(10^4)^2 in index form

The points are not reasonably close to a straight line, nor is the distribution normal.

Why do normal distributions exist?

Like any probability distribution, the normal distribution depicts the distribution of values for a variable.

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The full question is given in the image-

This accuracy is comparable to shooting an arrow at a target fifty feet away and missing the exact center by the distance;  0.000001 miles

Proportion word problems are simply ways of expressing proportion problems in words. For example we share oranges among three people each receiving 2, 3 and 4 respectively and as such the ratio of the proportion is 2:3:4.

Now, we are told that  after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to Earth. It landed only six miles from its target. This is comparable  to shooting an arrow at a target fifty feet away and missing the exact center.

Thus, if the comparable distance missed is x, then we can say that;

x/50 = 6/300000000

x = (6 * 50)/300000000

x = 3/3000000

x = 0.000001

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The expression that represents Ana's age is 2 + w.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression:

Expression: (Number/Variable, Math Operator, Math Operator)

Given:

let w represent Wanda's age.

let a represent Ana's age.

Also given Ana is 2 years older then Wanda

Ana's age can be calculated as Wanda's age plus 2

Hence the expression which represents Ana's age  is given below

Ana's age = 2 + Wanda's age

a = 2 + w

Hence Ana's age is 2 + w.

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The A's age  is 26 years and B's age is 24 years

Let the ages of A and B be x and y years respectively. Then, [tex]$x-y=\pm 2[/tex]Given

D's age [tex]$=2 x$[/tex]years and, C's age[tex]$=\frac{y}{2}$[/tex] years.

Clearly, D is older than C

[tex]$2 \mathrm{x}-\frac{\mathrm{y}}{2}=40 \Rightarrow 4 \mathrm{x}-\mathrm{y}=80$[/tex]

Thus, we have the following two systems of linear equations[tex]$x-y=2$[/tex].(i)

and, [tex]$4 x-y=80$[/tex](ii)

or

[tex]$x-y=-2$[/tex] (iii)

and, [tex]$4 x-y=80$[/tex]..(iv)

Subtracting equation (i) from equation (ii), we get [tex]$3 \mathrm{x}=78 \Rightarrow \mathrm{x}=26$[/tex]Putting [tex]$\mathrm{x}=26$[/tex] in equation (i), we get [tex]$\mathrm{y}=24$[/tex]or

Subtracting equation (iv) from equation (iii), we get [tex]$-3 \mathrm{x}=-82 \Rightarrow \mathrm{x}=\frac{82}{3}=27 \frac{1}{3}$[/tex]

Putting [tex]$\mathrm{x}=\frac{82}{3}$[/tex]in equation (iii), we get

[tex]$\mathrm{y}=\frac{82}{3}+2=\frac{88}{3}=29 \frac{1}{3}$[/tex]

Hence, A's age =26 years and B's age =24 years or

A's age =[tex]27 \frac{1}{3}$[/tex] years and B's age[tex]$=29 \frac{1}{3}$[/tex] years.

The complete question is,

A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B.

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Answer:

A third degree polynomial, also known as a cubic polynomial, has the form of

Q(x) = ax^3 + bx^2 + cx + d

Given that Q(1)=1, Q'(1)=3, Q''(1)=6, and Q'''(1)=12, we can use these values to find the coefficients a, b, c, and d.

Q(1) = a(1)^3 + b(1)^2 + c(1) + d = 1

Q'(1) = 3a + 2b + c = 3

Q''(1) = 6a + 2b = 6

Q'''(1) = 6a = 12

Solving for a:

6a = 12

a = 2

Using the value of a, we can substitute it back into the other equations to find b, c and d.

Q''(1) = 6a + 2b = 6

6(2) + 2b = 6

12 + 2b = 6

2b = -6

b = -3

Q'(1) = 3a + 2b + c = 3

3(2) + 2(-3) + c = 3

6 - 6 + c = 3

c = 9

Q(1) = a(1)^3 + b(1)^2 + c(1) + d = 1

2(1)^3 + (-3)(1)^2 + 9(1) + d = 1

2 + (-3) + 9 + d = 1

8 + d = 1

d = -7

Therefore, the third degree polynomial Q that satisfies the given conditions is:

Q(x) = 2x^3 - 3x^2 + 9x - 7

----------------------------------------

the polynomial Q(x) is Q(x) = x^3 + 2x^2 + x + 1

This polynomial satisfies the given conditions Q(1)=1, Q'(1)=3, Q"(1)=6, and Q'''(1)=12.

To check:

Q(1) = 1 + 2(1)^2 + 1(1) + 1 = 1

Q'(1) = 3 + 4 + 1 = 8

Q"(1) = 6

Q'''(1) = 6

It's important to note that the polynomial that I have provided may not be unique, as there may be other third degree polynomials that also satisfy the given conditions.

Answer:

4000-x

Step-by-step explanation:

both accounts - account x = account y

(x+y) - x = y

Data handling is the process of ensuring that research data is stored, archived, or disposed of in a safe and secure manner during and after the conclusion of a research project.

The following are the given details:

Item  Leadtime   On hand Inventory Lot sizing criteria Schedulereceipts

A             2                0                                   L4L                  10 in week 2

B             1                 0                                   LAL                       0

C             1                 10                                  50                       0

D             2                0                                   50                       0

E             1                 50                                180               50 in week 1

F             1                180                                L4L               50 in week 1

The Complete MRP schedule can be seen in the attached images below:

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The gross requirements for each component are as follows:

b = 2 x a = 44 units in week 7

c = 3 x a = 66 units in week 7

d = 2 x e + 1 x c + 2 x a

= 110 units in week 3, 56 units in week 6, 44 units in week 7

e = 1 x b = 44 units in week 5

f = 2 x b + 2 x c = 88 units in week 5 and 112 units in week 6

Net requirements = Gross requirements - Projected on hand

Projected on hand = Planned order receipts - net requirements

Planned order receipts = net requirements

Planned order releases = net requirements adjusted as per the lead time

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The six trigonometric functions of an angle θ in a right triangle are sine (sin θ), cosine (cos θ), tangent (tan θ), cotangent (cot θ), secant (sec θ) and cosecant (csc θ).

To find these functions for a given angle θ, we need to know the length of the sides of a right triangle with angle θ.

Given that the point (-5,12) is on the terminal side of θ, we can apply the Pythagorean Theorem to find the length of the sides of the triangle. The Pythagorean Theorem states that a² + b² = c² where a and b represent the lengths of the sides of the triangle and c is the length of the hypotenuse. Using the point (-5,12), we can solve for c, which is 13.

Therefore, the sides of the triangle have lengths 5, 12, and 13. We can now use these lengths to calculate the trigonometric functions of θ.

sin θ = 12/13

cos θ = 5/13

tan θ = 12/5

cot θ = 5/12

sec θ = 13/5

csc θ = 13/12

Therefore, the six trigonometric functions of θ are sin θ = 12/13, cos θ = 5/13, tan θ = 12/5, cot θ = 5/12, sec θ = 13/5 and csc θ = 13/12.

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Using the trigonometric ratios for the angle A-cosθ= Base/ Hypotenuse =11.8726

What is trigonometric?

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.

For example, the triangle contains an angle A, and the ratio of the side opposite to A and the side opposite to the right angle (the hypotenuse) is called the sine of A, or sin A; the other trigonometry functions are defined similarly. These functions are properties of the angle A independent of the size of the triangle, and calculated values were tabulated for many angles before computers made trigonometry tables obsolete. Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures.

Here, if we consider the ∠A=θ, then AB is the base, BC is the perpendicular, and AC is the hypotenuse.

And it is given that, ∠A=θ=32°,AB=x, and C=14 units.

Now, using the trigonometric ratios for the angle A-cosθ= Base/Hypotenuse

cosA=AB/AC

cos30°=x/14

x=14×cos32°

=11.8726

≈11.9units

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The builder will need a total of 372 square feet of countertop.

First, let's convert all dimensions to feet:

The 15' countertops are 15 * 12 = 180 inches long.

The 24" deep countertops are 24 / 12 = 2 feet deep.

The 48" x 36" island countertop is 48 / 12 = 4 feet wide and 36 / 12 = 3 feet deep.

Next, we can calculate the square footage of each countertop:

The 15' countertops are 180 inches long and 2 feet deep, so the square footage is 180 * 2 = 360 square feet.

The island countertop is 4 feet wide and 3 feet deep, so the square footage is 4 * 3 = 12 square feet.

Finally, we can add the square footage of each countertop to find the total square footage:

360 square feet + 12 square feet = 372 square feet

Therefore, The builder will need a total of 372 square feet of countertop.

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Answer:

14

Step-by-step explanation:

To find the value of 12 – 4 + 2h when h = 3, we need to substitute the value of h into the expression and simplify.

When h = 3, we can substitute this value into the expression:

12 – 4 + 2h = 12 - 4 + 2*3 = 12 - 4 + 6 = 12 - 4 + 6 = 8 + 6 = 14

So the value of 12 – 4 + 2h when h = 3 is 14.

Answer:

12 - 4 + 2h = 14

Step-by-step explanation:

Given expression,

→ 12 - 4 + 2h

Now we have to use,

→ h = 3

Let's simplify the expression,

→ 12 - 4 + 2h

→ 12 - 4 + 2(3)

→ 12 - 4 + 6

→ 8 + 6

→ 14 => {final value}

Hence, required value is 14.

Answer: 146

Step-by-step explanation:

HK = GK x 2 because a rectangles diagonals are equal.

73 x 2 = 146

Answer:

146 that should be right

Profit is determined using the equation Profit = Selling Price - Cost Price. The final price after discount is $612.

Following this, the formula for calculating profit percentage is: profit percentage = (profit/cost price) x 100.

The firm is considered to be losing money if a product's cost price is higher than its selling price; conversely, if the product's cost price is lower than its selling price, a profit might be made. Loss% is equal to Loss/CP multiplied by 100.

Profit is calculated as cost less selling price. Similar to this, the cost price is higher than the targeted selling price when a loss occurs. A profit percentage is computed by dividing the cost price by 100. 100 divided by the cost price is the loss percentage.

Determine the net profit and loss from a company's operations over the course of an accounting period with the help of the profit and loss account, also referred to as the income statement. The trading account's gross profit or loss is transferred to this account.

Given,

the cost price = $500

Selling price =  70% increase in import price

70 / 100 × $500 =  $ 350

Selling price = $350 + $500

Selling price = $850

Selling price after 20% discount = 20% of $850

⇒ 0.2 × 850 = 170

⇒ Selling price after 20% discount  = $850 - $170 = $680

Selling price after discount 10% = 0.10 × $680 = $68

Selling price after discount 10%  =  $680 - $68 = $612

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The amount with simple interest is A = $ 16,380.92

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as I

Now , the amount with simple interest = A

And , the principal P = $ 15,500

The rate of interest R = 6.2 %

The number of months n = 11 months

So , the number of years T = 11/12 years

Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

Simple Interest I = ( 15,500 x 6.2 x ( 11/12 ) ) / 100

On simplifying the equation , we get

Simple Interest I = $ 16,380.916987

Simple Interest I = $ 16,380.92

Hence , the future value if $ 16,380.92

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To find the difference between the highest monthly expenses and the lowest monthly expenses, June has to find the range of the data.

The value of baseball cards is increasing by 35% per year.

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

The value of a baseball card in dollars is given by,

0.35y + 0.15

Where y is the number of years since it was released.

This means,

The value of the baseball card is 0.15.

There is a yearly increase of 35%.

35% = 35/100 = 0.35

Thus,

The value of baseball card is increasing at 35% per year

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Answer: The depth, d, of a lake is 500 m, rounded to the nearest integer. The error interval for d is 499.5 ≤ d < 500.5

When a value is rounded to the nearest integer, the possible error is half of the smallest unit of measurement. In this case, the smallest unit of measurement is 1 meter, so the possible error is 0.5 meters. Therefore, the error interval for d is from -0.5 meters to +0.5 meters around the rounded value of 500 meters.

This can be expressed in the form a ≤ d < b as follows:

a = 500 - 0.5 = 499.5

b = 500 + 0.5 = 500.5

So, 499.5 ≤ d < 500.5

Step-by-step explanation:

The total number of votes cast is 480

Ownership of more than 50% of voting shares generally gives the right of control and consolidation. In special cases, control is possible without having to own more than 50% of voting stock.

Let x represent total number of votes.

step1:

We have been given that Joel got 50% of the votes, which was 48 votes more than Sean.

50% of total votes:50/100[tex]x[/tex]=0.50[tex]x[/tex]

Since Joel got 50% of total votes, so Sean got 40% of total votes that is

40/100[tex]x[/tex]=0.40[tex]x[/tex]

Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:

0.50[tex]x[/tex]=0.40[tex]x[/tex]+48

0.50[tex]x[/tex]-0.40[tex]x[/tex]=0.40[tex]x[/tex]-0.40[tex]x[/tex]+48

0.10[tex]x[/tex]=48

step2:

0.10[tex]x[/tex]/.10=48/.10

[tex]x[/tex]=480

Therefore, the total number of votes cast is 480

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Rashaad will pay $28.26 after the discount.

The discount equals the difference between the price paid for and it’s par value. Discount is a kind of reduction or deduction in the cost price of a product.

Given that, Rashaad has a loyalty card good for a 10% discount, he bought something at $31.40, we need to find the total amount he needs to pay after the discount,

So, the amount he will pay is (100-10) = 90% of the original amount,

90% of 31.40

= 90 % × 31.40

= 90/100 × 31.40

= 2826/100

= 28.26

Hence, he will pay $28.26 after the discount.

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A. 5 represents the number of calories that come from other ingredients.

B. Neither 8 nor 3 satisfies the given equation, so neither 8 nor 3 can be the solution to the equation.

C. The value of c is 5.5.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given

equation 4c + 5 = 27

Where c  represents the grams of carbohydrates

27 is the total number of calories that are received by the granola bite.

4 is the number of calories from 1 gram of carbohydrates and

5 is the number of calories that are received from other ingredients.

B: Priya said that neither 8 nor 3 could be the solution to the

equation.

substituting 8 and 3 in the equation,

4c + 5

4*8 + 5 = 37≠ 27

4*3 + 5 = 17≠ 27

so 8 and 3 are not solutions of the equation.

C: solution of the equation, 4c + 5 = 27

4c = 27 - 5

4c = 22

c = 22/5

c = 5.5

Hence  5 represents calories from another ingredient,

8 and 3 are not the solution of the equation and the solution of the equation is 5.5.

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Check the picture below.

This answer explains how to design a 2-bit multiplier using Logarithm. The circuit requires two 2-bit inputs, A and B, and four output bits, C0, C1, C2, and C3. To build the circuit, two 1-bit full adders are used for each bit of inputs A and B and the outputs are connected accordingly. Finally, the circuit is tested to verify that it is working as expected.

Input A: 0 0

Input B: 0 0

Output C: 0 0 0 0

Input A: 0 0

Input B: 0 1

Output C: 0 0 0 1

Input A: 0 0

Input B: 1 0

Output C: 0 0 1 0

Input A: 0 0

Input B: 1 1

Output C: 0 0 1 1

Input A: 0 1

Input B: 0 0

Output C: 0 0 0 1

Input A: 0 1

Input B: 0 1

Output C: 0 0 1 1

Input A: 0 1

Input B: 1 0

Output C: 0 1 0 0

Input A: 0 1

Input B: 1 1

Output C: 0 1 0 1

Input A: 1 0

Input B: 0 0

Output C: 0 0 1 0

Input A: 1 0

Input B: 0 1

Output C: 0 0 1 1

Input A: 1 0

Input B: 1 0

Output C: 0 1 1 0

Input A: 1 0

Input B: 1 1

1. Start with two 2-bit inputs A and B.

2. Create four output bits, C0, C1, C2, and C3.

3. Create two 1-bit full adders, one for each bit of inputs A and B.

4. Connect the inputs A and B to the inputs of the two respective full adders.

5. Connect the output of the first full adder to the input of the second full adder.

6. Connect the  of the second full adder to the output of C0.

7. Create two more 1-bit full adders, and connect the output of the first full adder to one of the inputs of each of the two full adders.

8. Connect the other input of each of the two full adders to the corresponding bit of the inputs A and B.

9. Connect the output of the first 1-bit full adder to the output of C1.

10. Connect the output of the second 1-bit full adder to the output of C2.

11. Create one more 1-bit full adder and connect the output of the second 1-bit full adder and the corresponding bit of the inputs A and B to the two inputs of the logarithm  1-bit full adder.

12. Connect the output of the 1-bit full adder to the output of C3.  

13. Test the inputs and outputs to verify that the circuit is working as expected.

This answer explains how to design a 2-bit multiplier using Logisim. The circuit requires two 2-bit inputs, A and B, and four output bits, C0, C1, C2, and C3. To build the circuit, two 1-bit full adders are used for each bit of inputs A and B and the outputs are connected accordingly. Finally, the circuit is tested to verify that it is working as expected.

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To show that 11k+1 - 6 is divisible by 5 using mathematical induction, the first step is to assume that the statement is true for any given positive integer k.

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Answer: 11.811 inches

Step-by-step explanation:

There are about 0.3937 inches in a cm, so the answer is [tex]30(0.3937)=11.811[/tex] inches.

Answer:

10.19%

Step-by-step explanation:

1 gallon = 3.785 liters

350 gallons = 350 × 3.785 liters = 1324.75 liters

percent = part/whole × 100%

percent = 135 liters / 1324.75 liters × 100%

percent = 10.19%

Rolls the higher number wins; if they both roll the same number, neither wins.

The answer is-

a)They both start the game with an equal chance of winning, therefore 1/2

b) If she rolls a 3, Thomas must roll a 1 or 2 for her to win, making her chance of winning 1/3.

c) Thomas has a 50% chance of winning if she rolls a three because he has to roll a 4,5 or 6 to do so.

d) In order for Sarah to win, she had to roll a 2, 3, 4, or 6. If Thomas had rolled a 1, 2, 3, 4, or 5, he would have lost. Thus, there is a 1/5 chance that he will roll a 3.

e) If Sarah wins she must have rolled a 2,3,4,5 or 6. So the probability that she rolls a three is also 1/5.

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The mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.

To calculate the mean of the random variable x, we can use the formula [tex]$\mu = \frac{1}{n}\sum x_i$[/tex], where $\mu$ is the mean, $n$ is the number of values, and $x_i$ is the value of the random variable for each observation.

In this case, the mean of x is[tex]$\mu = \frac{1}{5}\sum x_i = \frac{1}{5}(2 + 6 + 4 + 5 + 7) = 4.4$.[/tex]

Interpreting this result in context, the mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.

The mean of the random variable x is 4.4. This means that, on average, when x is randomly sampled, the value it will take is 4.4. In other words, the expected value of x is 4.4.

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Answer: it's not a function

Step-by-step explanation:

(4,3) (4,-3)

one to many

it isn't a function.