evaluate the expression . express your answer as a fraction or a decimal number rounded to four decimal places

Answer:

14.76482306

Step-by-step explanation:

distance equals the square root of (x2-x1)^2 + (y2-y1)^2.

think of your ordered pairs as set 1 and set 2. (-4, 6) would be set 1 and (3, -7) would be set 2. so your equation will look similar to: (3- -4)^2 + (-7-6)^2 then you square root the whole thing and you will have your answer.

Using relations in a right triangle, it is found that the length of y is given by:

\(y = 2\sqrt{6}\)

The relations in a right triangle are given as follows:

The hypotenuse of both triangles is found as follows:

sin(60º) = 6/x.

\(\frac{\sqrt{3}}{2} = \frac{6}{x}\)

\(x = \frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)

\(x = 4\sqrt{3}\)

Hence length y is found as follows:

\(\cos{45^\circ} = \frac{y}{4\sqrt{3}}\)

\(\frac{\sqrt{2}}{2} = \frac{y}{4\sqrt{3}}\)

\(2y = 4\sqrt{6}\)

\(y = 2\sqrt{6}\)

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Answer:

(x - 2, y -5)

Step-by-step explanation:

X:

To go from 4 to 2, we need to move to the left

Y:

To go from -2 to -7, we need to move down 5

Answer:

70° and 110°

Step-by-step explanation:

Supplementary angles sum to 180°

sum the parts of the ratio, 7 + 11 = 18 parts

Divide 180° by 18 to find the value of one part of the ratio.

180° ÷ 18 = 10° ← value of 1 part, thus

7 parts = 7 × 10° = 70°

11 parts = 11 × 10° = 110°

The 2 angles are 70° and 110°

If f(x,y) > 0 and is a continuous function defined over a rectangle R=[a,b]x[c,d], then the double integral over R of f(x,y) can be interpreted as the volume of a solid that lies in the first octant and under the graph of the function f(x,y) over the region R.

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0, where f is a continuous function defined on a rectangle R = [a,b] × [c,d] is given as follows:

The double integral of f(x,y) over R, if f(x,y) > 0, gives the volume under the graph of the function f(x,y) over the region R in the first octant.

Consider a point P (x, y, z) on the graph of f(x, y) that is over the region R, and let us say that z = f(x,y). If f(x,y) > 0, then P is in the first octant (i.e. all its coordinates are positive).

As a result, the volume of the solid that lies under the graph of f(x,y) over the region R in the first octant can be found by integrating the function f(x,y) over the rectangle R in the xy-plane, which yields the double integral.

The following formula represents the double integral over R of f(x,y) if f(x,y) > 0:

∬Rf(x,y)dydx

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0 is given by the volume of the solid that lies under the graph of the function f(x,y) over the region R in the first octant.

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Answer:

$52.50

Step-by-step explanation:

Divide to find the unit rate.

84 / 8 = $10.50 per lawn

Multiply.

10.5 * 5 = $52.50 for 5 lawns

Best of Luck!

Answer:

52.50

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

In normal distribution, the empirical rule (aka 68-95-99.7 rule) describes the approximate proportion of data that falls within certain distances from the mean of a normal distribution. Specifically, the rule states that:

Answer:

Step-by-step explanation:

a) Area of white square = side *side = 8 * 8 = 64 sq.mm

Area of 4 white square = 4 * 64 = 256 sq.mm

 compound shape

length = 3 cm = 30 mm

Width = 2 cm = 20 mm

Area of compound shape = length *width = 30 * 20 = 600 sq.mm

Area of the shaded part of the compound shape =

                        Area of compound shape - Area of 4 white square

= 600 - 256

= 344 sq.mm

b) Perimeter of compound shape = 2*(length + width)

     = 2*(30 +20)

      = 2* 50

      = 100 mm

Answer:

(13.5)/4 = 3.375

step-by-step explanation

The appropriate marginal tax rates for each individual based on their taxable income are: Teacher - 12%, Pediatrician - 35%, Mathematician - 24%, Registered Nurse - 22%.

1: Using the single taxable income tax brackets for 2018, select the appropriate marginal tax rate for each individual. Select the correct rates in the table. Individual Taxable Income Marginal Tax Rate Teacher $40,259 12% Pediatrician $194,680 35% Mathematician $93,810 24% Registered Nurse $55,350 22%

2: Tax Bracket 10% 12% 22% 24% 32% 35% 37% The given table shows the marginal tax rates for single taxable income tax brackets in the year 2018. The marginal tax rate refers to the tax rate that applies to the next additional dollar of income. It is essential to know the marginal tax rate for the calculation of the tax bill. Now, we have to select the appropriate marginal tax rate for each individual.

Teacher -Taxable Income = $40,259. The appropriate marginal tax rate for the teacher is 12%. The income of the teacher falls in the taxable income bracket of $38,701 to $82,500, and the marginal tax rate is 12%.

Pediatrician - Taxable Income = $194,680. The appropriate marginal tax rate for the pediatrician is 35%. The income of the pediatrician falls in the taxable income bracket of $157,501 to $200,000, and the marginal tax rate is 35%.

Mathematician - Taxable Income = $93,810. The appropriate marginal tax rate for the mathematician is 24%. The income of the mathematician falls in the taxable income bracket of $82,501 to $157,500, and the marginal tax rate is 24%.

Registered Nurse - Taxable Income = $55,350. The appropriate marginal tax rate for the registered nurse is 22%. The income of the registered nurse falls in the taxable income bracket of $38,701 to $82,500, and the marginal tax rate is 22%.

Thus, the appropriate marginal tax rate for each individual is as follows: Individual Taxable Income Marginal Tax Rate Teacher $40,259 12% Pediatrician $194,680 35% Mathematician $93,810 24% Registered Nurse $55,350 22%In summary, the marginal tax rate refers to the tax rate that applies to the next additional dollar of income. It is essential to know the marginal tax rate for the calculation of the tax bill. The appropriate marginal tax rate for each individual depends on their taxable income and taxable income bracket. The given table shows the marginal tax rates for single taxable income tax brackets in the year 2018.

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Explanation:

For any triangle, the three angles always add to 180 degrees.

In an isosceles triangle, the base angles are the same measure. For now we don't know what they are, so let's call them x. The vertex angle is 36.

Adding the three angles (x,x, and 36) and setting that equal to 180 will help us find the value of x.

x+x+36 = 180

2x+36 = 180

2x+36-36 = 180-36 .... subtract 36 from both sides

2x = 144

2x/2 = 144/2 .... divide both sides by 2

x = 72

This triangle has two base angles of 72 each and the vertex angle of 36. As a check, the three angles should add up to 180

72+72+36 = 144+36 = 180

So the answer is confirmed.

Answer: Both of the other angles equal 72 degrees individually.

Step-by-step explanation:

The measure of each of the other angles could be 72 degrees because isosceles triangles have two sides that have the same equivalence. Since a line has 180 degrees and its vertex angle measures 36 degrees, then the remaining angles have to be found by subtracting 180 with 36 in order to get 144. 144 divided by 2 because of the two angles then makes both sides equal to 72 degrees individually.

The problem states that 12 less than a variable, represented by 'm,' is no less than 132. The solution to the inequality is that 'm' is greater than or equal to 144.

To translate the given statement into an inequality, we can express "12 less than m" as "m - 12" and "no less than 132" as "≥ 132". Combining these expressions, we have the inequality: m - 12 ≥ 132. To solve for 'm,' we can add 12 to both sides of the inequality: m - 12 + 12 ≥ 132 + 12, which simplifies to m ≥ 144. Thus, the solution to the inequality is that 'm' is greater than or equal to 144. In interval notation, this can be written as [144, +∞), indicating that 'm' lies between 144 (inclusive) and positive infinity.

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Answer:

1. The required information are

The average annual bonuses, \(\bar {x}_1\) received by employees from company A

The average annual bonuses, \(\bar {x}_2\) received by employees from company B

The standard deviation, σ₁, of the average annual bonuses for employees from company A

The standard deviation, σ₂, of the average annual bonuses for employees from company A

The number of employees in company A, n₁

The number of employees in company B, n₂

2. The null hypothesis is H₀: \(\bar {x}_1\) - \(\bar {x}_2\) ≤ 100

The alternative hypothesis is Hₐ: \(\bar {x}_1\) - \(\bar {x}_2\) > 100

Step-by-step explanation:

1. The required information are

The average annual bonuses, \(\bar {x}_1\) received by employees from company A

The average annual bonuses, \(\bar {x}_2\) received by employees from company B

The standard deviation, σ₁, of the average annual bonuses for employees from company A

The standard deviation, σ₂, of the average annual bonuses for employees from company A

The number of employees in company A, n₁

The number of employees in company B, n₂

2. The null hypothesis is H₀: \(\bar {x}_1\) - \(\bar {x}_2\) ≤ 100

The alternative hypothesis is Hₐ: \(\bar {x}_1\) - \(\bar {x}_2\) > 100

The z value for the hypothesis testing of the difference between two means is given as follows;

\(z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}-\frac{\sigma _{2}^{2}}{n_{2}}}}\)

At 0.5 level of significance, the critical \(z_\alpha\) = ± 0

The rejection region is z > \(z_\alpha\) and z < -\(z_\alpha\)

Therefore, the value of z obtained from the relation above more than or less than 0, we reject the null hypothesis, and we fail to reject the alternative hypothesis.

Answer:

James is incorrect. The outcome of a coin toss is always random and independent of previous tosses. Each toss has a 50% chance of landing heads and a 50% chance of landing tails, regardless of the outcome of previous tosses. This is known as the principle of independence in probability theory.

Step-by-step explanation:

We have the following:

\(\huge\text{Hey there!}\)

\(\mathsf{\dfrac{2\times4^0\times6^2}{2^4 \times 4^{-1} \times6^1}}\\\\\mathsf{= \dfrac{2\times\bf 1\times36}{2^4 \times 4^{-1} \times6^1}}\\\\\mathsf{= \dfrac{2\times \bf 36}{2^4 \times 4^{-1} \times6^1}}\\\\\mathsf{= \dfrac{\bf 72}{2^4 \times 4^{-1} \times6^1}}\\\\\mathsf{= \dfrac{72}{\bf 16\times \dfrac{1}{4}\times6}}\\\\\mathsf{= \dfrac{72}{\bf 16\times6}}\\\\\mathsf{= \dfrac{72}{\bf 24}}\\\\\mathsf{= \bf 3}\)

\(\huge\textbf{Therefore, your answer should be: }\)

\(\huge\boxed{\mathsf{3}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

\( \displaystyle {\rm{ \frac{2 \times {4}^{0} \times {6}^{2} }{ {2}^{4} \times {4}^{ - 1} \times 6 } }}\)

\(\displaystyle {\rm{ \frac{2 \times \bold{1} \times {6}^{2} }{ {2}^{4} \times {4}^{ - 1} \times {6}^{1} } }}\)

\(\displaystyle {\rm{ \frac{2 \times 1 \times \bold{36}}{ {2}^{4} \times {4}^{ - 1} \times 6 } }}\)

\(\displaystyle {\rm{ \frac{2 \times 1 \times 36}{ \bold{16} \times {4}^{ - 1} \times 6 } }}\)

\(\displaystyle {\rm{ \frac{2 \times 1 \times 36}{16 \times \bold{ \frac{1}{4}} \times 4} }}\)

\( \left[ \because \: {x}^{ - m} = \frac{1}{ {x}^{m} } \right]\)

\(\displaystyle {\rm{ \frac{2 \times 1 \times 36}{ \cancel{16^4} \times \frac{1}{ \cancel4} \times 6 } }}\)

\(\displaystyle {\rm{ \frac{72}{24} }}\)

\(\displaystyle {\rm{ \frac{2 \times 2 \times 2 \times 3 \times 3}{2 \times 2 \times 2 \times 3} }}\)

\(3\)

Step-by-step explanation:

\( \frak{ \pink{Seolle...a_{prodite}}}\)

39 subjects were tested in this simple one-way ANOVA.

We are given that:

F(7 , 31) = 4.78

Step 1: Find the total degrees of freedom.

The treatment df = 7

The error df = 31

\(df_{treatment} &\ +df_{error} &\ = df_{total}\)

Hence, the total df = 7+31 = 38.

Step 2: Find the number of subjects tested.

We know that in a one-way ANOVA test:

df = n-1

⇒ 38 = n-1

⇒ n = 39.

Hence, 39 subjects were tested in this simple one-way ANOVA.

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A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 90% confidence interval for the proportion of all orders that arrive on time is 89% ± 6%.

a) The correct answer is A

b) The correct answer is B

c) The correct answer is C

d) The correct answer is D.

e) The correct answer is B.

a) Between 83% and 95% of all orders arrive on time.

The correct answer is A. This statement is correct.

b) 90% of all random samples of customers will show that 89% of orders arrive on time.

The correct answer is B. This statement is not correct. It implies certainty, but in reality, the statement refers to the confidence interval estimate for the proportion of orders that arrive on time based on the sample.

c) 90% of all random samples of customers will show that 83% to 95% of orders arrive on time.

The correct answer is C. This statement is not correct. No more than 95% of all orders arrive on time. The confidence interval represents the range within which the true proportion is estimated to fall, but it doesn't guarantee that all intervals will cover the true proportion.

d) The company is 90% sure that between 83% and 95% of the orders placed by the customers in this sample arrived on time.

The correct answer is D. This statement is not correct. The confidence interval provides an estimate of the proportion of orders that arrive on time, not a measure of the company's certainty.

e) On 90% of the days, between 83% and 95% of the orders will arrive on time.

The correct answer is B. This statement is not correct. It implies certainty about the proportion of orders arriving on time, but the confidence interval only provides an estimate based on the sample data and does not guarantee the exact proportion for every day.

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Answer:

81

Step-by-step explanation:

Take half of the x-term coefficient, and square it.

Half of 18 is 9.

9² = 81

Answer: 81

Answer:

If the question was find the value of a when a equal -2, then the answer is a = -2

The function f(x) = 150,000(0.85)^x can be used to determine the number of tickets the Houston Ballet Company will sell over time. In this function, the 150,000 represents the initial number of tickets sold before any time has passed (when x = 0).

It serves as the starting point or baseline for the exponential decay of ticket sales over time. As x increases, the function evaluates the number of tickets sold at a particular time, where each subsequent value of x represents a subsequent unit of time (such as days, weeks, months, etc.). The term (0.85)^x represents the decay factor, as it is less than 1 (0.85). Thus, the function models a situation where ticket sales decrease exponentially over time from the initial value of 150,000.

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Answer:

Translation 10 units right: (-5, 10) --> (5, 10)

Translation 5 units down: (5, 10) --> (5, 5)

(5, 5) is the final answer

Let me know if this helps!

Answer:

108 degrees

Step-by-step explanation:

A straight angle measures 180 degrees. So we have to find 3/5 of 180. To find it, multiply 3/5 x 180 which is equal to 540/5, and when you divide 540 by 5, you get 108. So 3/5 of it is 108 degrees.

Hope this helps!

Answer:

108 degrees

Step-by-step explanation:

A straight angle is 180 degrees.

3/5 x 180 = 540/5

540 ÷ 5 = 108

108 degrees is the answer.

Have a GOOD DAY!!!!!

Answer:

1. 64.4kg

2. 490.5g

3. 34.4cm

4. 503.25

Step-by-step explanation:

1. 56+(56×15/100)

2. 436+(436×12.5/100)

3. 43-(43×20/100)

4. 550-(550×8.5/100)

Answer:

the answer is -10p

We have derived the equation β = cv = 1 - (E₀ + KE₀)².

To derive the equation β = cv = 1 - (E₀ + KE₀)², we can begin with the given equations:

E² = p²c² + E₀²

K + E = ε₀ = 1 - β²

E = p²c² + E₀ = p²c² + mc²

K = E - E₀ = 1 - ρ²E₀² - E₀

We'll rearrange these equations to arrive at the desired equation.

Starting with equation 1, we have:

E² = p²c² + E₀²

From equation 3, we substitute E = p²c² + mc²:

(p²c² + mc²)² = p²c² + E₀²

Expanding and simplifying:

p⁴c⁴ + 2p²mc⁴ + m²c⁴ = p²c² + E₀²

Next, we focus on equation 4:

K = E - E₀ = 1 - ρ²E₀² - E₀

Substituting equation 1 into equation 4:

K = p²c² + E₀² - E₀ = 1 - ρ²E₀² - E₀

Now, we substitute equation 2 into equation 4:

K = 1 - β² - E₀

Substituting this value of K into our modified equation 4:

1 - β² - E₀ = p²c² + E₀² - E₀

Rearranging and simplifying:

β² = 1 - (E₀ + K E₀)²

Thus, we have derived the equation β = cv = 1 - (E₀ + KE₀)².

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Answer:

3p - q = 3(2-5) - (8x3) = -9 - 24 = -33. Therefore, 3p-q=-33.

The area οf the frame nοt cοvered by the picture is apprοximately 99.87 square inches.

The size οf a regiοn οn a surface is measured by its area. While surface area refers tο the area οf an οpen surface οr the bοundary οf a three-dimensiοnal οbject, the area οf a plane regiοn οr plane area refers tο the area οf a shape οr planar lamina.

Area can be interpreted as the quantity οf material with a particular thickness required tο create a mοdel οf the shape οr as the quantity οf paint required tο cοmpletely cοver a surface in a single cοat. It is the twο-dimensiοnal equivalent οf the vοlume οf a sοlid οr the length οf a curve (a οne-dimensiοnal cοncept) (a three-dimensiοnal cοncept).

The area οf the rectangular picture is:

20 inches x 12 inches = 240 square inches

The area οf the circular frame is:

\($ \pi r^2 = \pi(12 inches)^2 = 144\pi\) square inches

Tο find the area οf the frame nοt cοvered by the picture, we need tο subtract the area οf the picture frοm the area οf the frame:

144π square inches - 240 square inches ≈ 99.87 square inches

Therefore, the area of the frame not covered by the picture is approximately 99.87 square inches.

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a)The mean number of arrows that hit the bull's-eye is 10.32.

b)The standard deviation of the number of arrows that hit the bull's-eye     is approximately 1.215.

Let's denote the event of hitting the bull's-eye as a success (S) and missing the bull's-eye as a failure (F). Since the archer hits the bull's-eye 86% of the time, the probability of success is 0.86, and the probability of failure is 1 - 0.86 = 0.14.

We can model the number of arrows hitting the bull's-eye as a binomial distribution with parameters n = 12 (number of trials) and p = 0.86 (probability of success).

a) The mean number of arrows that hit the bull's-eye is given by the formula:

Mean = n * p

Mean = 12 * 0.86 = 10.32

Therefore, the mean number of arrows that hit the bull's-eye is 10.32.

b) The standard deviation of the number of arrows that hit the bull's-eye is given by the formula:

Standard deviation = \(\sqrt (n * p * (1 - p))\)

Standard deviation = \(\sqrt(12 * 0.86 * (1 - 0.86))\)

Using a calculator, we can evaluate this expression:

Standard deviation ≈ \(\sqrt(12 * 0.86 * (1 - 0.86))\) ≈ \(\sqrt (1.47728)\) ≈ 1.215

Therefore, the standard deviation of the number of arrows that hit the bull's-eye is approximately 1.215.

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