a curve in polar coordinates is given by: r=7 2cosθ.r=7 2cosθ. point pp is at θ=16π14. (a) Find polar coordinate r for P, with r>0 and ?<\theta<3\pi/2. r=____.(b) Find cartesian coordinates for point P. x=____ , y=____.(c) How may times does the curve pass through the origin when 0<\theta<2\pi

Answer:

10:23 am

Step-by-step explanation:

We Know

Ms. Brown left at 9:00 am

Her plane landed 1 hour and 23 minutes later.

What time does her plane land?

We Take

9:00 + 1:23 = 10:23 am

So, her plane landed at 10:23 am

Wage differential is due to discrimination = 700 - 700 = 0 .The Oaxaca decomposition is a method used to estimate the portion of the wage differential between two groups (in this case, male and female workers) that can be attributed to discrimination.

The decomposition breaks down the wage differential into two components: the explained component and the unexplained component.The explained component represents the portion of the wage differential that can be attributed to differences in observable characteristics between the two groups, such as years of schooling.

The unexplained component represents the portion of the wage differential that cannot be explained by observable characteristics and is often interpreted as the component related to discrimination or unobserved factors.

To calculate the Oaxaca decomposition, we need to follow these steps:

Step 1: Calculate the average wage of male workers (wm) and female workers (wf) using the given equations:

wm = 500 + 100s, where s = 14 years (average years of schooling for men)

wm = 500 + 100(14) = 1900

wf = 300 + 75s, where s = 12 years (average years of schooling for women)

wf = 300 + 75(12) = 1200

Step 2: Calculate the explained component of the wage differential by estimating the wage differential that can be explained by the differences in observable characteristics (years of schooling) between the two groups.

Explained wage differential = [500 + 100(14)] - [300 + 75(12)] = 700

Step 3: Calculate the unexplained component of the wage differential, which is the portion that cannot be explained by observable characteristics and may be attributed to discrimination or unobserved factors.

Unexplained wage differential = Actual wage differential - Explained wage differential

Unexplained wage differential = 700 - 700 = 0

In this case, the unexplained component of the wage differential is zero, indicating that none of the wage differential can be attributed to discrimination. All of the wage differential can be explained by the differences in observable characteristics (years of schooling) between male and female workers.

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The measurement units for each is described below.

The metric system is a measurement system. It is utilized in calculations and research all over the world. Here are some instances of how we use the metric system to measure things:

a. distance from Florida to Texas is:  Kilometers (km)

b. length of a car is :  Meters (m)

c. thickness of a cell phone is:  Millimeters (mm)

d. height of a coffee mug is: Centimeters (cm)

e. mass of a cookie is: Grams (g)

f. mass of a large watermelon is:  Kilograms (kg)

g. mass of small feather is:  Milligrams (mg)

h. capacity of a large bottle of lemonade is : Liters (L)

i. capacity of a small food coloring bottle is : i. Milliliters (mL)

j. capacity of a swimming pool is:  Cubic meters (m³)

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The area of the garden is 272 ft².

We have,

The garden has two shapes:

Rectangle and a triangle.

Now,

Length = 12 ft

Width = 20 ft

Area of the rectangle.

= Length x Width

= 12 x 20

= 240 ft²

And,

Base = 8 ft

Height = (20 - 12) = 8 ft

Area of the triangle.

= 1/2 x base x height

= 1/2 x 8 x 8

= 32 ft²

Now,

Area of the garden.

= 240 + 32

= 272 ft²

Thus,

The area of the garden is 272 ft².

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The correct option is B, the displacement is 1.5 meters.

Displacement is defined as the difference between the final position and the initial position.

Here we can see a graph that gives the velocity as a function of time.

The velocity at t = 7s is 0m/s

The velocity at t = 8s is  3m/s

Then the acceleration in that interval is:

A = (3m/s - 0m/s)/(8s - 7s) = 3m/s²

And the position will be:

P = (1/2)*3m/s²*(t - 7s)²

Now take the differenve between the positions at t = 8s and t = 7s, we will get:

displacement =  (1/2)*3m/s²*(8s - 7s)² -  (1/2)*3m/s²*(7s - 7s)² = 1.5m

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the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.

What is Taylor series?

The Taylor series is a representation of a function as an infinite sum of terms involving the function's derivatives at a particular point. It provides a way to approximate a function with a polynomial expression.

To find the degree 5 Taylor polynomial, denoted as T₅(x), of the function f(x) = cos(x) at a = 0, we need to compute the polynomial using the derivatives of f evaluated at x = 0.

The Taylor polynomial of degree n for a function f(x) centered at a is given by:

Tₙ(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + ... + (fⁿ(a)/n!)(x - a)ⁿ

In this case, a = 0, so the Taylor polynomial simplifies to:

T₅(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + (f⁴(0)/4!)x⁴ + (f⁵(0)/5!)x⁵

Now, let's calculate the derivatives of f(x) = cos(x) up to the 5th order:

f'(x) = -sin(x)

f''(x) = -cos(x)

f'''(x) = sin(x)

f⁴(x) = cos(x)

f⁵(x) = -sin(x)

Evaluating these derivatives at x = 0:

f(0) = cos(0) = 1

f'(0) = -sin(0) = 0

f''(0) = -cos(0) = -1

f'''(0) = sin(0) = 0

f⁴(0) = cos(0) = 1

f⁵(0) = -sin(0) = 0

Substituting these values into the Taylor polynomial formula:

T₅(x) = 1 + 0x + (-1/2!)x² + (0/3!)x³ + (1/4!)x⁴ + (0/5!)x⁵

Simplifying the expression:

T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴

Therefore, the degree 5 Taylor polynomial of f(x) = cos(x) at a = 0 is T₅(x) = 1 - (1/2!)x² + (1/4!)x⁴.

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Answer:

No

Step-by-step explanation:

"Looking" at our triangles

If Angle D is congruent to Angle G, and angle E is congruent to Angle H, lets call those the first and second vertices of each triangle.  If we're trying to prove the triangles congruent, we're trying to prove Triangle DEF is congruent to Triangle GHJ (in that order, since we're already given that the first and second angles correspond between triangles).

Could these triangle be congruent?  Yes!  As a quick example, imagine two Equilateral triangles with side lengths 5.  They are congruent, and they do have the first angle and second angle corresponding pairs congruent, and one of those sides from triangle 1 does match the length of one of the sides in triangle 2.  ...and they are congruent triangles.

The problem with the given scenario is that the side they give for triangle 1 (between vertex 1 and 2) is not the corresponding side of triangle 2 (between vertex 2 and 3).  This makes it so that we cannot guarantee that the triangles are congruent.

As can be seen in the attached image, I've made Side DE length 2, and put it on a coordinate plane so it's easy to see.  Side HJ is also definitely length 2.  Clearly, those triangles are not congruent.

When would triangles be congruent?

Going back to the definition of congruent triangles, three corresponding angles and three corresponding sides must be congruent.  That's 6 pairs of parts needed to be proven congruent to prove triangles congruent!

Fortunately, there are a number of theorems that can be proven to lessen the amount of pairs of parts needed to be proven congruent and still guarantee that the resulting triangles must be congruent.

There are exactly 5 cases:

It looks like a bunch of alphabet soup, but notice that all of them require 3 pieces of information (even HL, which is Hypotenuse-Leg... since there's a Hypotenuse, it must be a right triangle, so there are a pair of corresponding congruent right angles that are congruent that they don't talk about)

In order to remember which items work, remember that you MUST know 3 parts, and think about all of the way you could know 3 parts:

Scenario 1: Have all 3 side pairs (SSS)

There is only one way that all three sides can be equal, and yes, that is one of the triangle congruence shortcuts.

Scenario 2: Have 2 side pairs & 1 angle pair

There are two option here.  

Two sides with the angle between them is SAS (note the angle is between them).

Two sides with the angle not between them is ... (well, that can get you in trouble).  Conveniently, that is NOT one of the triangle congruence theorems.  So, stay out of trouble, and don't use this for triangle congruence.

Interestingly, HL, is a special case of this "trouble case".  Note that if you have the Hypotenuse and a leg, that's two Sides.  The right Angle is NOT the angle between those two sides (because the hypotenuse is always across from the right angle).  When that angle is 90 degrees, then the set of two sides and the angle not between them DOES work as sufficient to prove triangle congruence, and it's the only time that it's sufficient.

Scenario 3: Have 1 Side and 2 Angles

Again, there are two option here:

In either scenario, this is sufficient to prove the triangles are congruent.

Scenario 4: Have all 3 angles (AAA)

This definitely won't be enough to prove congruence.  Zoom in.  It's got the same angles, but not the same lengths.

So, only 5 short ways to prove triangles are congruent, and all of them require 3 parts of one triangle corresponding to 3 parts of another, each of the 3 pairs must be congruent.

If nominal wages and prices are not flexible, then the short-run aggregate supply curve is vertical.

This means that the economy is operating at full employment, and any increase in aggregate demand will not result in an increase in output but rather lead to higher prices.

In other words, the economy is supply-constrained, and there is no excess capacity to produce more output in response to an increase in demand.

In a severe recessionary gap, the economy is operating below its potential output, and there is excess capacity in the economy. However, if nominal wages and prices are not flexible, firms cannot adjust their prices downwards,

and wages cannot be reduced, leading to a situation where the short-run aggregate supply curve is vertical.

This results in a situation where any increase in aggregate demand will not lead to an increase in output, and the economy remains stuck in a recessionary gap with high unemployment and low output.

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The second term of the sequence is given as follows:

1.5.

We use a recursive rule for the sequence, as we have the rule to obtain the (n + 1)th term considering the nth term.

The (n+1)th term rule of a sequence is add 7 then multiply by 2, hence the recursive formula is given as follows:

[tex]a_{n+1} = 2(a_n + 7)[/tex]

The third term for this problem is given as follows:

[tex]a_3 = 17[/tex]

Hence the second term is obtained as follows:

[tex]a_{3} = 2(a_2 + 7)[/tex]

[tex]2a_2 + 14 = 17[/tex]

[tex]2a_2 = 3[/tex]

[tex]a_2 = 1.5[/tex]

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Answer:

Step-by-step explanation:To solve the quadratic equation x² - 3x - 10 = 0 using the quadratic formula, we first identify the values of a, b, and c:

a = 1

b = -3

c = -10

Now, we can apply the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we have:

x = (-(-3) ± √((-3)² - 4(1)(-10))) / (2(1))

Simplifying further:

x = (3 ± √(9 + 40)) / 2

x = (3 ± √49) / 2

x = (3 ± 7) / 2

This gives us two possible solutions:

x₁ = (3 + 7) / 2 = 10 / 2 = 5

x₂ = (3 - 7) / 2 = -4 / 2 = -2

Therefore, the solutions to the equation x² - 3x - 10 = 0 are x = 5 and x = -2.

Answer:

D. Yes

Step-by-step explanation:

Answer:

6000

Step-by-step explanation:

solved

In this problem, we are asked to find two numbers whose difference is 48 and whose product is a minimum.

To approach this problem, we can use the fact that the product of two numbers is minimized when the numbers are closest to each other. Therefore, we can let x be the smaller of the two numbers, and then the larger number is x + 48.

The product of these two numbers is:

P = x(x + 48) = x^2 + 48x

To find the minimum value of P, we can take the derivative of P with respect to x and set it equal to zero:

dP/dx = 2x + 48 = 0

Solving for x, we get:

x = -24

Substituting this value of x into the expression for P, we get:

P = (-24)^2 + 48(-24) = 576 - 1152 = -576

Therefore, the two numbers whose difference is 48 and whose product is minimized are -24 and 24. Note that the smaller number, -24, is negative, but this makes sense since the problem did not specify that the numbers had to be positive.

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Answer:

m = -1/4

Step-by-step explanation:

Slope = rise/run (y2 - y1) / (x2 - x1)

Points (−7, 5) (−3, 4)

We see the y decrease by 1, and the x increase 4, so the slope is

m = -1/4

There were 16 ounces of oil in the lantern at noon.

Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.

We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:

x - rt = y

where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:

x - 2r = 12

And at 4 pm:

x - 4r = 8

Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:

2r = 4

r = 2

Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:

x - 2(2) = 12

x - 4 = 12

x = 16

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To calculate the probability that at least 30 of the women in the sample will not meet the age requirement, we need to use the binomial distribution formula:

P(X >= 30) = 1 - P(X < 30)

where X is the number of women who do not meet the age requirement, and P(X < 30) is the cumulative probability of X being less than 30.

The probability of a woman not meeting the age requirement is given as 0.2, so the probability of a woman meeting the age requirement is 0.8. We are sampling 200 women, so the number of women who do not meet the age requirement follows a binomial distribution with n = 200 and p = 0.2.

Using a binomial calculator or software, we can find that P(X < 30) = 0.1656. Therefore, the probability of at least 30 women not meeting the age requirement is:

P(X >= 30) = 1 - P(X < 30) = 1 - 0.1656 = 0.8344

Therefore, the probability that at least 30 of the women in the sample will not meet the age requirement is 0.8344, or approximately 83.44%.

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Answer:

Bottom left

Step-by-step explanation:

It covers the most points

Answer:

2sqrt(26)

Step-by-step explanation:

sqrt(2^2+ 8^2+ 6^2)

=2×sqrt(26)

Answer:

x = 46

Step-by-step explanation:

These 2 angles would add up to 180 degrees.

So 41 + (3x+1) = 180

Let's solve for x.

41 + 3x + 1 = 180

Combine like terms.

42 + 3x = 180

subtract 42 from both sides

3x = 180-42

3x = 138

divide both sides by 3

x = 46

The magnitudes of the resultant forces and the locations where the resultant force is applied can be ranked from smallest to largest as described above. It is important to note that when there are equivalent values, they should be ranked as such and overlap.

To rank the magnitudes of the resultant forces for the six cases, we first need to determine the equivalent resultant load for each case. The equivalent resultant load is the single force that has the same effect on the beam as the distributed load or loads in the original problem.

The magnitudes of the equivalent resultant loads for each case are:

FR,A < FR,C = FR,D < FR,E < FR,B < FR,F

Therefore, we can rank the magnitudes of the resultant forces as follows, from smallest to largest:

FR,A < FR,C = FR,D < FR,E < FR,B < FR,F

When measuring from the left side of the beam, x¯A, x¯B, x¯C, x¯D, x¯E, and x¯F are the locations where the resultant force is applied in each of the six cases.

The locations where the resultant force is applied are:

x¯C < x¯D < x¯B < x¯E < x¯A < x¯F

Therefore, we can rank the locations where the resultant force is applied as follows, from smallest to largest:

x¯C < x¯D < x¯B < x¯E < x¯A < x¯F

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Answer:

1.440kg

Step-by-step explanation:

12 × 120=1440g

converting g to kg, divide by 1000 as 1000g = 1kg

Answer is therefore given as 1.440kg

1+b²+b⁴ ​can be resolved into factors (1+b²+b),(1+b²- b).

We will evaluate  1+b²+b⁴​ with the help of algebraic identities,

We can write 1+b²+b⁴ as,

1+b²+b⁴ = 1+(b)²+(b²)²

             = 1+(b)²+(b)²+(b²)²-b² (Adding and subtracting b²)

             = 1+2(b²)+(b²)²-(b)²

             = (1)²+2(b²)(1)+(b²)²- (b)²

Now using the identity (a + b)²= a²+b²+2ab, we have,

1+b²+b⁴ = (1+b²)²- (b)²

             = (1+b²+b)(1+b²- b)  [By using identity a²-b²= (a+b)(a-b)]

Therefore, the correct answer is  1+b²+b⁴​= (1+b²+b)(1+b²- b).

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:If triangle BCD is dilated by a scale factor of 3/4 to form triangle B’C’D’, and side CD measures 10, then the measure of side C’D’ would be 7.5.

Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).

Explanation:
To determine the depth at a particular node in a tree, we count the number of edges from the root to that node.
Without more information about the tree, it is impossible to determine the depths of nodes 23 and 70. However, if we assume that the root of the tree is at depth 0, and that the tree is binary (each node has at most two children), then we can make an educated guess.
Based on the given options, we can eliminate choices B and C, as they contradict each other.
Option A suggests that node 23 is two levels below the root, while node 70 is at the root level. This is possible if node 70 is the root of the tree, and node 23 is its child.
Option D suggests that node 23 is two levels below the root, while node 70 is three levels below the root. This is possible if node 70 is a grandchild of node 23.

Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).

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Based on the given assumptions, we can assume that the model predicts the number of disasters at a given temperature rise linearly. However, it is important to note that this model is based on certain assumptions that may or may not be accurate.

These assumptions include the mean value being linear in temperature rise and the actual number of disasters being normally distributed with constant variance.

Given the true value of 16 that was left out, we can use the standard error of prediction and the prediction from the regression line to calculate a t statistic. The null hypothesis is that the point belongs to this line under these assumptions.

To calculate the t statistic, we can use the formula:

t = (observed value - predicted value) / standard error of prediction

Using the given information, we can calculate the t statistic as:

t = (16 - predicted value) / standard error of prediction

Once we have the t statistic, we can calculate the p-value using a t-distribution table or a statistical software. The p-value represents the probability of getting a t statistic as extreme or more extreme than the one we calculated under the null hypothesis.

Based on the p-value, we can determine if we reject or fail to reject the null hypothesis. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that the point does not belong to the line. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the point belongs to the line.

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The correct expression which is equivalent to 12.8 - 3s + 15.5 + 8s is,

⇒ 5s + 28.3

We have to given that;

Expression to solve is,

⇒ 12.8 - 3s + 15.5 + 8s

Now, WE can simplify as;

⇒ 12.8 - 3s + 15.5 + 8s

Combine like terms,

⇒ 12.8 + 15.5 - 3s + 8s

⇒ 28.3 + 5s

⇒ 5s + 28.3

Thus, The correct expression is,

⇒ 5s + 28.3

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To convert the polar equation r = 4sin(θ) + 4cos(θ) into a Cartesian equation, we can use the identities:

x = r cos(θ)

y = r sin(θ)

Substituting r = 4sin(θ) + 4cos(θ) into these identities, we get:

x = (4sin(θ) + 4cos(θ))cos(θ) = 4sin(θ)cos(θ) + 4cos²(θ)

y = (4sin(θ) + 4cos(θ))sin(θ) = 4sin²(θ) + 4sin(θ)cos(θ)

Simplifying these expressions using the trigonometric identity sin²(θ) + cos²(θ) = 1, we obtain:

x = 4cos(θ) + 4cos²(θ)

y = 4sin(θ) + 4sin(θ)cos(θ) = 4sin(θ) + 4cos(θ)sin(θ)

Therefore, the Cartesian equation for the curve is:

(x - 4)² + y² = 16

This equation represents a circle with center (4, 0) and radius 4. The original polar equation r = 4sin(θ) + 4cos(θ) can be interpreted as the distance from the origin to a point on the circle, measured along a line that makes an angle of θ with the positive x-axis.

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