Write each expression as a single power of 10.
A. 10-2. 10-4
B. 106 10-1
104
107
.
C.
D. (10-3)4
10-8
E.
106

a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.

(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (500 - 694) / 112

z-score ≈ -1.732

Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.

So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (900 - 694) / 112

z-score ≈ 1.839

Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.

So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.

We use the z-score formula to find the z-score corresponding to the 99th percentile:

z-score = invNorm(0.99)

z-score ≈ 2.326

Now, we use the z-score to find the score corresponding to the 99th percentile:

X = mean + (z-score * standard deviation)

X = 694 + (2.326 * 112)

X ≈ 694 + 260.512

X ≈ 954.512

So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

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The sinusoidal equations for each of the six scenarios are listed below:

Case 1: h = 60 - 20 · cos 15t

Case 2: h = 60 - 30 · cos 15t

Case 3: h = 40 - 30 · cos 15t

Case 4: h = 40 - 30 · cos 18t

Case 5: h = 40 - 20 · cos 18t

Case 6: h = 60 - 20 cos 18t

In this problem we need to determine six sinusoidal equations, each associated with a scenario. The sinusoidal model is introduced below:

h = H - 0.5 · D · cos (2π · f · t)

Where:

Case 1

h = 60 - 20 · cos (5π · t)

h = 60 - 20 · cos 15.708t

h = 60 - 20 · cos 15t

Case 2

h = 60 - 30 · cos (5π · t)

h = 60 - 30 · cos 15.708t

h = 60 - 30 · cos 15t

Case 3

h = 40 - 30 · cos (5π · t)

h = 40 - 30 · cos 15.708t

h = 40 - 30 · cos 15t

Case 4

h = 40 - 30 · cos (6π · t)

h = 40 - 30 · cos 18.849t

h = 40 - 30 · cos 18t

Case 5

h = 40 - 20 · cos (6π · t)

h = 40 - 20 · cos 18.849t

h = 40 - 20 · cos 18t

Case 6

h = 60 - 20 · cos (6π · t)

h = 60 - 20 · cos 18.849t

h = 60 - 20 cos 18t

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The solution set to the given inequalities from the graph in the form (x,y) is (-1, 2)

In mathematics, inequality arises when two mathematical expressions or two numbers are compared that are not equal. Generally, inequalities may be either numerical or algebraic, or a mixture of both.

Linear inequalities require at least one linear algebraic expression, here the polynomial is of one degree and is compared with another algebraic expression of a degree less than or equal to 1.

In the given question, we are to graph the following linear inequalities

x + y > 1

-x + y < 3

The solution set to the given inequalities by plotting their graph shows that (x,y) is (-1, 2)

The points in each shaded region of the graph are:

(0, 3)  The point is a solution to either inequality

(0, 1)   The point is a solution to one of the inequality

(-3, 0)  The point is  not a solution to either inequality

(-1, 2)   The point is a solution to either inequality

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The x-component of A is Ax = 25.7 units and the y-component of A is Ay = 21.3 units (both rounded to one decimal place).

Given: Vector A has a magnitude of 33.5 units and it points in a direction 320° counterclockwise from the positive x-axis.

Solution:We can start by finding the x-component and y-component of vector A.

So, we can use the following formulas:

Ax = A cos θ

Ay = A sin θ

where A is the magnitude of the vector and θ is the angle that it makes with the positive x-axis.

The given angle is 320° counterclockwise from the positive x-axis.

So, the angle made by vector A with positive x-axis is

360° – 320° = 40°.

Now, we can substitute the values in the formulas:

A = 33.5 units

θ = 40°

Ax = 33.5 cos 40°

Ay = 33.5 sin 40°

Ax = 25.7 units (rounded to one decimal place)

Ay = 21.3 units (rounded to one decimal place)

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l

\(x1 = 8 \\ x2 = - 4\)

a. The winner can select 4 books from 14 in 1,001 ways (using combinations).

b. The winner can select and arrange the 4 books on a shelf in 24 ways (using permutations).

c. Part a. counts combinations without considering order, while part b. counts permutations with order included, leading to different results.

a. To determine the number of ways the winner can select 4 books from 14 different books in a box, we can use the concept of combinations. The number of ways to choose 4 books out of 14 is given by the binomial coefficient:

C(14, 4) = 14! / (4! * (14 - 4)!) = 14! / (4! * 10!)

Simplifying further:

C(14, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) = 1001

Therefore, the winner can select the 4 books in 1,001 different ways.

b. To calculate the number of ways the winner can select the 4 books and arrange them on a shelf, we need to consider the concept of permutations. Once the 4 books are selected, they can be arranged on the shelf in different orders. The number of ways to arrange 4 books can be calculated as:

P(4) = 4!

P(4) = 4 * 3 * 2 * 1 = 24

Therefore, the winner can select the 4 books and arrange them on a shelf in 24 different ways.

c. The answers to part a. and part b. are not the same because they involve different concepts. Part a. calculates the number of ways to choose a combination of 4 books from 14 without considering the order, while part b. calculates the number of ways to arrange the selected 4 books on a shelf, taking the order into account. In other words, part a. focuses on selecting a subset of books, whereas part b. considers the arrangement of the selected books.

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The given value is 255 millilitres of salt water. As per the given condition,1 litre = 1,000 millilitres the container contains 0.255 litres of salt water.

Given value is 255 millilitres of salt water. We have to convert it into litres.The conversion factor of millilitres to litres is 1 litre = 1,000 millilitres.So, to find the number of litres of salt water present in the container, we divide the given quantity of millilitres by 1000.

255 millilitres = 255/1000 liters

= 0.255 litres

Therefore, there are 0.255 litres of salt water in the container.

The container of 255 millilitres of salt water has 0.255 litres of salt water.

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Answer:

Step-by-step explanation:

The loop will run an infinite number of times

The integral S/2 sinθ(x) cos²(x) dx is equivalent to the integral (E) Sou du.

To determine the equivalent integral of S/2 sinθ(x) cos²(x) dx, we can use the trigonometric identity:

cos²(x) = (1 + cos(2x))/2

Substituting this into the integral, we have:

S/2 sinθ(x) cos²(x) dx = S/2 sinθ(x) (1 + cos(2x))/2 dx

Now, we can distribute the sinθ(x) term:

= S/4 [sinθ(x) + sinθ(x) cos(2x)] dx

Using the trigonometric identity sinθ(x) cos(2x) = (1/2)sin(2x)sinθ(x), we get:

= S/4 [sinθ(x) + (1/2)sin(2x)sinθ(x)] dx

Factoring out sinθ(x), we have:

= S/4 sinθ(x) [1 + (1/2)sin(2x)] dx

Now, comparing this with the given options, we can see that the equivalent integral is:

(E) S u du

Therefore, the integral S/2 sinθ(x) cos²(x) dx is equivalent to the integral (E) Sou du.

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On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56 Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

So, the maximum number of questions you may omit is 14. As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70

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Answer: B

Step-by-step explanation: This answer can be found by just doing process of elimination. A has the numbers switched around, C and D has 2 adding by ones and 7 multipying. Mathmaticlly finding the answer for B, 2 is multiplying my 2, 3 and 4. First, you have 4, then you have 6, and last you have 8. 7 is doing the same thing. 7 multiplied by 2 gives you 14, by 3 gives you 21 and by 4 gives you 28.

Answer:

3

5

8

Step-by-step explanation:

if x is 0 then

y= x+3

= 0+3

again x is 2 then

y= 2+3

also x is 5 then

y= 5+3

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

140° and 40°

Step-by-step explanation:

let x be one angle then the other is \(\frac{1}{2}\) x - 30

Since the angles are a linear pair, theis sum is 180° , then

x + \(\frac{1}{2}\) x - 30 = 180, that is

\(\frac{3}{2}\) x - 30 = 180 ( add 30 to both sides )

\(\frac{3}{2}\) x = 210 ( multiply both sides by 2 to clear the fraction )

3x = 420 ( divide both sides by 3 )

x = 140

and \(\frac{1}{2}\) x - 30 = \(\frac{1}{2}\) (140) - 30 = 70 - 30 = 40

The 2 angles are 140° and 40°

Answer:

y=-|x − 3|

Work

y = |x − 3| + 2

-2        -2

y = |x − 3|

add a neg before the absolute value

y=-|x − 3|

Transformation involves changing the position of a graph

The equation of the transformed graph is \(\mathbf{y = -|x -3| - 4}\)

The equation is given as:

\(\mathbf{y = |x -3| + 2}\)

The rule of reflection across the x-axis is:

\(\mathbf{(x,y) \to (x,-y)}\)

So, we have:

\(\mathbf{y = -|x -3| - 2}\)

The rule of translation 2 units down is:

\(\mathbf{(x,y) \to (x,y-2)}\)

So, we have:

\(\mathbf{y = -|x -3| - 2 - 2}\)

\(\mathbf{y = -|x -3| - 4}\)

Hence, the equation of the transformed graph is \(\mathbf{y = -|x -3| - 4}\)

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Answer:

70% of 30 =21

Step-by-step explanation:

The possible values of the solutions to the inequality 5x + 5 ≥ −9 are: I, II, and III.

To find the possible values of the solution to a given inequality, solve the inequality given using the properties of equality to isolate the variable.

Given the inequality:

5x + 5 ≥ −9

Subtract 5 from both sides:

5x + 5 - 5 ≥ −9 - 5 [subtraction property of inequality]

5x ≥ -14

Divide both sides by 5

5x/5 ≥ -14/5

x ≥ -2.8

This means that all the possible values of x are greater than or equal to -2.8.

1, 4, and 6 are greater than -2.8, therefore, the values of the solutions are: I, II, and III.

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15 liquids that can be found in a kitchen include:

15 solids in a kitchen are:

When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.

As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.

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Given :

A sixth-grade student bought three cans of tennis balls for $4 each.

The sales tax for each can was $0.95.

To Find :

The total amount the student spent.

Solution :

Price of each can including taxes :

p = $( 4 + 0.95 )

p = $4.95

So, price of 3 such cans including tax is :

P = p×3

P = $( 4.95×3 )

P = $14.85

Therefore, total amount spend by the student is $14.85 .

Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Answer:

c

Step-by-step explanation:

The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (9⁶ x 7⁻⁹)⁻⁴

Simplify the expression, we have

⇒ (9⁻⁶ x 7⁹)⁴

⇒ 9⁻²⁴ x 7³⁶

⇒ 7³⁶ / 9²⁴

Then the correct option is D.

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Answer:

Hypotenuse would be 14

Step-by-step explanation:

The probability that a presidential candidate selects a specific route of capitals is impossible to determine without knowing the specifics of the route.

The probability of a presidential candidate selecting a specific route of capitals depends on a variety of factors. For example, if the route includes a large number of states, then the probability of selecting that route decreases. If the route includes fewer states, then the probability of selecting that route increases. Additionally, the candidate's strategy and objectives in selecting the route also play a role in determining the probability. For example, if the candidate is trying to reach certain demographics or regions of the country, then the probability of selecting a certain route may be higher. Ultimately, the probability of a presidential candidate selecting a specific route of capitals is impossible to determine without knowing the specifics of the route.

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Answer:

4/15.

Step-by-step explanation:

1/3(1/5) + 1/5

1/15 + 1/5

1/15 + 3/15

4/15

Answer:

4/15

Step-by-step explanation:

\(( \frac{1}{3} \times \frac{1}{5} ) + \frac{1}{5} \\ \frac{1}{15} + \frac{1}{5} \\ \frac{1}{5} + \frac{3}{13} \\ \frac{1 + 3}{15} = \frac{4}{15} \)

Answer: After 7 years the population will be one-half the initial amount.

Step-by-step explanation:

Given: Initial population = 500,000

The population declines according to the equation:

\(P(t) = 500,000e^{ -0.099t}\), where P is the population in t years later.

One-half the initial amount = 0.5 x 500,000

= 250,000

Put P(t)=250,000, we get

\(250000=500000e^{-0.099t}\\\\\Rightarrow\ \frac{500000e^{-0.099t}}{500000}=\frac{250000}{500000}\\\\\Rightarrow\ e^{-0.099t}=\frac12\\\\\Rightarrow\ -0.099t=\ln \left(\frac{1}{2}\right)\\\\\Rightarrow\ t=\frac{1000\ln \left(2\right)}{99}=\frac{1000(0.69314)}{99}\\\\\Rightarrow\ t=7.00148\approx7\)

Hence, After 7 years the population will be one-half the initial amount.

This results in the matrix,

\($$\begin{bmatrix} 1 & 0 & 1 & -2 & 0 & -1 \\ 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & -2 \end{bmatrix}$$\)

To compute the reduced row-echelon form of the given matrix,

we perform elementary row operations and transform it into the identity matrix or into an equivalent matrix,

as follows:

\($$\begin{bmatrix} -2 & 3 & 1 & -3 & 1 & -2 \\ 1 & -1.5 & 0.5 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 0 \end{bmatrix}$$\)

We will use elementary row operations to get a matrix whose leading entries are 1, and 0 elsewhere.

For instance, \($$R_1\leftrightarrow R_2$$\)

This will interchange the 1st row and 2nd row, which results in the following matrix:

\($$\begin{bmatrix} 1 & -1.5 & 0.5 & 0 & 0 & 0 \\ -2 & 3 & 1 & -3 & 1 & -2 \\ 0 & 1 & 1 & 0 & 0 & 0 \end{bmatrix}$$\)

Next, we will apply the following operations to the matrix,

\($$R_2+2R_1 \to R_2$$\)

And

\($$R_1 + 1.5R_2 \to R_1$$\)

This yields:

\($$\begin{bmatrix} 1 & 0 & 1 & -2 & 1 & -3 \\ 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & -2 \end{bmatrix}$$\)

Lastly, we apply the following operations,

\($$R_1-R_3 \to R_1$$$$R_2-R_3 \to R_2$$\)

This results in the matrix,

\($$\begin{bmatrix} 1 & 0 & 1 & -2 & 0 & -1 \\ 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & -2 \end{bmatrix}$$\)

This is the reduced row-echelon form of the matrix.

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Shortest distance between start and end point is 55.9 miles

According to given statement,

Terry had to travel south 50 miles and then west 25 miles.

We are taking X as a start point and Z is end point.

In triangle XYZ, we are taking angle Y to be of 90 degrees, which qualifies the Triangle XYZ to qualify Pythagorean theorem [The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right angle triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.]

XY = 50 miles

YZ= 25 miles

XZ^2 = XY^2 + YZ ^2

XZ^2 = (50) ^2 + (25) ^2 = 3125

XZ = 55.9

Shortest distance between start and end point is 55.9 miles

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Answer:

bottom right rectangle: 5x − y

bottom circle: 6x

Step-by-step explanation:

First, solve for the bottom right rectangle by finding the difference between the top right rectangle and the middle right circle:

(9x + 4y) − (4x + 5y)

= (9x − 4x) + (4y − 5y)

= 5x − y

Next, to find the bottom circle, add the bottom left rectangle with the bottom right rectangle (the one we just solved for):

(x + y) + (5x − y)

= (x + 5x) + (y − y)

= 6x

9514 1404 393

Answer:

  (2x +y)(2x -y +6)

Step-by-step explanation:

The shaded area is the difference of the areas of the outer square and the inner square. In turn, those areas are the square of the edge dimension of the square. So, the shaded area is the difference of squares:

  area = (2x +3)² -(y -3)²

The difference of squares is a "special product" in that it has a factored form that is worth remembering.

  a² -b² = (a -b)(a +b)

Using this form for our area, we have ...

  area = ((2x +3) -(y -3))((2x +3) +(y -3))

  area = (2x -y +6)(2x +y)