Points D, E, and F are on circle C and EF ≅ DF.

What is the measure of ∠CDF?
14°
19°
26°
38°

Please explain, I want to know how to get the answer.

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

A polygon is any form having three sides. Although a circle is curved and devoid of sides and angles, it is not categorised as a polygon even if it is a plane figure.

If the polygon translates 3 units to the left and 1 unit down, the coordinates of the new vertices would be:

A' (0, 3)

B' (2, 2)

C' (0, 1)

D' (-2, 2)

To find the length of diagonal AC, we can use the distance formula:

AC = √[(3-3)^2 + (2-4)^2] ≈ 2 units

If the polygon translates 3 units further to the left and 4 units down, the coordinates of the new vertices would be:

A'' (-3, -1)

B'' (-1, -2)

C'' (-3, -3)

D'' (-5, -2)

To find the length of diagonal A'C', we can use the distance formula:

A'C' = √[(0-0)^2 + (1-3)^2] ≈ 2 units

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

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Chelsea has $13,385 in her savings account after 7 years.

A savings account is an effective way to store your money in a secure location where it can earn interest.

After 5 years, the amount in Chelsea's savings account will be:

a = 1000(1.03)^5 = 1000(1.159274) = 1159.27

Let's say that Chelsea sells her car for x dollars. She adds that to her savings account, so the new amount in her account is:

1159.27 + x

After two more years (i.e., 7 years after initially starting the savings account), the amount in her savings account will be:

a = (1159.27 + x)(1.03)^2 = (1159.27 + x)(1.0609) = 1232.56 + 1.0609x

To find the value of x, we need to know the current value of the car. Once we have that, we can substitute it into the equation above to find the final amount in Chelsea's savings account.

For example, let's say that Chelsea sold her car for $5000. Then, the final amount in her savings account would be:

a = 1232.56 + 1.0609(5000) = 13384.91

Therefore, to the nearest dollar, Chelsea has $13,385 in her savings account after 7 years.

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Answer:

Step-by-step explanation:

We need to show that the path given by r(t) = (e^t sin t, e^(-t) cos t, e) intersects the sphere 2y^2 + 2z^2 = 4 once, traveling from outside the sphere to inside as t goes from -∞ to +∞.

The equation of the sphere is 2y^2 + 2z^2 = 4. To find the intersection points of the path and the sphere, we need to substitute the components of r(t) into the equation of the sphere:

2y^2 + 2z^2 = 4

2(e^(-t) cos t)^2 + 2e^2 = 4

2e^(-2t) cos^2(t) + 2e^2 = 4

e^(-2t) cos^2(t) + e^2 = 2

Multiplying both sides by e^(2t), we get:

cos^2(t) + e^(4t) = 2e^(2t)

We can rewrite this equation as:

e^(4t) - 2e^(2t)cos^2(t) + cos^2(t) - 1 = 0

This is a quadratic equation in e^(2t) with solutions:

e^(2t) = cos^2(t) ± sqrt(cos^4(t) - 4(cos^2(t) - 1))

We want to show that there is only one intersection point, which means we want to show that the discriminant of the quadratic is negative, i.e.:

cos^4(t) - 4(cos^2(t) - 1) < 0

Expanding the left-hand side, we get:

cos^4(t) - 4cos^2(t) + 4 < 0

Simplifying, we get:

(cos^2(t) - 2)^2 < 0

Since the square of a real number is always non-negative, this inequality has no real solutions. Therefore, the discriminant of the quadratic is negative, and there is only one intersection point.

To show that the path travels from outside the sphere to inside as t goes from -∞ to +∞, we can observe that as t goes from -∞ to +∞, the first component of r(t) goes from -∞ to +∞, while the second and third components oscillate between 0 and +∞. This means that the path starts outside the sphere (at the point (0, +∞, +∞)) and ends inside the sphere (at the point (+∞, 1, 1)). Therefore, the path must intersect the sphere once, traveling from outside to inside.

Answer:
Black

Step-by-step explanation:

1/2 is half the bag of marbles so it's 50% likely to pick black.

The moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.

Since we know the tensions in cables AB and BC, we can find the horizontal and vertical components of the forces exerted by the cables at point B:

The horizontal component of the force exerted by the cable

AB = 630 cos(45) = 444.21 N

Similarly,

The vertical component of the force exerted by the cable  = 444.21 N

The horizontal component of the force exerted by the cable  = 637.55 N

The vertical component of the force exerted by cable  = 367.50 N

Total horizontal force = 444.21 N + 637.55 N = 1081.76 N

Total vertical force = 444.21 N + 367.50 N = 811.71 N

The moment about point O of the resultant force exerted on the tree by the cable at B is given by:

Moment = F * d

Using the Pythagorean theorem, we can find the magnitude of the resultant force,
= 1351.44 N

Perpendicular distance = 4 m * sin(45) = 2.828 m

Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is,

Moment = F * d = 1351.44 N * 2.828 m = 3830.06 N·m

Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.

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Vera's location after three hours is thus 2,100 feet above sea level.

Division is a basic arithmetic operation used to find how many times one number (the divisor) is contained within another number (the dividend). The result of a division operation is the quotient. Division is often represented using the symbol "÷" or "/".  Sometimes division results in a remainder, which is the amount left over after dividing as much as possible.  Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. It is used in a wide variety of mathematical and real-world contexts, such as sharing equally, calculating rates, and solving equations.

Here,

To find Vera's location after three hours of climbing down the mountain, we first need to convert three hours into minutes. There are 60 minutes in one hour, so three hours is:

3 hours x 60 minutes/hour = 180 minutes

Vera descends at a rate of five feet per minute, so after 180 minutes, she will have descended:

180 minutes x 5 feet/minute = 900 feet

3,000 - 900 = 2,100

Therefore, Vera's location after three hours is 2,100 feet above sea level.

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The exact perimeter of the triangle is: 8+3√17 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:
The distance formula between two points (x1, y1) and (x2, y2) is:

[tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

So, to find the lengths of the sides of the triangle with vertices (-3, 5), (-3, 2), and (-1, -3), we can use the distance formula as follows:

Between (-3, 5) and (-3, 2):

[tex]d =\sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}[/tex]

= [tex]\sqrt{[(2 - 5)^2 + (-3 - (-3))^2]}[/tex]

= [tex]\sqrt{[(-3)^2 + 0^2]}[/tex]

= [tex]\sqrt{9}[/tex]

= 3

Between (-3, 2) and (-1, -3):

[tex]d = \sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}[/tex]

= [tex]\sqrt{[(-3 - 2)^2 + (-1 - (-3))^2]}[/tex]

= [tex]\sqrt{[(-5)^2 + 2^2]}[/tex]

= [tex]\sqrt{29}[/tex]

Between (-1, -3) and (-3, 5):

[tex]d = \sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}[/tex]

= [tex]\sqrt{[(5 - (-3))^2 + (-3 - (-1))^2]}[/tex]

= [tex]\sqrt{[8^2 + (-2)^2]}[/tex]

= [tex]\sqrt{68}[/tex]

Now we can add up the lengths of the sides to get the perimeter:

[tex]P = 3 + \sqrt{29} + \sqrt{68}[/tex]

So the exact perimeter of the triangle is:

8 + 3√17 units.

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Answer:

16 units.

------------------

According to triangle inequality theorem, any side of a triangle is less than the sum of the other two.

Let the missing side is largest, then it must be less than:

The closest whole number less than 17 is 16.

The annual percentage yield for money invested at the rates are:

To solve for the APY in the first question:

APY = [tex](1+ r/n)^n^-^1[/tex]

r= interest rate

n= number of times interest is compounded per year

We put in the values

APY = [tex]( 1 + 0.0441/12)^1^2^-^1[/tex]

APY = 4.5%

To solve for the second one

4.42% compounded quarterly

plug in the values into the formula

[tex](1 + 0.0442)/4^4^-^1[/tex]

APR = 4.49%

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2.183 miles is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two buildings.

Distances between two things or places can sometimes be measured qualitatively and sometimes quantitatively. A physical length or an estimate based on other criteria might be referred to as distance in physics or everyday language. The entire movement of an item, independent of direction, is called distance. No matter where an item starts or ends, distance may be described as the amount of ground it has covered.

Given that,

If the White House is located at (−8,−6) and the Pentagon is located at (−1,10).

Then, distance = √(-8-(-1))² + (-6 -10)² × 0.125

= 2.183 miles

Thus, 2.183 miles is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two buildings.

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The linear function that models this problem is y = 25x + 25 and the cost for 6 hours is $175

To solve this problem, we have to find the slope and y-intercept of the line.

m = y2 - y1 / x2 - x1

Taking two points from the line;

A = (2, 75)

B = (5, 150)

Substituting the values into the formula;

m = 150 - 75 / 5 - 2

m = 25

Using the slope;

y = mx + c

150 = 25(5) + c

150 = 125 + c

c = 150 - 125

c = 25

The equation of line is ;

y = 25x + 25

The cost for 6 hours will be

y = 25(6) + 25

y = 175

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Answer:

14 in^2

Step-by-step explanation:

4+3=7 in. Area of the triangle is BH/2=7*4/2=14 in^2.

The dogs were fed, 7/8 of them. 98 dogs in the shelter received food. 112 dogs are total in the shelter.

Human habitations come in a wide variety. Huts made of mud, branches, and leaves are possible. People may reside in large apartment complexes made of steel, cement, and glass or in houses made of wood, masonry, or stone. They might make use of portable structures like tents, houseboats, trailers, or even rvs (RVs). There are three types of shelter: temporary, semi-permanent, and permanent. One of the fundamental necessities for survival is shelter.

When we find the total number of dogs in the shelter, we obtain:

Let , Total number of dogs = y.

Dogs were fed , [tex]\frac{7}{8}[/tex] of y =98

⇒y×[tex]\frac{7}{8}[/tex]= 98

⇒y =98× [tex]\frac{8}{7}[/tex]

⇒y = 14×8= 112.

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Answer:

$69

Step-by-step explanation:

25% = 0.25

17.25 ÷ 0.25 = 69

69 × 0.25 = 17.25

The original price of the hammer from the online retailer is $23.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given that,

Discount percentage = 25%

Amount after the discount = $17.25

We have to find the original price of the hammer.

Let x be the original price of the hammer.

x - 25% of x = 17.25

x - 0.25x = 17.25

0.75x = 17.25

x = $23

Hence the original cost of the hammer is $23.

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The value of x in the line segment is - 7 / 3.

A line segment is a section of a line bounded by two points or connecting two points. The value of x if U is between T and V can be found as follows:

TU = 7x + 35

UV = 4(x + 7)

TU ≅ UV

Therefore, let's find x as follows:

7x + 35 = 4(x + 7)

7x + 35 = 4x + 28

7x - 4x = 28 - 35

3x = - 7

x = -7  /3

Therefore,

x = - 7 / 3

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Answer:

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

    |          /

    |        /

    |      /

    |    /

-----|------------------

    | /         \

    |/            \

    /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

   |          /

   |        /

   |      /

   |    /

-----|------------------

   | /         \

   |/            \

   /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

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Answer:

there were 15 almonds in the snack pack.

Step-by-step explanation:

Let's use variables to represent the unknown quantities. Let's call the number of almonds in the snack pack "a", and the number of cashews in the snack pack "c".

we can use the following equations to represent the problem:

c = 2a (the number of cashews is twice the number of almonds)

c - 10 = a + 5 (there are 5 more cashews than almonds after Sylvia eats 10 cashews)

Substituting the first equation into the second equation, we get:

2a - 10 = a + 5

Solving for "a", we get:

a = 15

So there were 15 almonds in the snack pack.

Answer50.5

ffffffffffffffff

Based on the information in the paragraph, we can infer that the order of the terms is as follows. Expected value, permutation and combination.

Some probability situations involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.

There are two ways to sort or combine dependent event results. Permutations are groupings in which the order of the objects matters. Combinations are groupings in which the content matters but the order does not. In accordance with the above, the terms must be arranged in the following order:

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Answer:

The investment in the fund was $19000 x 0.12 = $2280

The investment in the stock was $19000 - $2280 = $16720

The net profit was $520, so the amount of the profit from the fund was $520 x (2280/16720) = $136

The amount of the loss from the stock was $520 - $136 = $384

Answer:

The answer is A my friend! Good luck on your test Mr Rush.

the variance will be 0.6217.

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

A small data analysis class has six computer science majors among the fourteen total students.

Three people are chosen at random to form a group.

here this is hypergeometric distribution with parameter n=sample size =3 ; N =population size =14

and k=computer sience major =6

a) E(X) =nk/N =3*6/14 =18/14 =9/7 =1.2857

b)|varaince =σ²=(nk/N)*(1-k/N)*(N-n)/(N-1)) =(3*6/14)(1-6/14)*(14-3)/(14-1)= 0.6217

Hence, the variance will be 0.6217.

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Answer:

Step-by-step explanation:

o divide 6029 by 28, we can use long division:

             215

          ---------

28 |    6029

             56

             ---

            182

           168

             ---

           144

          140

           ---

            4

So 6029 divided by 28 is 215 with a remainder of 4. Therefore, the answer to the problem is:

6029/28 = 215 R 4

To determine the height of the rock at a specific time, we need to substitute the time value into the equation y = 20t - 1.87t². For example, to find the height of the rock after 3 seconds, we substitute t = 3 into the equation:

y = 20(3) - 1.87(3)²

y = 60 - 16.83

y = 43.17

Therefore, the height of the rock after 3 seconds is 43.17 meters.

The probability that the arrow will land on an even number is 1/2.

Option D) 1/2 is the correct answer.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

the probability that the arrow will land on an even number:

Given that;

Total number of Integers on the spinner = 8

Total number f even integers on the spinner = 4

Probability that the arrow will land on an even number = ?

The probability that the arrow will land on an even number will be;

P = Total number f even integers on the spinner / Total number of Integers on the spinner

P = 4 / 8

P = 1/2

Therefore the probability that the arrow will land on an even number is 1/2.

Option D) 1/2 is the correct answer.

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The value for the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3.

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

Given:

We have given the graph, from the graph we can se a red dot.

So, the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3

Also, limit is defined as a value that a function approaches the output for the given input values.

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If a basketball player makes 40% of his shots from the free throw line, then the mean for  the number of shots that he makes is 0.928

Since the basketball player makes 40% of his shots from the free throw line and he takes 3 shots, the number of shots he makes, x, can take on the values 0, 1, 2, or 3.

The probability of making a shot is 0.4, so the probability of missing a shot is 0.6. Since each shot is independent, we can use the binomial probability formula to calculate the probability of making x shots:

P(X = x) = (3 choose x) × (0.4)^x × (0.6)^(3-x)

where (3 choose x) is the binomial coefficient that represents the number of ways to choose x items from a set of 3.

To find the mean for x, we need to multiply each possible value of x by its probability and then sum the results:

E(X) = 0 × P(X = 0) + 1 × P(X = 1) + 2 × P(X = 2) + 3 × P(X = 3)

Substituting the binomial probabilities into this formula, we get:

E(X) = 0 × (1) × (0.6)^3 + 1 × (3 choose 1) × (0.4)^1 × (0.6)^2 + 2 × (3 choose 2) × (0.4)^2 × (0.6)^1 + 3 × (1) × (0.4)^3 × (0.6)^0

E(X) = 0 + 0.432 + 0.432 + 0.064

E(X) = 0.928

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Substitute the expression for y in the second equation into the first equation and solve for x:

4x + 3(-1/3x + 6) = 36

4x - x + 18 = 36

3x = 18

x = 6

Now substitute x = 6 into the second equation to solve for y:

y = (-1/3)(6) + 6

y = 4

Therefore, the solution to the system of equations is the ordered pair (6, 4).

The value of n(A) is 35 if n(B) = 35, n(A nB) = 15, and n(A U B) = 55.

A set is a collection of well defined objects.

We can use the formula: n(A U B) = n(A) + n(B) - n(A nB)

Substituting the given values, we get:

55 = n(A) + 35 - 15

Simplifying, we get:

55 = n(A) + 20

Subtracting 20 from both sides, we get:

n(A) = 35

Therefore, the value of n(A) is 35.

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