What is the equation of the line that passes through the point (-9,6) and is perpendicular
to the line 3x-5?
M
Oy--x-3
О У - 3x + 21
Oy - 3x +33

If a square base has a volume of 4 cubic feet, the dimensions that minimize the surface area are: x = 2√2 and h = 4/x^2 = 1/2.

Let x be the side length of the square base and h be the height of the box. Since the volume is 4 cubic feet, we have:

V = x^2h = 4

Solving for h, we get:

h = 4/x^2

The surface area of the box, A, is given by:

A = x^2 + 4xh

Substituting h in terms of x, we get:

A = x^2 + 4x(4/x^2) = x^2 + 16/x

To minimize A, we take the derivative with respect to x and set it equal to zero:

dA/dx = 2x - 16/x^2 = 0

Solving for x, we get:

x = 2√2

To ensure that this is a minimum, we take the second derivative:

d^2A/dx^2 = 2 + 32/x^3

At x = 2√2, this is positive, indicating a minimum.

The box has a square base with side length 2√2 feet and height 1/2 feet.

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The distance between Thomas St and Denny Way on Broad St is 0.1 miles.

0.45 miles on Aurora Ave is equivalent to the distance between Mercer St and Denny Way on Broad St.

0.2 miles on Aurora Ave is equivalent to the distance between Thomas St and Denny Way on Aurora Ave.

We say X  be the distance between Thomas St and Denny Way on Broad St,

and have the following proportion:

0.45 miles / (Mercer St to Denny Way on Broad St) = 0.2 miles / (Thomas St to Denny Way on Broad St)

Solving for x, we get:

x = 0.45 miles x  (Thomas St to Denny Way on Broad St) / (Mercer St to Denny Way on Broad St) = 0.45 * 0.2 / 0.7 = 0.1286 miles

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Complete question:

Use the following information and the map of downtown Seattle to answer questions one and two. Harrison St, Thomas St, and Denny Way are parallel. On Broad St, the distance between Mercer St and Denny Way is 0.7 miles. The distance between those same streets on Aurora Ave is 0.45 miles.

a) On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles. What is the distance

between these two streets on Broad St? Round your answer to the nearest tenth of a mile.

The simplified difference quotient for the function [tex]\(f(x)=6\) is \(\frac{x+h-1}{h/6}\).[/tex]

The difference quotient for the function \(f(x)=6\) is given by the formula \( \[tex]frac{f(x+h)-f(x)}{h}\)[/tex]. To simplify this difference quotient, substitute the given value of \(f(x)\) into the equation:

[tex]\( \frac{f(x+h)-f(x)}{h} = \frac{f(x+h)-6}{h} \).[/tex]  Next, substitute the value of \(f(x)\) into the numerator:

[tex]\frac{6(x+h-1)}{h} \\[/tex]  .

Finally, divide both sides of the equation by 6 to simplify the equation:

[tex]\( \frac{6(x+h-1)}{h} = \frac{x+h-1}{h/6} \)[/tex]

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90% people entering the emergency department is within the interval of [0.1559, 0.2933].

The confidence interval of the percent of patients entering the emergency department who are admitted to the hospital is [0.1763, 0.3137]. It is not reasonable for the hospital to assume that 25% of people who enter the emergency department are admitted to the hospital. Here's why.How to calculate a 90% two-sided confidence interval for p, the percent of people entering the emergency department who are admitted to the hospital:$$CI_p =\bigg(\hat{p}-Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\bigg)$$ where $\hat{p} = \frac{x}{n}$, $\alpha = 0.10$, $Z_{\alpha/2} = 1.645$ (for a 90% confidence interval), and $n = 187$. The margin of error is given by $$ME = Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$Plugging in the values, we get $$\hat{p} = \frac{42}{187} = 0.2246$$$$ME = 1.645 \cdot \sqrt{\frac{0.2246\cdot 0.7754}{187}} \approx 0.0687$$Therefore, the confidence interval for $p$ is $$CI_p = (0.2246-0.0687, 0.2246+0.0687) = (0.1559, 0.2933)$$The 90% two-sided confidence interval for the percent of people entering the emergency department who are admitted to the hospital is [0.1559, 0.2933].Since the interval doesn't include 0.25, the hospital should not use the assumption that 25% of people who enter the emergency department are admitted to the hospital. This is because the interval does not overlap with the value of 0.25. As a result, we are 90% confident that the true proportion of people who are admitted to the hospital after entering the emergency department is within the interval of [0.1559, 0.2933].

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Therefore , the solution of the given problem of probability comes out to be there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

The primary goal of the form of patterns defined as hyper parameters is to calculate the likelihood that a remark is accurate or a specific event will occur. Any number between 0 but instead 1, where 1 usually denotes assurance and range 0 typically connotes possibility, can be used to represent chance. A probability diagram shows the chance that a specific event will occur.

Here,

We must count the number of outcomes in which there are 3 or 4 thunderstorms in order to calculate the chance that a thunderstorm will occur on at least 3 of the following 4 days using the simulation.

We can see from the programme that there are 6 scenarios where there are at least 3 thunderstorms:

=>  1-2-3-4

=>  1-2-4-3

=>  1-3-2-4

=>  1-3-4-2

=>  1-4-2-3

=>  1-4-3-2

Since there are a total of 16 potential outcomes (since a thunderstorm can occur every day or not), the likelihood of at least 3 thunderstorms is:

=> 6/16 = 0.375

This means that there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

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Answer:

d. 27/4, or 6.75

Step-by-step explanation:

[tex]2( \frac{1}{8} + 4) - ( \frac{3}{16} \times 8)[/tex]

[tex]2( \frac{33}{8} ) - \frac{3}{2} [/tex]

[tex] \frac{33}{4} - \frac{3}{2} = \frac{33}{4} - \frac{6}{4} = \frac{27}{4} = 6.75[/tex]

Answer:

Tip is $34

Round up bill amount $170

Step-by-step explanation:

20/ 100 x 170 = $34

Tip is $34

BILL plus tip is $204

Answer:

-11.

Step-by-step explanation:

We know that the velocity function v(t) is the derivative of the position function x(t).

So, we can integrate v(t) to find x(t) up to a constant of integration:

∫v(t) dt = ∫(4 - 6t^2) dt = 4t - 2t^3 + C

where C is the constant of integration.

We can find the value of C by using the initial condition that the particle is at position x=7 at t=1:

x(1) = 4(1) - 2(1)^3 + C = 7

C = 5

So, the position function is:

x(t) = 4t - 2t^3 + 5

To find the position of the particle at time t=2, we can substitute t=2 into the position function:

x(2) = 4(2) - 2(2)^3 + 5 = -11

Therefore, the position of the particle at time t=2 is -11.

In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right-angled triangle ABC with drawn with angle B = 90°.

A line BD is drawn which is perpendicular to AC.

The angle BDC is also 90 degrees.

The measure for line segment AD = 12 and CD = 40.

The measure for line segment BD is x.

The side BD is common for triangle ABC and BDC.

So, by the formula of indirect measurement we have -

DC / BD = BD / AD

Substitute the values in the equation -

40 / x = x / 12

x² = 480

x = 21.908

x = 21.91

Therefore, the value of x is obtained as 21.91.

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Answer:

Sin Q

7/25

Cos Q

24/25

Tan Q

7/24

Sin R

24/25

Cos R

7/25

Tan24/7

Step-by-step explanation:

Robert is currently 10 years old.Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)

We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.

Let x = Robert's current age

Let y = Robert's age five years ago

Given that Sharon is five years older than Robert, we can set up the following equation:

x + 5 = Sharon's current age

Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:

y + 5 = 2(y)

Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:

y + 5 = 2(Sharon's current age - 5)

Solving this equation for y, we get y = (Sharon's current age - 5)/2.

Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:

y = (x + 5 - 5)/2

Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.

Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.

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Answer:

Step-by-step explanation:

[tex]D=\frac{\theta}{360} \times2\times\pi \times r[/tex]

[tex]D=\frac{60}{360} \times2\times\pi \times 42[/tex]

    [tex]=\frac{1}{6} \times84\times\pi[/tex]

    [tex]=12\pi cm^2[/tex]

According to the conditions, in right angled triangle, the value of x is 6.

What is angle ?

In mathematics, an angle is a geometric figure formed by two rays (or line segments) that share a common endpoint, known as the vertex of the angle.

In a right-angled triangle, the sum of the two acute angles is always 90 degrees. Therefore, we can use this fact to find the value of x.

We are given that one of the acute angles is 60 degrees, and the other angle is 7x - 12 degrees. So we can write:

60 + (7x - 12) = 90

Simplifying this equation, we get:

7x + 48 = 90

Subtracting 48 from both sides, we get:

7x = 42

Dividing both sides by 7, we get:

x = 6

Therefore, in right angled triangle, the value of x is 6.

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If the shoppers spent a total of $197 in books, the amount that Eric spend is $144.

Let's assume that Todd spent x dollars in the bookstore.

According to the problem, Eric spent $15 less than three times the amount that Todd spent, which can be written as:

3x - 15

The total amount spent by both shoppers is $197, so we can set up the equation:

x + (3x - 15) = 197

Simplifying and solving for x, we get:

4x - 15 = 197

4x = 212

x = 53

Therefore, Todd spent $53 in the bookstore.

To find how much Eric spent, we can substitute Todd's value into the expression we derived for Eric's spending:

3x - 15 = 3(53) - 15 = 144

So Eric spent $144 in the bookstore.

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Answer: 3000m

Step-by-step explanation:

Half of 6 km is 3 km

To convert to meters multiply 3 times 1000

That will give you 3000m=3km

The OLS assumption that is violated when predicted errors have a kurtosis of 5 is normality. The correct option is (d). Kurtosis is a statistical measure of the peak of a probability distribution curve. It measures how the tails of the distribution compare to a normal distribution.

Oridinary Least Squares (OLS) is a regression technique that assumes that the response variable has a linear relationship with the explanatory variable(s) and that the response variable has normal distribution error terms. However, in some cases, such as when the predicted errors have a kurtosis of 5, this assumption of normality is violated. If the distribution has more of its observations in the tails than a normal distribution, it is said to be leptokurtic. If it has fewer of its observations in the tails than a normal distribution, it is said to be platykurtic.

Kurtosis of 5 means that the distribution is leptokurtic and has fatter tails than the normal distribution.Assuming normality of the errors means that the residuals or errors are normally distributed. If the errors are not normally distributed, then the residuals will not be normally distributed either. This will affect the accuracy of the confidence intervals and hypothesis tests. The coefficient estimates may be biased and the confidence intervals may be too wide or too narrow. Therefore, normality of the errors is an important assumption of OLS regression and in this case it has been violated.

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Answer:

Step-by-step explanation:

You want the coordinates of triangle ABC after dilation by a factor of 1/2.

When the center of dilation is the origin, each of the coordinates is multiplied by the dilation factor:

  (x, y) ⇒ (x/2, y/2)

  A(-4, 0) ⇒ A'(-2, 0)

  B(0, 2) ⇒ B'(0, 1)

  C(2, -2) ⇒ C'(1, -1)

Answer:

34.28 meters

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the horizontal distance between the boy and the pole "d". Then we can draw a right triangle with the boy's height (5m) as one leg, the distance "d" as the other leg, and the hypotenuse being the distance from the boy's eyes to the top of the pole (which we don't know yet).

We can use the angle of elevation to find the length of this hypotenuse. The angle of elevation is the angle between the horizontal and the line of sight from the boy's eyes to the top of the pole. Since the boy is looking up at the bird, this angle is also the same as the angle between the hypotenuse and the vertical (i.e. the angle at the top of the triangle). So we have:

tan(30°) = opposite/adjacent

where "opposite" is the height of the pole (20m) and "adjacent" is the hypotenuse. Solving for "adjacent", we get:

adjacent = opposite/tan(30°) = 20/tan(30°)

We can simplify tan(30°) to 1/√3, so:

adjacent = 20/(1/√3) = 20√3

Now we can use the Pythagorean theorem to find the horizontal distance "d":

d^2 + 5^2 = (20√3)^2

Simplifying and solving for "d", we get:

d = √[(20√3)^2 - 5^2] = √(1200 - 25) = √1175

So the horizontal distance between the boy and the pole is approximately 34.28 meters (rounded to two decimal places

a) Sample space = {36}

b) Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6

c) Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.

We need to find, What is the size of the sample space? Probability of the sum of the dice is a 7 ?Probability of the sum of the dice is at least a 7? Solution a)Sample space is defined as the set of all possible outcomes. Suppose that you roll two 6 sided dice. So, The possible outcomes of each die is {1,2,3,4,5,6}.The total outcomes for rolling two dice are {1,1}, {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,1}, {2,2}, {2,3}, {2,4}, {2,5}, {2,6}, {3,1}, {3,2}, {3,3}, {3,4}, {3,5}, {3,6}, {4,1}, {4,2}, {4,3}, {4,4}, {4,5}, {4,6}, {5,1}, {5,2}, {5,3}, {5,4}, {5,5}, {5,6}, {6,1}, {6,2}, {6,3}, {6,4}, {6,5}, and {6,6}.Therefore, Sample space = {36}.b)Let E be the event that the sum of the dice is a 7.The events where the sum of the dice is a 7 are {1,6}, {2,5}, {3,4}, {4,3}, {5,2}, and {6,1}.The number of events where the sum of the dice is a 7 is 6.Therefore, Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6.c)Let F be the event that the sum of the dice is at least a 7.Therefore, F = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (2,6), (3,5), (4,4), (5,3), (6,2), (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), and (6,5)}The number of events where the sum of the dice is at least a 7 is 21.Therefore, Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.a) Sample space = {36}.b) Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6.c) Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.

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When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.

The base angles are equivalent because the LNOP is an isosceles trapezoid. As a result, mP = mL. Since we now know that a quadrilateral's total angles equal 360°, we can say. 360° = mL + mN + mO + mP Inputting the values provided yields: m∠L + 84° + (4y-4)° + m∠L = 360° When we simplify the equation, we obtain: 2m∠L + 4y + 80 = 360 2m∠L = 280 - 4y m∠L = 140 - 2y The non-parallel sides of LNOP are congruent since it is an isosceles trapezoid. As a result, mN = mO. We are aware of: 180° - mL = mN + mO Inputting the values provided yields: 84° + (4y-4)° = 180° - (140-2y)° When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.

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In response to the given question, we can state that we know that sum of all angles in a triangle is 180. m∠C = 4*11.67+43 = 89.68 = =90

A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.

we know that sum of all angles in a triangle is 180.

2x - 12 + 4x + 43 + 9x - 26 = 180

15x  + 5 = 180

15x = 175

x = 11.67

m∠C = 4*11.67+43 = 89.68 = =90

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Answer:

m∠C = 119°

Step-by-step explanation:

According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

From inspection of the given triangle, the exterior angle is (9x - 26)° and the two non-adjacent interior angles are ∠B and ∠C.

Equate the sum of the two non-adjacent angles to the exterior angle and solve for x:

⇒ (2x - 12)° + (4x + 43)° = (9x - 26)°

⇒ 2x - 12 + 4x + 43 = 9x - 26

⇒ 6x + 31 = 9x - 26

⇒ 57 = 3x

⇒ x = 19

To calculate the measure of angle C, substitute the found value of x into the expression for the angle:

⇒ m∠C = (4x + 43)°

⇒ m∠C = (4(19) + 43)°

⇒ m∠C = (76 + 43)°

⇒ m∠C = 119°

Answer:

8 apples

Step-by-step explanation:

Step-by-step explanation:

n = Nancy's apples.

j = Jay's apples.

a = Ava's apples.

n = 22

n = j × 2

j = n / 2 = 22/2 = 11

j = a + 3

a = j - 3 = 11 - 3 = 8

Ava has 8 apples.

Answer:

1 game, for $5.75

Step-by-step explanation:

To find this answer, all you need to do is create an equation for both Rock and Bowl and the Super Bowling and then set them equal to each other to find out and solve which value of x games makes them equal.

The first equation is 2.75x +3

The second one is 2.25x + 3.5

2.75x + 3 = 2.25x + 3.5

2.75x = 2.25x + .5

From here, you can either solve for x or realize that x being equal to 1 makes both values equal.

So, the answer is 1 game now to plug it into one of our equations, we get

2.75(1) + 3 which we know is equal to the other equation too which is $5.75 dollars

Due to Alex's salary falling inside the 22% tax bracket, his short-term capital gains would be subject to the same rate of taxation as his income.

A profit realized from the sale of a capital asset, such as a piece of personal or investment property, that has been possessed for one year or less is referred to as a short-term gain.

These profits are classified as ordinary income subject to tax at your personal income tax rate. Gain earned by selling assets that are held for a year or less are called short-term capital gains.

Alex is a single taxpayer who has taxable income of $80,000.

His investment income is made up of $2,000 in short-term capital gains and $500 in qualifying dividends.

As a result of his tax rate income falling between 38,601 and 425,800, which is below 15%, his qualifying dividends would be subject to a 15% tax.

Hence, we must deduct 15% of 500 and 22% of 2000 before combining them.

15% x 500

= 15 x 5

=  75

22% x 2000

= 22 x 20

= 440.

The total is = 75 + 440 = 515.

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Answer:

6.2 × 10-2

Step-by-step explanation:

The volume of ice cream that fills one waffle cone to the top is 13.09 cubic inches.

The waffle cone has the shape of a circular cone. The volume of a cone is given by the formula [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.

The diameter of the cone is given as 5 inches, so the radius is half of the diameter, or 2.5 inches. The height is given as 6 inches. Substituting these values into the formula, we get:

V = [tex](1/3) * 3.14 * (2.5 inches)^2 * 6 inches[/tex]

V = 13.09 cubic inches

Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches (rounded to two decimal places).

To find the volume of ice cream that fills the waffle cone completely to the top, we first note that the waffle cone has the shape of a circular cone. We use the formula for the volume of a cone, which is [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.

We are given the diameter of the cone, which is 5 inches, and we find that the radius is half of the diameter, or 2.5 inches. We are also given the height of the cone, which is 6 inches. Substituting these values into the formula, we can calculate the volume of the cone as 13.09 cubic inches (rounded to two decimal places). Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches.

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Answer:

13/20 written as a decimal is 0.65 and as a percent is 65%

1) Make the denominator 100 (20 x 5)

2) Multiply by five from the numerator too (13 x 5 = 65)

The length QR of the right angle triangle is 26 cm.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of a right angle triangle can be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

24² + 10² = QR²

576 + 100 = QR²

QR² = 676

QR = √676

QR = 26 cm

Therefore,

length of QR = 26 cm

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