What is the measure of the missing angle? *
H
60°
82%

Step-by-step explanation:

(6+r)^2 = 81 + r^2

36 + 12r+ r^2 = 81 + r^2

12r = 81-36 = 45

r = 15/4 = 3.75

The given set is {(x, y) | x ≠ −3}, open and connected. Option a and b are correct.

The set is open because for any point (x, y) in the set, we can find a small neighborhood around it (an open ball) that is entirely contained within the set. Specifically, we can choose a radius smaller than the distance from x to -3 to get an open ball around x that does not intersect -3.

The set is connected because any two points in the set can be connected by a continuous path within the set. This follows from the fact that the set is an open interval in the x-axis, which is a connected space.

The set is not simply connected because it has a "hole" at x = -3. Specifically, any closed curve in the set that encircles x = -3 cannot be continuously shrunk to a point within the set. This means that the set fails to satisfy the more stringent condition of simply connectedness, which requires that every closed curve in the set can be continuously shrunk to a point within the set. Option a and b are correct.

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The area of the clock  = 315.41 inch\(squre\)

The clock's face has been provided to us, and it is =  63 inch

Explanation?

The clock's face has been provided to us, and it is =  63 inch

So the circumference of the clock is also that amount.

given that the clock has a circular shape.

\(2\pi (r)= 63inch\)

So

We will use this information to compute the radius\((r)\) (of the circular clock.

Then

\(2\pi (R) = 63 inch =63/2\pi =10.2 inch\)

The area of the circle equation will now be changed to include this value of (r) in order to obtain the area of the clock.

Now  

\(\pi ( r)^{2} = \pi (10.02)^{2} = 315.41 in^{2}\)

The area of the clock's face is therefore = \(315.41in^{2}\)

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The point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the points at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j, we need to find the gradient vector of the function and equate it to the given direction vector.

The gradient vector of the function f(x, y) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x - 2

∂f/∂y = 2y - 6

Setting the gradient vector equal to the given direction vector i + j:

[2x - 2, 2y - 6] = [1, 1]

Equating the corresponding components, we have:

2x - 2 = 1

2y - 6 = 1

Solving these equations, we get:

2x = 3  =>  x = 3/2

2y = 7  =>  y = 7/2

Therefore, the point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

i guess it is "not enough information"

Let's say the original amount both Jane and Rory started with is x dollars.

According to the problem, Jane has saved twice the sum of the original amount and 3 dollars. So, Jane has saved 2x + 3 dollars.

On the other hand, Rory has saved 4 times the difference of the original amount and 4 dollars. The difference of the original amount and 4 dollars is (x - 4), so Rory has saved 4(x - 4) dollars, which simplifies to 4x - 16 dollars.

Now we know that Jane and Rory have saved the same amount, so:

2x + 3 = 4x - 16

Solving for x:

19 = 2x

x = 9.5

Therefore, both Jane and Rory started with $9.5.

So, the correct answer is not listed. The answer is: E. $9.5.

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Answer:

Step-by-step explanation:

The measure of sides of ΔPQR are PQ=13 units, QR=5 units and RP=2 units.

Given that, triangle PQR whose vertices are located at P(-5, 2), Q(7,-3), R(7, 2).

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x1, y1) and (x2, y2) is Distance = √[(x2-x1)²+(y2-y1)²].

Using distance formula,

PQ =√[(7+5)²+(-3-2)²]

= √169

= 13 units

QR =√[(7-7)²+(2+3)²]

= √25

= 5 units

RP =√[(-5+7)²+(2-2)²]

= √4

= 2 units

Therefore, the measure of sides of ΔPQR are PQ=13 units, QR=5 units and RP=2 units.

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Answer:

40 cm³

Step-by-step explanation:

To solve this problem, it's easiest to imagine this figure as a half of a whole retangular prism. You can find the volume of that rectangular prism and divide the answer by 2. So, to find the volume, multiply each dimension by the others.

5 · 8 · 2 = 80

The volume of the rectangular prism we imagined is 80 cm³. So to find the volume of the original figure instead, divide this answer in half, to find 40 cm³. The answer is B, 40 cm³. Be sure to use the cubed symbol, '³' , to show volume. Hope this helps ^^ Good luck

The researcher is using a within-subjects factorial design.

According to statement

A researcher conducts an experiment to determine whether the type of car and color of the car impact how fast people drive.

This can be done by within-subjects factorial design.

In a within-subjects factorial design, all of the independent variables are manipulated within subjects. This would mean that each participant was tested in all conditions.

Another common example of a within-subjects design is medical testing.

So, The researcher is using a within-subjects factorial design.

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Answer:

12

Step-by-step explanation:

your question is wrong

Answer:

1.6

Step-by-step explanation:

Given the expression:

if r = 16.8, then we have the following:

thus, the simplified expression is 19.2

Answer:

y=4/5x-3 - (-5, -7)

Step-by-step explanation:

So to solve this, lets just plug in each value for x, and see if the y value we get is equal to one of our answers.

So we have (-10, 5)

Well plug in -10 for 4/5x we get:

-40/5=-8

Next we take that value and solve:

y=-8-3

y=-11

The answer for this was 5, not -11.

Ill skip a few steps:

(10, -11):

Plug in 10 we get:

y=8-3 which is y=5. This is not right, for it needed to be -11.

Next we have (5, -1)

This gets us y=4-3 this is y=1 which is not -1. So thats not right.

Finally we have (-5, -7):

This gets us y=-4-3 this is y=-7. What was our y value? -7!

So the answer is (-5, -7)

I hope this helps! :)

The equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

Let's assume that Aj runs x yards each week. Then, the number of yards that Aj walks each week would be (x + 90) yards, since he walks 90 more yards than he runs.

The total distance that Aj covers each week would be the sum of the distance that he runs and the distance that he walks, which is given as 400 yards.

So, we can write an equation as:

Distance covered by Aj = Distance that he runs + Distance that he walks

or,

Simplifying this equation gives:

Therefore, the equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

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Step-by-step explanation:

so the answer is would be X = 15

They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

This type of decision making is known as bounded rationality. Bounded rationality acknowledges that people often make decisions based on incomplete and imperfect information but seek the best possible outcome. People use heuristics and mental shortcuts to make decisions and tend to satisfice, which means they settle on a satisfactory solution rather than searching for the optimal solution. This type of decision making is often used when the complexity of a problem is too great to be solved analytically.

Bounded rationality is a type of decision making which acknowledges that people often make decisions based on incomplete and imperfect information, and seek the best possible outcome using heuristics and mental shortcuts. They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

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Answer:Therefore, the range is 32 and the standard deviation is approximately 10.523 for the given data set.

Step-by-step explanation:To calculate the range and standard deviation for the given data set {40, 65, 33, 46, 55, 50, 61}, we can follow these steps:

Step 1: Find the range.

The range is calculated by subtracting the minimum value from the maximum value in the data set.

Range = Maximum value - Minimum value

Range = 65 - 33

Range = 32

Step 2: Calculate the mean.

The mean is calculated by summing up all the values in the data set and dividing by the total number of values.

Mean = (40 + 65 + 33 + 46 + 55 + 50 + 61) / 7

Mean = 350 / 7

Mean = 50

Step 3: Calculate the deviation for each value.

Deviation is calculated by subtracting the mean from each value in the data set.

Deviation for 40 = 40 - 50 = -10

Deviation for 65 = 65 - 50 = 15

Deviation for 33 = 33 - 50 = -17

Deviation for 46 = 46 - 50 = -4

Deviation for 55 = 55 - 50 = 5

Deviation for 50 = 50 - 50 = 0

Deviation for 61 = 61 - 50 = 11

Step 4: Square each deviation.

Squared deviation for -10 = (-10)^2 = 100

Squared deviation for 15 = 15^2 = 225

Squared deviation for -17 = (-17)^2 = 289

Squared deviation for -4 = (-4)^2 = 16

Squared deviation for 5 = 5^2 = 25

Squared deviation for 0 = 0^2 = 0

Squared deviation for 11 = 11^2 = 121

Step 5: Calculate the variance.

Variance is calculated by summing up all the squared deviations and dividing by the total number of values.

Variance = (100 + 225 + 289 + 16 + 25 + 0 + 121) / 7

Variance = 776 / 7

Variance ≈ 110.857

Step 6: Calculate the standard deviation.

The standard deviation is the square root of the variance.

Standard Deviation ≈ √110.857

Standard Deviation ≈ 10.523

Answer:

can you Please put screen shot in there

Step-by-step explanation:

22.34 miles much farther does Jane travel than her trainer.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Here, given that,

she leaves the health club and bikes 16 miles south.

Then, She then runs 12 miles west.

so, we have,

It must be, hypotenuse = 16 miles

                  base= 12 miles

We have to find, the height.

by Pythagorean theorem, we get,

the distance Jane's trainer bikes=√16²-12² miles

                                                       =√32 miles

                                                       =5.66 miles

So. she travels in total = 28 miles

22.34 miles much farther does Jane travel than her trainer.

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Answer:

y = 0.5x + 3

Step-by-step explanation:

The dimensions of the rectangle are width = 8 inches and length = 12 inches if its area is 96 square inches.

Let's denote the width of the rectangle as x inches. According to the given information, the length of the rectangle will be (x + 4) inches since it exceeds the width by 4 inches.

The formula for the area of a rectangle is length multiplied by width. We know that the area is 96 square inches, so we can set up the following equation:

Area = Length × Width

96 = (x + 4) × x

To solve this quadratic equation, we can rearrange it and set it equal to zero:

x² + 4x - 96 = 0

Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we can factor the equation:

(x + 12)(x - 8) = 0

Setting each factor equal to zero gives us two possible solutions:

x + 12 = 0

x = -12 (ignore negative value since dimensions cannot be negative)

x - 8 = 0

x = 8

Therefore, the width of the rectangle is 8 inches. Since the length exceeds the width by 4 inches, the length will be (8 + 4) = 12 inches.

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Answer:

the length is 12 inches where as the width is 8 inches

Step-by-step explanation:

assume that the width is x and since its length exceeds in by 4, we can assume that its lenght is x+4 and the area ia 96 so

(x)(x+4)=96

x^2+4x=96

x^2+4x-96=0 hence now we have a quadratic equation

the factors are + 12 and -8

hence,

x^2+12x-8x-96=0

x(x+12)-8(x+12)=0

take (x+12) common

(x-8)(x+12)=0

now lets find the two solutions

x-8=0

x=0+8

x=+8

x+12=0

x=0-12

x=-12

we'll consider +8 only as the length width or height of any shape can't be in negative so lets put 8 into the orignal equation

(x)(x+4)

=(8)(8+4)

=(8)(12)

=96 and so it works

the length is 12 inches where as the width is 8 inches

The number which best completes the sequence is 31.

To identify the pattern in this sequence, we can observe that it alternates between adding 7 and adding 4. Let's see this step by step:

1. 2 + 7 = 9
2. 9 + 4 = 13
3. 13 + 7 = 20
4. 20 + 4 = 24
5. 24 + 7 = 31

However, there's a discrepancy in the sequence provided: the number 5, which should have been 20, and the number 10, which should have been 24. With the corrected sequence, it should look like this: 2, 9, 20, 13, 24, 19, 17.

The best number to complete the corrected sequence is 31, following the pattern of alternately adding 7 and 4.

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Answer: Didn't get that

Step-by-step explanation:

What do you mean

Answer:

1,2,5,6 is the coefficient and the constant is y2 and the term is 5x

Step-by-step explanation:

try that as your answer

Answer:

y-inter10

Explanation:

Given the function f(x) defined below:

The y-intercept of any function is the value of f(x) when x=0.

The y-intercept of f(x) is 10.

Answer:

$1529

Step-by-step explanation:

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the final amount (balance) in the account

P = the initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = the annual interest rate (as a decimal)

t = the time period (in years)

Plugging in the given values, we get:

A = 1000e^(0.0855)

A = 1000*e^0.425

A = 1000*1.529

A = 1529

Therefore, the balance after 5 years with continuous compounding at 8.5% interest rate is $1529.

Answer: -2

Step-by-step explanation: