Find the area of a circle with diameter = 16 units.

a. The probability that a randomly selected American who moved in 2004 was an owner is 0.31. b. 0.38 c. 0.03 .

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a fair coin and getting heads is 0.5, because there are two equally likely outcomes (heads or tails).

a. Probability that a randomly selected American who moved in 2004 was an owner:

Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million

Number of Americans who moved in 2004 and were owners = 11.7 million

Therefore, the probability that a randomly selected American who moved in 2004 was an owner is:

11.7 million / 38 million = 0.31 (rounded to the nearest hundredth)

b. Probability that a randomly selected American who moved in 2004 moved within the same state:

Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million

Number of Americans who moved in 2004 and moved within the same state = 11.7 million + 2.8 million

Therefore, the probability that a randomly selected American who moved in 2004 moved within the same state is:

(11.7 million + 2.8 million) / 38 million = 0.38 (rounded to the nearest hundredth)

c. Probability that a randomly selected American who moved in 2004 was a renter who moved to a different country:

Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million

Number of Americans who moved in 2004 and were renters who moved to a different country = 1.0 million

Therefore, the probability that a randomly selected American who moved in 2004 was a renter who moved to a different country is:

1.0 million / 38 million = 0.03 (rounded to the nearest hundredth)

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Answer:

(a) [tex]\frac{1}{6}[/tex] ≈ 0.167%

(b)  [tex]\frac{3}{6}[/tex] = 50%

(c) [tex]\frac{1}{6}[/tex] ≈ 0.167%

Step-by-step explanation:

We Know

A dice has 6 faces.

Numbers: 1, 2, 3, 4, 5, 6

(a) The number showing is a 2;

The probability is : [tex]\frac{1}{6}[/tex] ≈ 0.167%

(b) The number showing is an even number;

The probability is : [tex]\frac{3}{6}[/tex] = 50%

(c) The number showing is greater than 5;

The probability is :  [tex]\frac{1}{6}[/tex] ≈ 0.167%

Answer:

[tex]\textsf{B.} \quad m\overset{\frown}{BC}=56^{\circ}[/tex]

Step-by-step explanation:

To find the measure of arc BC, first calculate the measures of arc ABC and arc BCD.

Definitions:

The measure of an inscribed angle is half the measure of the intercepted arc.

Therefore, we can use the inscribed angle theorem to calculate the measures of arcs ABC and BCD:

[tex]\boxed{\begin{aligned}\angle ADC&=\dfrac{1}{2} \overset{\frown}{ABC}\\\\\implies 70^{\circ}&=\dfrac{1}{2} \overset{\frown}{ABC}\\\\ \implies \overset{\frown}{ABC}&=140^{\circ}\end{aligned}}[/tex]       [tex]\boxed{ \begin{aligned}\angle BAD&=\dfrac{1}{2} \overset{\frown}{BCD}\\\\\implies 98^{\circ}&=\dfrac{1}{2} \overset{\frown}{BCD}\\\\ \implies \overset{\frown}{BCD}&=196^{\circ}\end{aligned}}[/tex]

The sum of the arcs is 360°. Therefore:

[tex]\overset{\frown}{ABC}+\overset{\frown}{CD}+\overset{\frown}{AD}=360^{\circ}[/tex]

Substitute the given measure of arc AD and the found measure of arc ABC and solve for arc CD:

[tex]\implies 140^{\circ}+\overset{\frown}{CD}+80^{\circ}=360^{\circ}[/tex]

[tex]\implies \overset{\frown}{CD}=140^{\circ}[/tex]

The measure of arc BCD is the sum of arcs BC and CD. Therefore:

[tex]\overset{\frown}{BC}+\overset{\frown}{CD}=\overset{\frown}{BCD}[/tex]

To find the measure of arc BC, substitute the found measures of arc CD and arc BCD and solve for BC:

[tex]\implies \overset{\frown}{BC}+140^{\circ}=196^{\circ}[/tex]

[tex]\implies \overset{\frown}{BC}=56^{\circ}[/tex]

Therefore, the measure of arc BC is 56°.

Therefore, the balance after 3 years of continuous compounding at an annual interest rate of 3.1% is approximately $2,701.85.

Percent is a way of expressing a number as a fraction of 100. The word "percent" means "per hundred," so when we say something is, for example, 25%, we mean it is 25 out of 100, or 0.25 as a decimal. Percentages are often used to express ratios or proportions, such as in statistics, finance, and everyday life. Some common examples include: Interest rates: A bank might advertise a 5% annual interest rate on a savings account, which means that the account balance will increase by 5% (or 0.05) each year. Discounts: A store might offer a 20% discount on a product, which means that the price will be reduced by 20% (or 0.20) of the original price. Grades: A student might receive a grade of 85% on a test, which means that they answered 85 out of 100 questions correctly. Percentages can be converted to decimals or fractions, and vice versa, using simple arithmetic operations. For example, to convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100 and add a percent sign (%).

Here,

The formula for continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A is the ending balance, P is the principal amount, r is the annual interest rate (as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 2340 * [tex]e^{0.031*3}[/tex]

Simplifying the exponent, we get:

A = 2340 * [tex]e^{0.093}[/tex]

Using a calculator, we get:

A ≈ $2,701.85

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Answer:

The answer is y=2x+6

Step-by-step explanation:

add the 6x to the other side so its 3y=6x+18

then you divide by 3 so its y=2x+6

Option C. Based on the given line graph, it is not possible to determine how stock prices performed between March 2015 and August 2015 as there is no information provided for that time period.

The line graph only provides information for the period from January 2015 to March 2015 and from August 2015 to November 2015. The information provided on the graph shows how the stock prices performed during those time periods. Therefore, there is not enough information on the graph to determine how the stock prices performed between March 2015 and August 2015. It is possible that the stock prices increased, decreased, or remained the same during that time period, but the graph does not provide any information to confirm any of those possibilities.

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the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).

What is axis reflection ?

An axis reflection is a transformation in geometry that involves reflecting a point, a line, or an object across a given axis. In two dimensions, there are two axes of reflection: the x-axis and the y-axis.

When reflecting over the x-axis, all points stay in the same horizontal position but change their vertical position, so a point (x,y) is reflected to (x,-y).

When reflecting over the y-axis, all points stay in the same vertical position but change their horizontal position, so a point (x,y) is reflected to (-x,y).

Axis reflections can be used to transform geometric shapes such as polygons, circles, or lines. These transformations have important applications in various fields, including physics, engineering, computer graphics, and art.

To find the composition of transformations that map ABCD to EHGF, we first need to determine the individual transformations that are needed.

Reflecting over the y-axis will change the x-coordinates of the points, but leave the y-coordinates unchanged. So, to reflect over the y-axis, we negate the x-coordinates of the points.

The translation (x+4, y+7) will move each point 4 units to the right and 7 units up.

Therefore, the composition of transformations is:

Reflect over the y-axis by negating the x-coordinates:

A'(-2, 3), B'(-4, 2), C'(-4, 0), D'(-2, -1)

Translate by (4,7):

A''(2, 10), B''(0, 9), C''(0, 7), D''(2, 6)

Therefore, the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).

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STANDARD FORM is [tex]3x^2 + 24x + 32y + 192 = 0[/tex] ,parabola has a maximum point at its vertex, which is (2, -3).

to write the equation for the given parabola in standard form, we need to use the vertex form of the equation of a parabola, which is:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola and 'a' is the coefficient that determines the shape and direction of the parabola.

We know that the x-intercepts of the parabola are -2 and 6. This means that the parabola intersects the x-axis at these two points. Therefore, the roots of the quadratic equation are -2 and 6.

We also know that the y-intercept of the parabola is -48, which means that the point (0, -48) lies on the parabola.

Since the parabola is symmetric about the vertical line passing through its vertex, the x-coordinate of the vertex is the midpoint of the x-intercepts, which is (6 - 2)/2 = 2.

Therefore, the vertex of the parabola is (2, k), where k is the y-coordinate of the vertex.

Now we can use the vertex form

[tex]y = a(x - 2)^2 + k[/tex]

We need to determine the values of 'a' and 'k' to complete the equation.

Since the parabola passes through the point (0, -48), we can substitute x = 0 and y = -48 into the equation:

[tex]-48 = a(0 - 2)^2 + k[/tex]

-48 = 4a + k

Similarly, since the x-intercepts are -2 and 6, we can substitute x = -2 and x = 6 into the equation to get:

[tex]0 = a(-2 - 2)^2 + k[/tex]

0 = 16a + k

0 = a(6 - 2)^2 + k

0 = 16a + k

Solving these three equations for 'a' and 'k', we get:

a = -3/8 and k = -3

Substituting these values into the vertex form equation, we get:

[tex]y = (-3/8)(x - 2)^2 - 3[/tex]

Therefore, the equation for the parabola in standard form is:

[tex]3x^2 + 24x + 32y + 192 = 0[/tex]

This parabola has a maximum point at its vertex, which is (2, -3).

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According to the question we can conclude that expanding the garden will increase its area by 48 square feet.

Let's call the base of the original right triangle "b" and the height "h". The area of the right triangle is given by the formula:

Area = (1/2) * base * height

So we have:

16 = (1/2) * b * h

When we factor in a single of the variables, then obtain:

b * h = 32

Now, the new triangle will have twice the base and twice the height of the original triangle, so the new base will be 2b and the new height will be 2h. The area of the new triangle is given by the formula:

(Half) * Additional Base * Increased Height = New Area

Plugging in the new values, we get:

New area = (1/2) * 2b * 2h

Simplifying:

New area = 2bh

Now we need to find by how much the area has increased, which is the difference between the new area and the old area:

Area increase = Current area minus Old area.

Area increase = 2bh - 16

Substituting bh = 32, we get:

Area increase = 2(32) - 16

Area increase = 48

Therefore, expanding the garden will increase its area by 48 square feet.

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Answer:

x = 70°

Y = 20°

Step-by-step explanation:

We Know

x + 20° = 90°

x = 70°

Y is the vertical angle to the 20° angle, meaning y must have the same measure as the 20° angle.

So, Y = 20°

Answer:

x=70

y=20

Step-by-step explanation:

We can see that y is a vertial angle and so it is 20 and x+20=90 wich means that x=70

Answer:

59 degrees

Step-by-step explanation:

Since all of those angles would add up to 180 degrees (since they are on a line), we need to subtract 31 degrees (from angle VYT) and 90 degrees (from the right angle on angle WYX) from 180 to get the measure of angle VYW:

180-31-90 = 59.

happy to help :)

Finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.

To find the total volume of a composite figure, you'll need to break it down into simpler shapes and calculate their individual volumes.

Then, you can add up these volumes to get the total volume of the composite figure.

Here are the general steps you can follow:

Identify the simpler shapes: Look for the individual shapes that make up the composite figure, such as cubes, rectangular prisms, pyramids, cylinders, or spheres.

Calculate the volume of each shape: Use the appropriate formula for each shape to find its volume. For example, the volume of a cube is calculated by multiplying the length, width, and height of the cube.

Add up the volumes of all the simpler shapes: Once you have found the volume of each simpler shape, add them up to get the total volume of the composite figure.

Adjust for overlapping shapes: If there are any overlapping shapes, subtract the volume of the overlapped portion to avoid double-counting.

Check your work: Double-check your calculations and make sure your final answer makes sense based on the dimensions of the composite figure.

Overall, finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.

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Answer:

y = -3/7

Step-by-step explanation:

The polygons are similar, therefore the missing lengths are: 12) 4; 13) 24

13. The triangles are similar by the SAS similarity theorem; 14. They are not.

Recall that every pair of corresponding sides of similar triangles are always proportional to each other.

11. Let the missing side be x.

x/24 = 6/36

x/24 = 1/6

Cross multiply

6x = 24

x = 24/6

x = 4

12. x/20 = 36/30

x/20 = 6/5

Cross multiply:

5x = 120

x = 120/5

x = 24

13. m<VWU ≅ m<SWR based on vertical angles theorem [one pair of congruent included angles]

WV/WS = 40/5 = 8

WU/WR = 40/5 = 8 [two pair of proportional sides]

Therefore, both triangles are similar by the SAS similarity theorem.

14. The triangles are not similar because:

56/24 ≠ 28/13

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After answering the prοvided questiοn, we can cοnclude that  Tο circle cοmplete the cοpied triangle, draw a pοlygοn thrοugh pοints D, E, and F.

A circle appears tο be a twο-dimensiοnal cοmpοnent that is defined as the cοllectiοn οf all pοints in a jet that are equidistant frοm the hub. A circle is typically depicted with a capital "O" fοr the centre and a lοwer sectiοn "r" fοr the radius, which is the distance frοm the οrigin tο any pοint οn the circle.

The fοrmula 2r gives the girth (the distance frοm the centre οf the circle), where (pi) is a prοpοrtiοnality cοnstant rοughly equal tο 3.14159. The fοrmula r² cοmputes the circumference οf a circle, which refers tο the amοunt οf space inside the circle.

Fοllοw these steps tο duplicate the οriginal triangle using οnly twο οf its sides and the included angle:

Find the pοint where the ray and the circle intersect. Place the tip οf the cοmpass at pοint E and draw an arc that intersects the circle twice. Label the pοint that is οn the same side οf side AC as pοint B as pοint F.

Tο cοmplete the cοpied triangle, draw a pοlygοn thrοugh pοints D, E, and F.

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Answer:

[tex]1 = - 1(4) + b[/tex]

[tex]1 = - 4 + b[/tex]

[tex]b = 5[/tex]

[tex]y = - 1x + 5[/tex]

Answer: 5 [tex]\frac{7}{12}[/tex] cups

Step-by-step explanation:

   Subtract whole number values:

8 - 3 = 5 cups

   Subtract fractions:

* Get common denominators

5/6 ➜ 10/12

1/4 ➜ 3/12

* Subtract

10/12 - 3/12 = 7/12

   Answer:

5 7/12 cups

Answer:

67/12 cups of rice

Step-by-step explanation:

We Know

Jayden has 8 5/6 cups of rice.

8 5/6 = 53/6

He uses 3 1/4 cups to make dinner.

3 1/4 = 13/4

How many cups of rice does Jayden have left?

We Take

53/6 - 13/4 = 212/24 - 78/24 = 134/24 = 67/12

So, Jayden has  67/12 cups of rice left.

Answer:

Daisy made 50 and Oscar made 40.

Step-by-step explanation:

Daisy: Oscar: total

5            4       5+4 = 9

Taking the total made and dividing by 9.

90/9 = 10

Multiply each term in the ratio by 10.

Daisy: Oscar: total

5*10      4*10      9*10

50           40        90

Daisy made 50 and Oscar made 40.

Answer: 9 kg of cat food costs £57.42.

Step-by-step explanation: 1 kg of cat food costs £6.38, so you must multiply the cost by 9 to see how much 9 kg is worth.

6.38 x 9 = 57.42

Therefore, 9 kg of cat food is £57.42.

The value of the bond is multiplied by the factor [tex](1 + 0.04)[/tex], which is the same as multiplying by 1.04. After t years, the value of the bond will be multiplied by this factor t times, giving the formula:

[tex]100(1.04)t[/tex].

So, the value of the bond after t years is given by 100 • 1.04t.

A factor in mathematics is an expression or number that divides another expression or number without producing a residue. In other terms, a factor is a unit of measurement that may be multiplied by another unit of measurement to yield a specific outcome.

For example, 2 and 3 are factors of 6, because 2 multiplied by 3 equals 6. Similarly, (x + 1) and (x - 3) are factors of the expression [tex]x^2 - 2x - 3[/tex], because when these factors are multiplied together, they produce the expression:

[tex](x + 1) \times (x - 3) = x^2 - 2x - 3[/tex]

The bond is worth $100 initially, and it grows in value by 4% each year. This means that after one year, the value of the bond will be:

[tex]100 + 0.04(100) = 100(1 + 0.04) = 100(1.04)[/tex]

In other words, the value of the bond after one year is the initial value (100) multiplied by a factor of 1.04.

Similarly, after two years, the value of the bond will be:

[tex]100(1.04) + 0.04(100)(1.04) = 100(1.04)^2[/tex]

After three years, the value of the bond will be:

[tex]100(1.04)^2 + 0.04(100)(1.04)^2 = 100(1.04)^3[/tex]

In general, after t years, the value of the bond will be:

[tex]100(1.04)t[/tex]

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Answer: x= −6

              x=4

Step-by-step explanation:

The newspaper's claim was incorrect, as the percent error of the prediction was 0.76%, which is greater than 2%.

It is the difference between the observed value and the true value, expressed as in percentage. It is used to quantify how accurately a given measurement, prediction or other value matches the true value.

The percent error of the prediction can be calculated using the following formula:

[(Predicted Price - Actual Price) / Actual Price] × 100.

For this problem, the percent error

= [(4.10 - 4.069) / 4.069] × 100

= 0.76%.

Therefore, the newspaper's claim was incorrect since the percent error did not fall within the specified 2%.

In this case, the newspaper's prediction of the price of gasoline in two years did not match the true value as closely as expected, since the percent error was 0.76%.

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Answer:

The arithmetic mean of two numbers is found by adding them together and dividing the sum by 2.

So, the arithmetic mean of 4 and 18 is:

(4 + 18) / 2 = 22 / 2 = 11

Therefore, the arithmetic mean of 4 and 18 is 11.

Step-by-step explanation:

Answer:

STEP 1:let the arithmetic mean be p, q, r hence 4,p, q, r, 18

STEP 2:U5=18=a+4d

a+4d=18

we're a=4 therefore

4+4d=18

STEP 3:4d/4=(18-4)÷4=14/4

d=14/4=3.5

p=U2=a+d=4+3.5=7.5

q=U3=a+2d=4+(2×7.5)

=

In conclusion  the value that correctly fills in the blank in the table is 0.69.

Why it is?

To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.

We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):

Relative frequency for boys = (40 + 43) / 120 ≈ 0.69

Rounding to the nearest hundredth, we get:

Relative frequency for boys ≈ 0.69

Therefore, the value that correctly fills in the blank in the table is 0.69.

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The length of the third side of the triangle is 8.

The image is that of a right angled triangle. A right angled triangle is a triangle in which one of the angles measure 90 degrees. The sum of angles in the triangle measure up to 180 degrees.

In order to determine the length of the third side, the Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

In the triangle, 15 is the length and 17 is the hypotenuse.

a²  + 15²  = 17²

a²  = 17²  - 15²

a = √(17² - 15² )

a = √(289 -225)

√64 = 8

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Answer:

Step-by-step explanation:

The matches are:

Point A rounded to the nearest whole Number is 35, and rounded to the nearest ten is 40.

Let's analyze the vertical number line and Point A:

1. The number line is labeled 30 to 40, with tick marks every one unit.
2. Point A is slightly above the tick mark 35.

Now, we need to round Point A to the nearest whole number and the nearest ten.

To round to the nearest whole number:
1. Observe the position of Point A on the number line.
2. Since Point A is slightly above 35, it's closer to 35 than 36.
3. Therefore, Point A rounded to the nearest whole number is 35.

To round to the nearest ten:
1. Observe the position of Point A (35) in relation to the tens (30 and 40) on the number line.
2. Since 35 is exactly halfway between 30 and 40, it is equidistant from both.
3. In this case, we round up to the next ten, which is 40.
4. Therefore, Point A rounded to the nearest ten is 40.

In summary, Point A rounded to the nearest whole number is 35, and rounded to the nearest ten is 40.

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Answer:

The speed of the helicopter is 160mph.

Step-by-step explanation:

The speed of the helicopter is 160mph.

Speed

Speed =Distance/Time

450miles/s-35mph = 702miles/s+35

450×s+35 = 702×s-35

450s+15,750 = 702s-24,570

Collect like terms

702s-450s = 15,750 + 24,570

252s= 40,320

Divide both side by 252s

s= 40,320/252

s= 160mph

Inconclusion the speed of the helicopter is 160mph.

He can buy less οr equal tο 14 shirts with the mοney left and The inequality that represents this situatiοn is s (stands fοr shirts) ≤ 14.

In Mathematics, it is the relatiοnship between twο values that are nοt equal. Inequality means twο values that are nοt equal. When the situatiοn is  tο cοmpare the values, '≤' οr '≥' sign are used.

Hey team can spend nο mοre than $300 οn shirts the team has already spent $80.

300- 80 = 220

220/ 15 = 14.6

Let us say s be the number οf shirts.

Then the inequality will be s≤14

As the numbers οf shirts cant be a fractiοnal term sο we cοnvert the fractiοnal term tο the integer οne.

Hence, the inequality that represents the situatiοn is s≤14.

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