place to the right.  It makes the number bigger.

Examples:

3.1 x 10 = 31

3.1 x 10 x 10 = 31 x 10 = 310

Each time you multiply by another 10, the decimal point moves one more place.

In your exercise, \(10^3\) says you're going to multiply by 10 three times in a row.  So that will move the decimal point 3 places to the right.

So what do you get if you move the decimal in 4.25 three places to the right?

The resultant vector on the car would be a vector pointing north with a magnitude of 2 miles per hour.

The resultant vector is the net effect of two or more individual vectors on an object. It is the overall force or movement that is produced when all the individual vectors are combined. To find the resultant vector, you would add together all of the individual vectors using vector addition. The resultant vector would be represented by a single vector with a certain magnitude and direction.

If a car is rolling south at 8 miles per hour, and a man pushes the car north at 10 miles per hour, subtract the southward velocity from the northward velocity.

10 mph northward - 8 mph southward= 2 mph northward

Therefore, the resultant vector on the car is 2 mph northward.

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The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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A number is a restriction on a rational expression if the number makes the denominator of the rational expression equal to zero.

Hence, option (b) is correct choice.

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.

A rational expression's denominator is undefined when it equals zero, hence it cannot be employed in the expression.

For that particular value of the number, the limitation renders the value of the rational statement undefinable.

To put it another way, the number is a limitation since it cannot be used as the input for the rational expression because the output would be an undefined value.

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The missing option may be:

(a) 1

(b) 0

(c) always positive

(d) Indefinite

Answer:

10

Step-by-step explanation:

Since a rectangle has 2 sets of congruent sides we can set up the equation:

48=2x+2y

We have our x value/length (14) so we can plug that in to the equation.

48=2(14)+2y

Then we have to simplify

48=28+2y

20=2y

Then simply solve for the y value, which is your width

10=y

The slope of the line tangent to the curve y³-xy²+x³=5 at the point (1,2) is option (B) 1/8.

To find the slope of the line tangent to the curve at the point (1,2), we first need to find the derivative of the curve with respect to x, and then evaluate it at x=1, y=2.

Taking the derivative of both sides of the equation y³-xy²+x³=5 with respect to x using the product rule, we get

3y²(dy/dx) - y² - 2xy(dy/dx) + 3x² = 0

Simplifying this expression and solving for dy/dx, we get:

dy/dx = (y² - 3x²)/(3y² - 2xy)

Substituting x=1 and y=2, we get:

dy/dx = (2² - 3(1)²)/(3(2)² - 2(1)(2))

dy/dx = (4 - 3)/(12 - 4)

dy/dx = 1/8

Therefore, the correct option is (B) 1/8

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a) The probability that a person spent more than $28 is of: 0.2033 = 20.33%.

b) The probability that a person spent between $9 and $21 is given as follows: 0.3608 = 36.08%.

c) The middle 95% of the amounts falls between $11.24 and $34.76.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the problem are given as follows:

\(\mu = 23, \sigma = 6\)

The probability of a person spending more than $28 is one subtracted by the p-value of Z when X = 28, hence:

Z = (28 - 23)/6

Z = 0.83

Z = 0.83 has a p-value of 0.7967

1 - 0.7967 = 0.2033.

The probability of a person spending between $9 and $21 is given by the p-value of Z when X = 21 subtracted by the p-value of Z when X = 9, hence:

Z = (21 - 23)/6

Z = -0.33

Z = -0.33 has a p-value of 0.3707

Z = (9 - 23)/6

Z = -2.33

Z = -2.33 has a p-value of 0.0099.

0.3703 - 0.0099 = 0.3608 = 36.08%.

The middle 95% of amounts is between the 2.5th percentile(Z = -1.96) and the 97.5th percentile, Z = 1.96, hence:

-1.96 = (X - 23)/6

X - 23 = -1.96 x 6

X = 11.24.

1.96 = (X - 23)/6

X - 23 = 1.96 x 6

X = 34.76.

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Answer:

Large pizzas= 12 Medium= 8

Step-by-step explanation:

if you 12 by 5 and 8 by 6 and add them together you get 108

The expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).

To rewrite the expression (16x^3y^2) - 24x^4y^4 as a product of the greatest common factor multiplied by a binomial, we need to find the greatest common factor of the two terms. The greatest common factor of 16x^3y^2 and 24x^4y^4 is 8x^3y^2.

We can factor out 8x^3y^2 from both terms to get:

(16x^3y^2) - (24x^4y^4) = 8x^3y^2(2 - 3x^1y^2)

Therefore, the expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).

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The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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Answer:

2 million 2 3 divided by 3= 20000

Step-by-step explanation:

add and divide

Answer: The answer is after 10 months.

Step-by-step explanation:

So you first start trying to input random numbers up until you get to 10. You multiply 22 by 10 and add an additional 80 making it 300. While when you multiply 30 by 10 you get 300 also.