simplify -9 with an exponent of -3

The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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The probability that the article will have no errors is approximately 0.0233.

To solve this problem, we can use the formula for the probability of an event, which is the number of favorable outcomes divided by the total number of outcomes.

Let's first find the probability that the article is typed by the first typist. Since the article is equally likely to be typed by either typist, this probability is 1/2.

Now, we need to find the probability that the article has no errors given that it is typed by the first typist. We know that the average number of errors per article typed by the first typist is 3.5, so the probability that an article typed by the first typist has no errors is given by the Poisson distribution with λ = 3.5:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-3.5) * 3.5^0 / 1 = e^(-3.5) ≈ 0.0302

Similarly, we can find the probability that the article has no errors given that it is typed by the second typist. This probability is given by the Poisson distribution with λ = 4.1:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-4.1) * 4.1^0 / 1 = e^(-4.1) ≈ 0.0164

Finally, we can use the law of total probability to find the probability that the article has no errors:

P(X = 0) = P(X = 0 | typed by first typist) * P(typed by first typist) + P(X = 0 | typed by second typist) * P(typed by second typist)

= 0.0302 * 1/2 + 0.0164 * 1/2

= 0.0233

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Triangle ABC is similar to triangle ADE by AA test of similarity

Similarity is a property which says that the respective angles of two triangles are of equal measure and corresponding sides are in proportion.

here, we have,

There are different types of similarity test by which we can prove the similarity of triangles.

We are given that BC is parallel to Line DE

As the lines are parallel the respective angle are corresponding angles

hence Angle D = Angle B

And Angle E = Angle C

And both triangle have angle A as common angle

By AA test of similarity we can say that the two triangles are similar

Hence by AA test similarity the two triangles are similar

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Based on the given information, the terminal side of angle 0 lies in quadrant III.

To determine the quadrant in which the terminal side of angle 0 lies based on the given information, we can analyze the signs of the trigonometric functions:

(a) Since sine < 0 and cotangent < 0, we can determine the quadrant as follows:

Sine < 0 implies that the y-coordinate (vertical component) of the point on the unit circle corresponding to angle 0 is negative.

Cotangent < 0 implies that the x-coordinate (horizontal component) of the point on the unit circle corresponding to angle 0 is negative.

In quadrant III, both the x and y-coordinates are negative. Therefore, quadrant III is the correct answer in this case.

(b) The information provided in this option is incorrect. "esce" is not a recognized trigonometric function, and "cos > 0" does not provide enough information to determine the quadrant.

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Answer: 1 / 8806

Step-by-step explanation: not no noticeable way of it being a mixed number.

Answer:

Graphs 1, 2, 3

Step-by-step explanation:

Graph 1 represents a linear function with a domain containing all real numbers, as any input substituted into the equation or function will produce a corresponding output. The arrows on the opposite ends of the line represents the infinite input values that have its corresponding output values.

Graph 2 represents a quadratic function with a domain containing all real numbers, as it does not have any constraints in terms of input values.  As it opens up, the graph of the parabola infinitely widens (horizontally).

Graph 3 represents an absolute value function with a domain containing all real numbers. Similar to the explanation for graph 2 on quadratic functions, the downward-facing graph of the given absolute value function widens infinitely horizontally, as it does not have any constraints on input values.

The expression is H(2) = -∫(2 to 1.5) sin(x)ln(x) dx - 4

The Fundamental Theorem of Calculus (FTC) states that if f(x) is continuous on an interval [a, b] and F(x) is an antiderivative of f(x) on that interval, then:

∫(a to b) f(x) dx = F(b) - F(a)

We can apply the FTC to the given function H'(x) = sin(x)ln(x) to find its antiderivative H(x). Using integration by parts, we can solve for H(x) as:

H(x) = -cos(x)ln(x) - ∫ sin(x)/x dx

Evaluating the integral using trigonometric substitution, we get:

H(x) = -cos(x)ln(x) + C - Si(x)

where C is the constant of integration and Si(x) is the sine integral function.

To find the value of C, we use the initial condition H(1.5) = -4, which gives:

-4 = -cos(1.5)ln(1.5) + C - Si(1.5)

Solving for C, we get:

C = -4 + cos(1.5)ln(1.5) + Si(1.5)

Now, we can evaluate H(2) using the antiderivative H(x) as:

H(2) = -cos(2)ln(2) + C - Si(2) + cos(1.5)ln(1.5) - C + Si(1.5)

Simplifying the expression, we get:

H(2) = -cos(2)ln(2) + cos(1.5)ln(1.5) + Si(1.5) - Si(2)

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Answers:

========================================================

Explanation:

Answer:

Class C has least variability and Class B has highest variability.

I think it will help you

Range= Large- Small Data

Step-by-step explanation:

Forty-eight boys are in the class.

4:8

24 students

24 represents 12 parts

24/12=2

2×4=8

8×2=16

Answer: 12.48

Step-by-step explanation:

38x38+bxb=40x40

1444+b=1600

1600-1444=156

\(\sqrt156\)=12.48

The base of the house is 12.48 foot far from the foot of the ladder.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

It is given that A 40-foot ladder reaches 38 feet up the side of a house.

We need to find that How far from the base of the house is the foot of the ladder.

Using Pythagoras theorem, we get;

\(38^2 + b^2 =40^2\\\\1444 + b^2 = 1600\\ \\b^2 = 1600 - 1444 \\\\b^2= 156\\\\b = 12.48\)

Therefore, the base of the house is 12.48 foot far from the foot of the ladder.

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Percentage change = 10%

We can use the formula:

Percent change = \(\frac{New-Old}{Old}\) x 100

Percent change = \(\frac{77-70}{70}\)x100

Percent change = \(\frac{7}{70}\) x 100

Percent change = 0.1 x 100

Percent change = 10%

Answer: 53.9

Step-by-step explanation:

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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Answer:

C.

Step-by-step explanation:

The correct answer is C. when using the Graphing Properties Rule.

Feel free to give brainliest.

I hope everyone has an outstanding day!

Answer:

1/2

Step-by-step explanation:

Probability is equal to the amount of desirable outcomes divided by the total amount of outcomes. Each coin has two sides, and there are three of them. This accounts for a total of 2^3 or 8 outcomes. Now, we need to find the amount of outcomes where two or more coins land on heads. We can start by listing those possibilities: THH, HTH, HHT, and HHH. Notice that the first three are just three ways of rearranging the same result. We can see that there are four desirable outcomes. This means the probability is 1/2.

So, Tracy paid $12.50 for the encyclopedia and $45.50 for the math book.

In mathematics, an equation is a statement that shows the equality between two expressions. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. An equation usually has an equals sign (=) between the two expressions. The equals sign indicates that the two expressions have the same value.

Here,

Let's use variables to represent the prices of the math book and the encyclopedia.

Let x be the price of the encyclopedia.

According to the problem, the price of the math book is 8 dollars more than 3 times the price of the encyclopedia. So, the price of the math book can be represented as:

=3x + 8

The total cost of the two books is given as 58 dollars. Therefore, we can write the equation:

x + (3x + 8) = 58

Simplifying and solving for x, we get:

4x + 8 = 58

4x = 50

x = 12.50

So, the price of the encyclopedia is $12.50.

To find the price of the math book, we can substitute x = 12.50 into the expression we derived earlier:

=3x + 8

= 3(12.50) + 8

= 37.50 + 8

= 45.50

Therefore, the price of the math book is $45.50.

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Answer:

30 Miles per hour.

Step-by-step explanation:

60 mph = 1 mile per minute.

Returning took 3 times as long so 1 mile per 3 minutes.

Average speed is total distance divided by time.

120 miles divided by 4 minutes.

120 / 4 = 30

Answer:

-16/3 =x

Step-by-step explanation:

3(x-2)+4x=10(x+1)​

Distribute

3x -6  +4x = 10x +10

Combine like terms

7x -6 = 10x+10

Subtract 7x from each side

7x-6-7x = 10x-7x +10

-6 = 3x+10

Subtract 10 from each side

-6-10 = 3x+10-10

-16 = 3x

Divide by 3

-16/3 = 3x/3

-16/3 =x

Answer:

C

Step-by-step explanation:

B and D have repeat x values , which do not make functions.

Linear means goes in the same direction

A starts big gets smaller and then gets bigger

C starts big and keeps getting bigger.  This is a linear function

Answer:

C.

Step-by-step explanation:

It isn't B because that is a vertical line x = 1 which is not a linear function. A linear function is of the form y = mx + b where m = slope and b = y-intercept.

To check for a linear function we find the slopes between adjacent points. If the slope is constant between each pair of points then it's linear.

A:

slope = (4 - 8) / (0 - -2) = -4/2 = -2.

(3 - 4) / (2 - 0) = -1/2

So its not A.

C. (12-7)/(0--2) = 5/2

(17-12)/(2-0) = 5/2

(22-17)/(4-2) = 5/2

This is a line of slope 5/2

This is a linear function.

Answer:

d

Step-by-step explanation:

edg 2021

Answer:

d

Step-by-step explanation:

The general solution for the differential equation: -2ty 4e^-t^2 is y = √(π^3) * e^(t^2) * erf(t).

To find the general solution of the given differential equation, we'll use the method of integrating factors. The differential equation is:

-2ty + 4e^(-t^2) = 0

To solve this, we can rewrite the equation in standard form:

y' + (-2t)y = 4e^(-t^2)

The integrating factor (denoted as μ) for this differential equation is given by:

μ = e^(∫(-2t) dt) = e^(-t^2)

Now, we'll multiply both sides of the equation by the integrating factor:

e^(-t^2)y' + (-2t)e^(-t^2)y = 4e^(-t^2)e^(-t^2)

Simplifying this equation, we get:

(d/dt)(e^(-t^2)y) = 4e^(-2t^2)

Now, we can integrate both sides with respect to t:

∫(d/dt)(e^(-t^2)y) dt = ∫4e^(-2t^2) dt

Integrating the left side yields:

e^(-t^2)y = ∫4e^(-2t^2) dt

The integral on the right side is not easily solvable in terms of elementary functions. However, we can express the solution using the error function (erf), which is a special function often used in the context of integrating Gaussian distributions. The integral can be rewritten as:

e^(-t^2)y = 2√π * ∫e^(-2t^2) dt = 2√π * ∫e^(-t^2) e^(-t^2) dt

This integral can be expressed in terms of the error function:

e^(-t^2)y = 2√π * (1/2) * √(π/2) * erf(t)

Simplifying further:

e^(-t^2)y = √(π^3) * erf(t)

Finally, solving for y:

y = √(π^3) * e^(t^2) * erf(t)

Therefore, the general solution of the given differential equation is:

y = √(π^3) * e^(t^2) * erf(t)

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Answer: It is 1-3. Afraid of racial policies. Meaningful government. War hero.

Step-by-step explanation:

If you can pick multiple answers = 2 or more answes

If can pick one answer = one answer

Answer: \(\dfrac{7}{15}\)

Step-by-step explanation:

Given

There are 16 girls and 14 boys

The favorable chances that a boy name comes up are 14

Probability is given by the ratio of favorable chances to the total chances

So, the probability that a boy's  name will be pulled is

\(\Rightarrow P=\dfrac{14}{14+16}\\\\\Rightarrow P=\dfrac{14}{30}\\\\\Rightarrow P=\dfrac{7}{15}\)

Answer:

Step-by-step explanation:

you have to solve for x i think

Answer: SOLVE FOR X !

Step-by-step explanation:

For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.

In this question we must determine the amount of money needed to pay in taxes by the purchase of an item with a discount. Sales taxes are an example of indirect taxes, this kind of indirect tax is usually calculated on the basis of total costs, including discounts. The amount of money need for the sales tax is described below:

t = (r / 100) · (1 - d / 100) · c     (1)

Where:

If we know that d = 30, r = 5 and c = 10, then the sales tax total is:

t = (5/ 100) · (1 - 30 / 100) · 10

t = 0.35

For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.

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Step-by-step explanation:

\( - \frac{1}{5} - ( - \frac{3}{8} ) = - \frac{1}{5} + \frac{3}{8} = \frac{ - 8 + 15}{40} = \frac{7}{40} \)

Answer:I think its 2×-3

Step-by-step explanation:Hope it helps kiddo

Deon drive the truck for approximately 258 miles.

Let the number of miles Deon drove the truck be x miles.

Additional charge for each mile driven = $0.87.

Total cost of renting the truck for x miles = Base fee + additional charges for x miles= $18.95 + $0.87x.

The cost of renting the truck for x miles is given as $244.20.

This can be represented mathematically as:$18.95 + $0.87x = $244.20.

To solve for x, we can use the following steps: $0.87x = $244.20 - $18.95$0.87x = $225.25x = $225.25 ÷ $0.87x = 258.3333 miles (approx.).

Therefore, Deon drive the truck for approximately 258 miles.

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To the nearest tenth of a year, it will take 31.1 years until the population reaches 41,500.Given that a town has a population 14,000.

It increases at a rate of 4.5% each year. We need to determine to the nearest tenth of a year how long it will be until the population will reach 41,500.

Let t be the number of years it will take for the population to reach 41,500.

Then the population after t years will be:

P(t) = \(14,000(1 + 0.045)^t\)

Notice that we are multiplying by (1 + 0.045) rather than adding 0.045.

This is because the population is increasing by 4.5% of the previous year's population, not just by a flat 4.5% of 14,000.

Now we need to solve the equation:

P(t) =\(41,50014,000(1 + 0.045)^t\)

= \(41,500(1.045)^t\)

Divide both sides by

14,000: \((1.045)^t\)= 2.964286...

Take the natural log of both sides of the equation:

t * ln(1.045) = ln(2.964286...)t

= ln(2.964286...) / ln(1.045)

≈ 31.1 years

Therefore, to the nearest tenth of a year, it will take 31.1 years until the population reaches 41,500.

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