What is 1.004 in scientific Notation?​

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

Answer: The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

The unit tangent vector for the parametrized curve is \(\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}\).

In this question we know a three-dimension parametrized curve, of which we must derive its unit tangent vector in accordance with the following formula:

\(\vec T(t) = \frac{\vec R'(t)}{\|\vec R'(t)\|}\)

Where:

First, determine the first derivative of the parametrized curve:

\(\vec R'(t) = -\sin t \,\hat{i} + \cos t \,\hat{j} + \cos t \,\hat{k}\)

Second, derive the magnitude of the parametrized curve:

\(\|\vec R'(t)\|\) = √[(- sin t)² + (cos t)² + (cos t)²]

\(\|\vec R'(t)\|\) = √(1 + cos² t)

Third, substitute every term in the unit tangent curve formula:

\(\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}\)

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Answer:

1-23.5

2-2

3-5.59

4-0.278

Answer: Answer:

The probability that a given student is a graduate, given that he or she is on financial aid, is 30.8%.

Step-by-step explanation:

To determine what is the probability that a given student is a graduate, given that he or she is on financial aid, the following calculation must be performed:

6101 = 100

1879 = X

1879 x 100/6101 = X

187,900 / 6101 = X

30,798 = X

Therefore, the probability that a given student is a graduate, given that he or she is on financial aid, is 30.8%.

Step-by-step explanation:

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

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PLATO

i got it correct :)

Answer:

21/32

Step-by-step explanation:

0.65625 = \(\frac{65625}{100000}\) = \(\frac{13125}{20000}\) = \(\frac{2625}{4000}\) = \(\frac{525}{800}\) = \(\frac{105}{160}\) = \(\frac{21}{32}\)

When the number, 0.65625 is converted to a fraction, the result would be 21/32.

To convert a decimal to a fraction, you first need to determine the place value of the decimal. In this case, 0.65625 ends in the fifth decimal place, so it's in the hundred-thousands place.

However, this fraction can be simplified. Both 65625 and 100000 are divisible by 25. Dividing both the numerator and the denominator by 25 gives us:

= 2625/400

= 105/160

We can simplify this one more time by dividing both the numerator and the denominator by 5, resulting in:

= 21/32

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Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

Answer:

No.

Step-by-step explanation:

The numbers aren't going up at a constant rate. Say each lap costs 2 dollars. On lap 4, you have paid 8 dollars total. On lap 9, you have paid 18 dollars total. But the 10th lap is free, which means you pay 0 dollars. In order for this pattern to be constant, you would need to pay 20 dollars, but instead you pay 0.

Answer:

1526.8...........hope this helps:)

Answer:

The lesser placed value becomes smaller.

Step-by-step explanation:

In rounding off, we seek to approximate to a nearest digit as the case may be.

For example in approximating 7956 to the nearest tens, we have 7960.

Now in the initial number 7956,the lowest place value is units which is 6 followed by 5 tens then 9 hundred and 7 thousand.

So when approximating, usually, the lower place value, becomes smaller.

well, he has left only 6 oz.

now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5\)

Answer:

104

Step-by-step explanation:

115-11=104

196-92=104

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Thus, the probability of passing the test via random guessing is roughly 0.184, or 18.4%.

the likelihood that a specific occurrence will occur. (2): an area of mathematics involving the investigation of probabilities, defined as the ratio of a number of alternatives in an exhaustive collection of equally probable scenarios that cause a report “ to the entirety of the potential outcomes.

A passing grade itself determines the likelihood of completing the quiz with a passing score. Assume that 30 out of 50 accurate answers are required for a passing grade, or 60%.

For each question, there is a 1/4, or 0.25, chance that the correct answer will be selected at random. The likelihood of getting a question wrong is 3/4, or 0.75.

The probability of getting exactly 30 correct answers out of 50 is given by the binomial distribution with parameters n=50 and p=0.25:

P(X = 30) = (50 choose 30) × (0.25)³⁰ × (0.75)²⁰

Where (50 choose 30) is the number of ways to choose 30 questions out of 50.

P(X = 30) ≈ 0.114

This means that the probability of getting exactly 30 correct answers out of 50 by random guessing is about 0.114 or 11.4%.

However, to pass the quiz, we need to get at least 30 correct answers. The probability of getting 30 or more correct answers is the sum of the probabilities of getting exactly 30, 31, 32, ..., 50 correct answers:

P(X ≥ 30) = P(X = 30) + P(X = 31) + ... + P(X = 50)

With the aid of a calculator and statistical package, we can determine:

P(X ≥ 30) ≈ 0.184

This means that the probability of passing the quiz by random guessing is about 0.184 or 18.4%.

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9514 1404 393

Answer:

  x ≤ -14

Step-by-step explanation:

We assume you want to solve ...

  x/(-7) +14 ≥ 16

Subtract 14, then multiply by -7.

  x/(-7) ≥ 2 . . . . subtract 14

  x ≤ -14 . . . . . . multiplying by a negative number reverses the inequality

The solution is shown on the number line below.

Answer:

x = -6 + \(\sqrt{7}\), x = -6 - \(\sqrt{7}\)

Step-by-step explanation:

(x + 6)² = 7

x + 6 = + or - \(\sqrt{7}\)

x = -6 + \(\sqrt{7}\), x = -6 - \(\sqrt{7}\)

The solution of the quadratic equation is x = -6 +√7, x = -6 - √7.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant. Finding the maximum or minimum value of the function and when it occurs is one application of completing the square.

Given that the quadratic equation is x² + 12x + 36 = 7.

(x + 6)² = 7

x + 6 = ±√7

x = -6 + √7 , x = -6 - √7

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Answer:

Ans. Given, A1 = $2000 profit = A1 + (n-1)d d = $400 = -2000+(12-1)400 n = 12 = $2400

The required profit in the twelfth month is $2400.

Arithmetic progression is the series of numbers that have common differences between adjacent values

To solve this problem, we need to use the arithmetic sequence formula to find the profit of each month, then add up the profits for the first 12 months to find the profit in the twelfth month.

The first term (a₁) is -2000, the common difference (d) is 400, and we need to find the twelfth term (a₁₂).

We use the formula for the nth term of an arithmetic sequence:

an = a₁ + (n - 1)d

So, substituting the given values, we get:

a₁₂ = -2000 + (12 - 1)400

a₁₂ = -2000 + 11*400

a₁₂ = -2000 + 4400

a₁₂ = 2400

Therefore, the profit in the twelfth month is $2400.

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Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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Answer:

-7

Step-by-step explanation:

All the white cubes represent 1, therefore there are 5 cubes.  So the equation is 5 + -x = -2.  Since 5 + -7 = -2, then -7 is our answer.

Answer:

cosine

Step-by-step explanation:

fundamental trigonometric identities

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}\\\)

From the question we have

\(m = \frac{7 - 1}{17 - 16} = \frac{6}{1} = 6 \\ \)

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Answer:

The slope of line is 1

Step-by-step explanation:

We need to find slope of line given points (16,1),(17,7)

The formula used to find slope of line is: \(Slope=\frac{y_2-y_1}{x_2-x_1}\)

We are given:

\(x_1=16, y_1=1, x_2=17 \ and \ y_2=7\)

Finding slope using formula:

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-6}{17-16}\\Slope=\frac{1}{1}\\Slope=1\)

So, the slope of line is 1

The statement that describes the mean number of hours worked through which the relation is satisfied is The mean is the highest number or hours worked by any students in the group

What about mean?

In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is often called the arithmetic mean, and it is calculated by adding up all the values in the set and then dividing the result by the total number of values.

The formula for the mean is:

mean = (sum of all values) / (total number of values)

For example, suppose we have a set of four numbers: 2, 5, 8, and 11. To find the mean of this set of numbers, we add them up and divide by the total number of values:

mean = (2 + 5 + 8 + 11) / 4

mean = 26 / 4

mean = 6.5

Therefore, the mean of this set of numbers is 6.5. The mean is a commonly used measure of central tendency in statistics and data analysis, and it provides a way to summarize the general trend or average of a data set.

According to the given information:

Mean of the given condition is,

⇒    \(\frac{3 + 5 + 4 + 4 + 2 + 5}{6}\)

⇒    \(\frac{23}{6}\)

⇒    3.83 mean of the given condition.

So, it indicate that The mean is the highest number or hours worked by any students in the group.

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Answer:

i really don't know because i'm only in 7th grade but if this helps then yea

Step-by-step explanation:

Step 1: Set up the synthetic division. ...

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply c by the value just written on the bottom row. ...

Step 4: Add the column created in step 3.

Answer:

Step-by-step explanation:

The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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