what is a rectangles area formula

Answer:

he has to pay 4980$ in tax So its C) 4,980

The amount of income tax that the electrician has to pay is $4980. Then the correct option is C.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

An electrician has an income of $41,500.

The income tax the electrician has to pay is 12%.

Then the amount of income tax that the electrician has to pay will be

Amount of income tax = 0.12 × $41500

Amount of income tax = $ 4980

Thus, the amount of income tax that the electrician has to pay is $4980.

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Answer:

The area of the segment AYB is 271.0413985 cm²

Step-by-step explanation:

The rule of the area of a sector is A = \(\frac{\alpha }{360}\) × π r², where

The area of a triangle is A = \(\frac{1}{2}\) × s1 × s2 × sinФ

∵ Area of the segment AYB = Area the sector AOB - Area ΔAOB

∵ The radius of the circle is 21 cm

∴ r = 21 cm

∵ The central angle of the sector is 120°

∴ α = 120°

∵ π = \(\frac{22}{7}\)

→ Substitute them in the rule of the area of the sector to find it

∵ Area sector AOB = \(\frac{120}{360}\) × \(\frac{22}{7}\) × (21)²

∴ Area of sector AOB = 462 cm²

∵ OA and OB are the radii of the circle

∴ s1 = OA and s2 = OB

∴ s1 = s2 = 21 cm

∵ The angle included between them is 120°

∴ Ф = 120°

→ Substitute them in the rule of the area of the triangle to find it

∵ Area of the Δ = \(\frac{1}{2}\) × 21 × 21 × sin(120)

∴ Area of the Δ = 110.25√3 cm²

∵ Area of the segment AYB = Area the sector AOB - Area ΔAOB

∴ Area of the segment AYB = 462 - 110.25√3

∴ Area of the segment AYB = 271.0413985 cm²

Answer:

These are all equivalent expressions

Step-by-step explanation:

6x+12

6(x+2)

12(.5x+1)

1.5(4x+12)

Answer:

\(\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \frac{20}{23}\:\\ \:\mathrm{Decimal:}&\:x\ge \:0.86956\dots \\ \:\mathrm{Interval\:Notation:}&\:[\frac{20}{23},\:\infty \:)\end{bmatrix}\)

Step-by-step explanation:

\(-\frac{2}{3}\left(2x-\frac{1}{2}\right)\le \frac{1}{5}x-1\)

Expand \(-\frac{2}{3}\left(2x-\frac{1}{2}\right)\le \frac{1}{5}x-1\) \(-\frac{4}{3}x+\frac{1}{3}\)

\(-\frac{4}{3}x+\frac{1}{3}\le \frac{1}{5}x-1\)

\(\mathrm{Subtract\:}\frac{1}{3}\mathrm{\:from\:both\:sides}\)

\(-\frac{4}{3}x+\frac{1}{3}-\frac{1}{3}\le \frac{1}{5}x-1-\frac{1}{3}\)

\(Simplify\)

\(-\frac{4}{3}x\le \:-\frac{4}{3}+\frac{1}{5}x\)

\(\mathrm{Subtract\:}\frac{1}{5}x\mathrm{\:from\:both\:sides}\)

\(-\frac{4}{3}x-\frac{1}{5}x\le \:-\frac{4}{3}+\frac{1}{5}x-\frac{1}{5}x\)

\(Simplify\)

\(-\frac{23}{15}x\le \:-\frac{4}{3}\)

\(\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\)

\(\left(-\frac{23}{15}x\right)\left(-1\right)\ge \left(-\frac{4}{3}\right)\left(-1\right)\)

\(\mathrm{Simplify}\)

\(\frac{23}{15}x\ge \frac{4}{3}\)

\(\mathrm{Multiply\:both\:sides\:by\:}15\)

\(15\cdot \frac{23}{15}x\ge \frac{4\cdot \:15}{3}\)

\(Simplify\)

\(23x\ge \:20\)

\(\mathrm{Divide\:both\:sides\:by\:}23\)

\(\frac{23x}{23}\ge \frac{20}{23}\)

\(\mathrm{Simplify}\)

Hence the final answer is \(\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \frac{20}{23}\:\\ \:\mathrm{Decimal:}&\:x\ge \:0.86956\dots \\ \:\mathrm{Interval\:Notation:}&\:[\frac{20}{23},\:\infty \:)\end{bmatrix}\)

a) Graham's employer contributes $561.60 per year towards his coverage.

b) Claudia contributes 28.2% towards the total coverage cost.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is typically represented by the symbol "%", and is often used to express a change or a part of a whole.

a) Graham makes $62,800 per year, which is less than $65,000, so he pays $52 per month for individual coverage. His yearly contribution is 10% of the total cost, so his employer contributes 90% of the total cost. To find the total cost, we can multiply the monthly cost by 12: $52/month * 12 months/year = $624/year. So Graham's employer contributes $624 * 90% = $561.60 per year towards his coverage.

b) Claudia's annual salary is $75,400, which is at least $65,000, so she pays $122 per month for family coverage. Her employer contributes $1,052 per month towards her total coverage cost. To find the total cost, we can multiply the monthly cost by 12: $122/month * 12 months/year = $1,464/year. To find the percentage Claudia contributes, we divide her contribution by the total cost and multiply by 100: $1,464-$1,052 / $1,464 * 100 = 28.2%. So Claudia contributes 28.2% towards the total coverage cost.

Hence,

a) Graham's employer contributes $561.60 per year towards his coverage.

b) Claudia contributes 28.2% towards the total coverage cost.

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(i) State whether the term is a variable name or a variable value.

(ii) State the level of measurement.

A. age

(i) Variable name.

(ii) Ratio.

Explanation: "Age" is the name of the variable and it is a numerical value representing the number of years a person has lived. It is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

B. conservative

(i) Variable name.

(ii) Nominal.

Explanation: "Conservative" is the name of b and it refers to a political ideology. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., conservative, liberal, socialist) and have no meaningful mathematical operations.

C. strongly oppose

(i) Variable value.

(ii) Ordinal.

Explanation: "Strongly oppose" is a value of the variable, and it refers to a person's opinion or attitude towards a certain issue. It is measured on an ordinal scale, meaning it has a rank or order (e.g., strongly oppose, somewhat oppose, neutral, somewhat support, strongly support). However, the difference between two values is not necessarily equal (e.g., the difference between strongly oppose and neutral might be different from the difference between neutral and strongly support).

D. region

(i) Variable name.

(ii) Nominal.

Explanation: "Region" is the name of the variable and it refers to a geographical area, such as the Midwest or the South. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Midwest, South, West, Northeast) and have no meaningful mathematical operations.

E. 57 years

(i) Variable value.

(ii) Ratio.

Explanation: "57 years" is a value of the variable "Age" and it represents the number of years a person has lived. As mentioned above, "Age" is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

F. strictly enforced

(i) Variable value.

(ii) Ordinal.

Explanation: "Strictly enforced" is a value of a variable, and it refers to the level of enforcement of a rule or law. It is measured on an ordinal scale, meaning it has a rank or order (e.g., not enforced, loosely enforced, strictly enforced). However, the difference between two values is not necessarily equal (e.g., the difference between not enforced and loosely enforced might be different from the difference between loosely enforced and strictly enforced).

G. Catholic

(i) Variable name.

(ii) Nominal.

Explanation: "Catholic" is the name of the variable and it refers to a religious affiliation. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Catholic, Protestant, Jewish, Muslim) and have no meaningful mathematical operations.

H. Gender

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Answer:

Step-by-step explanation:

For missing hypotenuse: \(\sqrt({a^{2} + b^{2})\)

Plug in the side lengths that are known to find the hypotenuse.

1. No, the angle is less than 18 degrees (closer to 15), so it is not safe

2. The length rounded to the nearest tenth is approximately 15.5 feet.

The remote interior angles of ∠1 are ∠2 and ∠6.

Corresponding angles in a triangle are those angles which are contained by a congruent pair of sides of two similar (or congruent) triangles.

The remote interior angles of ∠1 is determined by applying the principle of corresponding angles as shown below;

∠1 = ∠2 ( vertical opposite angles are equal )

∠1 = 180 - ∠5 ( corresponding angles  are equal )

180 - ∠5  = ∠ 6 ( vertical opposite angles are equal )

So we can conclude that, ∠1 = ∠6.

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Main Answer: The value of f(n) = 16(f(k))^4 when n = 3k.

Supporting Question and Answer:

How can we determine the value of f(n) when n = 3k using the given recurrence relation and initial condition?

By analyzing the given recurrence relation f(n) = 2f(n/3)^4 and the initial condition f(1) = 1, we can recursively calculate the value of f(n) for n = 3k. Using the recurrence relation, we can express f(n) in terms of f(n/3) and apply it iteratively. The value of f(n) when n = 3k is given by f(n) = 16(f(k))^4, where f(1) = 1 is used as the base case.

Body of the Solution:To find the value of f(n) when n = 3k, where f satisfies the recurrence relation f(n) = (2f(n/3))^4 with f(1) = 1, we can use the recurrence relation to recursively calculate the values of f(n).

Given that f(1) = 1, we can calculate the values of f(n) for n = 3, 9, 27, and so on.

f(3) = (2f(3/3))^4

= ((2f(1)))^4

= 2^4(1)^4

= 16

f(9) = (2f(3))^4

= (2(16))^4

= 1048576

f(27) =(2f(9))^4

= (2(1048576))^4

=(2097152)^4

Therefore, f(n) when n = 3k is given by:

f(3K)  =16(f(k))^4

So, f(n) =16(f(k))^4  when n = 3k, where f satisfies the given recurrence relation and f(1) = 1.

Final Answer:Therefore, f(n) =16(f(k))^4 when n = 3k.

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Answer:8

Step-by-step explanation:

it is the only one without a variable.

Answer:

\(\boxed {\tt 8}\)

Step-by-step explanation:

A constant is a term without a variable.

Let's analyze each term of the expression: 13x³+x²-4x+8

13x³: this has a variable of x³

x²: this has a variable of x²

-4x: this has a variable of x

8: this has no variable

Since 8 is the term without a variable, 8 is the constant.

The least number of pens each boy can have brought is 60

We have:

Vincent = 6 packs

Aidan = 20 boxes

Factorize 6 and 20

6 = 1 * 2 * 3

20 = 1 * 2 * 2 * 5

Multiply all factors

LCM = 1 * 2 * 2 * 3 * 5

Evaluate the product

LCM = 60

Hence, the least number of pens each boy can have brought is 60

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If a researcher finds that the probability of a word recognition program correctly interpreting a hand-written word is 9/10 . The number of  words that  the researcher expect the program to interpret correctly out of 40 words is 36 words.

Using this formula to find the number of words

Number of words = Probability of correctly interpreting a hand-written word × Expected words

Let plug in  the formula

Number of words = 9/10 × 40

Number of words = 36 words

Therefore we can conclude that the number of words is 36 words.

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A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Answer:

y = 2x - 1

Step-by-step explanation:

Given equation: 2x - y = 1

We're being asked to solve for y. This is also known as the Slope-Intercept Form. It is represented by the following formula:

y = mx + b

where:

Steps:

1. Subtract 2x from both sides:

\(\sf 2x-2x - y = 1-2x\\\\\implies-y=-2x+1\)

2. Divide both sides by -1:

\(\sf \dfrac{-y}{-1}=\dfrac{-2x+1}{-1}\\\\\implies y=2x-1\)

This equation has a slope of 2, and a y-intercept of -1.

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The solution to the inequality ||8-3p|| ≥ 2 is:p ≤ 2 or p ≥ 10/3. To solve the inequality ||8-3p|| ≥ 2, you'll first want to isolate the absolute value expression.

Once you've done that, you'll be left with two inequalities to solve. How to solve the inequality ||8-3p|| ≥ 2?The first inequality is 8-3p ≥ 2.

To solve for p, you can start by subtracting 8 from both sides to get:-3p ≥ -6.

Then divide both sides by -3 to get:p ≤ 2. The second inequality is -(8-3p) ≥ 2. To solve for p, you can start by distributing the negative sign to get:-8 + 3p ≥ 2.

Then add 8 to both sides to get:3p ≥ 10. Finally, divide both sides by 3 to get:p ≥ 10/3. So the solution to the inequality ||8-3p|| ≥ 2 is:p ≤ 2 or p ≥ 10/3.

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Answer:

Step-by-step explanation:

take 45 degree as reference angle

using sin rule

sin 45=opposite/hypotenuse

1/\(\sqrt{2}\)=l/11\(\sqrt{2}\) (do cross multiplication)

l\(\sqrt{2}\)=11\(\sqrt{2}\)

l=11\(\sqrt{2}\)/\(\sqrt{2}\)

l=11

Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Answer: I would need to see the coordinate plane

Step-by-step explanation:

The solution to the equation -1/2w - 3/5 = 1/5w is w = -6/7, meaning that w equals negative six-sevenths when the equation is true.

To solve the equation -1/2w - 3/5 = 1/5w, we'll start by simplifying and rearranging the terms to isolate the variable w.

First, we'll combine like terms on the left side of the equation:

-1/2w - 3/5 = 1/5w

To make the equation easier to work with, let's get rid of the fractions by multiplying every term in the equation by the common denominator, which is 10:

10 * (-1/2w) - 10 * (3/5) = 10 * (1/5w)

This simplifies to:

-5w - 6 = 2w

Next, we'll group the w terms on one side of the equation and the constant terms on the other side:

-5w - 2w = 6

Combining like terms, we have:

-7w = 6

Now, we'll isolate the variable w by dividing both sides of the equation by -7:

(-7w)/(-7) = 6/(-7)

This simplifies to:

w = -6/7

Therefore, the solution to the equation -1/2w - 3/5 = 1/5w is w = -6/7.

In conclusion, w is equal to -6/7 when the equation -1/2w - 3/5 = 1/5w is satisfied.

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Answer:

-50x - 66

Step-by-step explanation:

Answer:

-50x - 66

Step-by-step explanation:

Answer:

Merton will have about 6,000 more people than Hapville

Step-by-step explanation:

Merton

y = 12,000(1.04)^(30)

y = 12,000(3.24339)

y = 38,920.77012

Hapeville

y = 18,000 + (30 x 500)

y= 18,000 + 15,000

y = 33, 000

Merton - Hapeville

38,920.77012 - 33,000 = 5920.77012

Therefore Merton will have about 6,000 more people than Hapville

Answer:

53

Step-by-step explanation:

Bivariate regression can not demonstrate when the two variables are causally related.

The term variables in math means an alphabet or term that represents an unknown number or unknown value or unknown quantity.

Here we have to find the term that must not demonstrate the bivariate in math.

In order to find the resulting term, we must know the definition of bivariate regression.

The term bivariate regression in statistics is defined as the simple linear regression model which is used to predict one variable referred to as the outcome, criterion, or dependent variable from one other variable referred to as the predictor or independent variable.

Based on these definition we have identified that if the two variables are related then the regression process is not possible.

Therefore, option (d) is correct.

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Answer:

The mean weight of an adult is 66 kilograms with a variance of 144. If 123 adults are randomly selected, the sample mean would follow a normal distribution with a mean of 66 kilograms and a standard deviation of sqrt(144/123) = 3/sqrt(123) kilograms.

We can standardize the sample mean to find the probability that it would be greater than 66.7 kilograms. The standardized value for 66.7 is (66.7 - 66) / (3/sqrt(123)) = 2.3094.

Using a standard normal distribution table, we find that the probability of a standard normal variable being greater than 2.3094 is approximately 0.0104.

Therefore, the probability that the sample mean would be greater than 66.7 kilograms is approximately 0.0104, rounded to four decimal places.

Step-by-step explanation:

What is the most likely conclusion that can be drawn about how this table would look in December 2013?

Answer: It would look different because exchange rate tables change constantly.

Answer:

1. Look at the screenshot below.

2. If a line intersects a parabola at a point, the coordinates of the intersection point must satisfy the equation of the line and the equation of the parabola.

Since the equation of the line is y = c, where c is a constant, the y-coordinate of the intersection point must be c.

It follows then that substituting c for y in the equation for the parabola will result in another true equation: c = −x^2 + 5x.

Subtracting c from both sides of c = −x^2 + 5x and then dividing both sides by −1 yields 0 = x^2 − 5x + c.

The solution to this quadratic equation would give the x-coordinate(s) of the point(s) of intersection.

Since it’s given that the line and parabola intersect at exactly one point, the equation 0 = x^2 − 5x + c has exactly one solution.

A quadratic equation in the form 0 = ax^2 + bx + c has exactly one solution when its discriminant b 2 − 4ac is equal to 0. In the equation 0 = x^2 − 5x + c, a = 1, b = −5, and c = c.

Therefore, (−5)^2 − 4(1)(c ) = 0, or 25 − 4c = 0.

Subtracting 25 from both sides of 25 − 4c = 0 and then dividing both sides by −4 yields c = 25/4 .

Therefore, if the line y = c intersects the parabola defined by y = −x^2 + 5x at exactly one point, then c = 25/4 .

Either 25/4 or 6.25

Answer:

Part A:  \(\frac{2}{9} \\\)

Part B:  \(\frac{1}{9}\)

Step-by-step explanation:

Calculate compound independent probabilities by multiplying the probability of each together.

Part A

Probability of landing green: 1/3

Probability of an odd number: 2/3

Probability of green and odd:  \(\frac{1}{3} *\frac{2}{3} = \frac{2}{9}\)

Check work: Only two possibilities with green and odd condition are green+1 and green+3.

Part B

Probability of landing blue:  1/3

Probability of landing 2: 1/3

Probability of blue and 2:  \(\frac{1}{3} * \frac{1}{3} = \frac{1}{9}\)

Check work: Only possibility with blue and 2 are just that:  Blue + 2

Answer:

3355

Step-by-step explanation:

55 x 61 = 3355

Answer:

\(\frac{1}{25}\) = \(5^{-2}\)

Step-by-step explanation:

Using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\) , thus

\(log_{5}\) (\(\frac{1}{25}\) ) = - 2, then

\(\frac{1}{25}\) = \(5^{-2}\)