Use the data in the table below, which shows the employment status of individuals in a particular town by age group. A person from the town is randomly selected; what is the probability that the individual is employed full-time, given that he or she is between 18 and 49 years of age?

The inequality that is equivalent to 3+ 4/x ≥ X+2/x is 2x ≥ -2

From the question, we have the following parameters that can be used in our computation:

3 + 4/x ≥ X+2/x

Multiply through the inequality by x

So, we have

3x + 4 ≥ x + 2

Collecting the like terms

So, we have

3x - x ≥ 2 - 4

Evaluating the like terms

So, we have

2x ≥ -2

Hence, the inequality that is equivalent to 3+ 4/x ≥ X+2/x is 2x ≥ -2

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Answer:

A. Circle

To draw a regular polygon, one can use a circle as a geometric figure. A regular polygon is a polygon with all sides and angles equal. By inscribing a polygon inside a circle, the vertices of the polygon are evenly spaced on the circumference of the circle, and the radius of the circle is equal to the distance between the center of the circle and the vertices of the polygon. This ensures that all sides of the polygon are of equal length, and all angles between the sides are equal. Therefore, by using a circle as a geometric figure, Rachael can draw a regular polygon with ease.

When solved, the expressions below that will have a 1 in the tenths place is A) 24.321 x 100 and  C) 96.51 x 10

From the question we were told to find the the expressions that will have a 1 in the tenths place which implies that we will need to find the simplification of each expression by perforimgmultiplication operation on eaqch of the given expression which can be done  as ;

The first option;

24.321 x 100 = 2432.1

The second option;

25.671 x 10 = 256.71

The third option;

96.51 x 10 = 965.1

The fifth option;

89.15 x 100 = 8915

We can see that in option A and option C that the have a 1 in the tenths place.

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The point P should be chosen at 1.07 units to maximize the angle.

From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.

Using pythagoras theorem,

tan M = a/(b - x)

M = tan⁻¹(a/(b - x))

Also, we can say that:

tan N = c/x

N = tan⁻¹(c/x)

Angle θ is given by:

θ = 180 - M - N

θ = 180 - tan⁻¹(a/(b - x)) - tan⁻¹(c/x)

Given that a = 3 units, b = 5 units, and c = 8 units. Thus:

θ = 180 - tan⁻¹(3/(5 - x)) - tan⁻¹(8/x)

To maximize angle θ, the differentiation of θ with respect to x must be equal to zero.

i.e. dθ/dx = - 3/(x² - 10x + 34) + 8/(x² + 64) = 0

8/(x² + 64) = 3/(x² - 10x + 34)

8(x² - 10x + 34) = 3(x² + 64)

8x² - 80x + 272 = 3x² + 192

5x² - 80x + 80 = 0

Using quadratic equation calculator gives:

x = 1.0718

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Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

We have ,

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

Hence, Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

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Answer: 118

Step-by-step explanation:

Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.

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The required, we get a population of 543694 after 12 years.

To find the population of the city after 12 years, we need to apply the formula for compounding:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

In this case, P = 210,000, r = 0.0825 (8.25% expressed as a decimal), n = 1 (since the growth is yearly), and t = 12. Plugging in these values, we get:

A = 210,000(1 + 0.0825/1)¹ˣ¹²

A = 210,000(1.0825)¹²

A ≈ 543693.51

Rounding this to the nearest whole number, we get a population of 543694 after 12 years.

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The equation of the circle is (x – 3)² + (y + 1)² = 25.

D. is the answer.

The general equation of a circle is given by:

(x – h)² + (y – k)² = r²,

where (h, k) is the coordinate of the circle's center, and r is the radius.

Thus, (h, k) = (3, -1) and the circle passes through (-2, -1) i.e. (x, y) =  (-2, -1). Substituting into the equation, we can get the radius. That is:

(x – h)² + (y – k)² = r²

(-2 – 3)² + (-1 – (-1))² = r²

(-5)² = r²

25 = r²

r² = 25

Substitute only h, k and r² back into the general equation to get the equation of the graph. That is:

(x – h)² + (y – k)² = r²

(x – 3)² + (y – (-1))² = 2

(x – 3)² + (y + 1)² = 25

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There is only one solution. The measurements of the angles are ;

B = 54. 6 degrees

C = 41. 6 degrees

Option B

To determine the value of the angle, we need to know the law of sines.

It is represented as;

sin A/a = sin B/b

Such that;

From the information given, we have;

sin 83.8/11.1 = sin B/9.1

cross multiply the values, we get

sin B = 9. 0467/11.1

Divide the values

sin B = 0. 8150

find the inverse

B = 54. 6 degrees

Note that the sum of the angles in a triangle is 180

C = 180 - 138. 4 = 41. 6 degrees

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A payday loan for $2300 due in 13 days with a rate of $120, because it has the shorter period and this will have a higher effective interest rate, Therefore option B is correct.

The effective interest rate (EIR) takes into account the whole value of the loan such as fees and the period of the loan.

In this situation, both loans have the equal rate of $120, so the full price is the same.

However, the mortgage due in thirteen days has a shorter length, meaning that the hobby is being charged over a shorter amount of time, resulting in a better effective interest rate compared to the mortgage due in 15 days.

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The solution to the equation 3x(x + 4) + 3(x + 4) = 0 is x = -4 or x = -1.

Given the equation in the question:

3x(x + 4) + 3(x + 4) = 0

To determine the solution to the equation.

First, factor out the common factor of (x + 4) from the left-hand side of the equation:

3x(x + 4) + 3(x + 4) = 0

3(x + 4)(x + 1) = 0

The equation is now in factored form, and we can use the zero product property to find the values of x that satisfy the equation:

3(x + 4)(x + 1) = 0

(x + 4)(x + 1) = 0 (Divide both sides by 3)

Using the zero product property, we know that:

(x + 4) = 0 and (x + 1) = 0

Solving for x, we get:

x + 4 = 0 and x + 1 = 0

x = -4 and x = -1

Therefore, the solution s are x = -4 and x = -1.

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Answer:

Step-by-step explanation:

The situation that can be represented by the given equation 340 + 5x - 650 - 8x is:

Sierra started with savings of $340 and spends $8 of her savings every week. Brian started with savings of $650 and adds $5 to his savings every week. The equation represents the difference in savings between Sierra and Brian after x weeks. The term "340 + 5x" represents the total savings of Sierra after x weeks, where she starts with $340 and adds $5 per week. The term "- 650 - 8x" represents the total savings of Brian after x weeks, where he starts with $650 and subtracts $8 per week. By equating the two expressions, we can find the value of x, which represents the number of weeks needed for Sierra and Brian to have the same amount of savings.

The total distance El had biked when he finally reached the library is 119/20 miles

Given that Eli biked for [tex]1\frac{1}{10}[/tex] miles two times extra as he missed a book at home.

The distance between the Elis house and library is [tex]3\frac{3}{4}[/tex] miles

We have to find the total distance Eli biked

Total distance  = [tex]1\frac{1}{10} +1\frac{1}{10} +3\frac{3}{4}[/tex]

=11/10+11/10+15/4

20 is LCM of 10, 10 and 4

= 22+22+75/20

=119/20 miles

Hence, the total distance El had biked when he finally reached the library is 119/20 miles

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Answer:

A=25%

B=6.25%

C=3.125%

D=12.5%

F=~12.5%

Step-by-step explanation:

they look like it

i cant read the letters so not sure.

if its by scale then im right

Answer:

Piece A- 25%

Piece B- 6.25%

Piece C- 3.125%

Piece D- 15.625%

Piece E- 37.5%

Piece F- 12.5%

Step-by-step explanation:

To find each shape's area as a percentage, each shape should be compared to the whole larger square, so we will first find the total area in the large square.

The question states that the square is 4cm x 4 cm, and using the equation for the area of a square, length x width, we know that the large square's area is 16cm squared.

Square A is 2cm long and 2cm wide, so similarly, we can use the length x width formula to get 4cm squared for its area. To find its percentage relative to the larger square, we must divide its area, 4, by the large square's area, 16. 4/16 = 0.25, which can be converted to a percentage by multiplying it by 100%. This means that piece A takes up 25% of the large square's area.

Square B is 1cm long and 1cm wide. Once again, we will multiply its length and width to get an area of 1cm squared. Again, we must divide this number by the total area of the large square. 1/16= 0.0625, or, after converting it to a percentage, 6.25%.

Piece C is triangular, and so we will use the formula for an area of a triangle instead: Base x height x 1/2. We know from seeing it above square B that its base is 1cm wide. It also ends vertically at square A. Because it starts after square B, which is 1cm long, and square A is 2cm long, we know that the triangle's height is 2cm - 1cm, or, 1cm long. The base multiplied by the height is 1, and dividing it by 2 gets us 1/2cm squared for its area. To find the percentage, we divide 1/2 by 16, which gives us 0.03125, or 3.125%.

Piece D is an irregular shape, however we can instead imagine it as two separate shapes- a square near the bottom and a triangle on top. The square section is 1cm wide, since the large square's side is 4cm and so far, squares A and B are lying on that side, taking up 3cm. it is also as tall as square B, making it 1cm long vertically. Using the formula for the area of a square, length x width, we know that the area of that section is 1cm squared.

The triangle section is right on top of it, making its base 1cm wide as well. The side of the triangle goes until the top of the large square, and because the square section already took up 1cm of the 4cm long side, we know that the triangle is 3cm tall. Using the area of a triangle formula, base x height x 1/2, we can multiply 1 x 3 x 1/2 to get an area of 3/2cm squared.

To find the total area of piece D, we then have to add the area of the square and triangle sections together. 1 + 3/2 = 5/2cm squared area total. Dividing 5/2 by 16 gets 0.15625, or 15.625% of the large square's area.

Piece E as well can be split up into a square and a triangle. The square section ends where square A ends, and takes up half of the large square's side, meaning it is 2cm wide and 2 cm long. Multiplying its length and width gets an area of 4cm squared.

The triangle also takes up half of the larger square's side horizontally and vertically, so it has a base and height of 2cm. Using the area of a triangle formula, base x height x 1/2, we can get 2 x 2 x 1/2, or 2cm squared for its area.

Adding the areas of the square and triangle sections, Piece E will have a total area of 6cm squared. Then, we divide that by 16, and 6/16= 0.375, or 37.5% of the large square's area.

Piece F is diagonal, so it is harder to tell the measurements of its base and height. however, we know that its sides are the hypotenuses of two other triangles we have measured. The hypotenuse is the longest side of a triangle, facing opposite of its 90 degree angle. If we name the hypotenuse "c" and the other two sides of the triangles "a" and "b", we can use the Pythagorean theorem, a^2+b^2=c^2, to find the lengths of Piece F.

For piece C, the base and height of the triangle are both 1cm, so if those are a and b, then 1^2+1^2=c^2, with c being the base of piece F. 1*1=1, so 1+1=c^2, making c^2=2. We can then isolate c by taking the square root of both sides, making c=[tex]\sqrt{2}[/tex].

We can do the same thing with the triangle taken from piece E, though this time a and b will both equal 2cm.  If we plug those values into the equation, then 2^2+2^2=c^2. 2*2=4, so 4+4=c^2, or c^2=8. Taking the square root of both sides, we find that c=[tex]\sqrt{8}[/tex].

Basically, piece F has a base of [tex]\sqrt{2}[/tex]cm, and a height of [tex]\sqrt{8}[/tex]cm. We can plug those into the equation for the area of a triangle, base x height x 1/2, to get [tex]\sqrt{8}[/tex] x [tex]\sqrt{2}[/tex] x 1/2, or 2cm squared for the area of piece F. 2/16= 0.125, so piece F takes up 12.5% of the large square's area.  

Answer:

Find the incenter of the triangle

Step-by-step explanation:

Step 1: We draw angle bisectors for 2 angles and mark their intersection.

Step 2: Next, we drop a perpendicular line from the incenter of the circle to one edge of the triangle.

The value of test statistics is -0.87.

We have,

n=25, mean= 24.4, s=9.2 and a=.05

As t = (x - [tex]\mu[/tex])/(s/√(n))

t = (24.4 - 26)/(9.2/√(25))

t = -0.8695652173913

t = -0.87

The sample size is n = 25, so df= 25 - 1= 24

So, the probabilities for the one tailed test are 0.20 and 0.15 respectively.

The p-value is between 0.15 and 0.20

The p-value is not less than α.

So, we can't reject the null hypothesis H0

We fail to reject the null hypothesis H0

Thus, the mean age of the prison population in cone city is 26 years.

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The Venn diagram shows 12 students, 3 are in the Math Club, 4 are in the Volleyball Club, and 2 are in both clubs. There are 7 students who are not members of either club. The probability that a randomly selected student is in either club is 5/12.

We are given that there are 3 students in the Math Club, 4 students in the Volleyball Club, and 2 students in both clubs. This means that there are 3 - 2 = 1 student in only the Math Club and 4 - 2 = 2 students in only the Volleyball Club. There are also 12 - (1 + 2 + 2) = 7 students who are not members of either club.

Let's use this information to find the probabilities of the given events

P(A) = probability that the student is in the Volleyball Club = 4/12 = 1/3

P(B) = probability that the student is in the Math Club = 3/12 = 1/4

We can also find the probability of the event "the student is in both the Volleyball and Math Clubs" as:

P(A ∩ B) = probability that the student is in both clubs = 2/12 = 1/6

Finally, we can use the formula for the probability of the union of two events to find the probability of the event "the student is in either the Volleyball or Math Club (or both)"

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 1/3 + 1/4 - 1/6

P(A ∪ B) = 5/12

So, the probability that a randomly selected student is in either the Volleyball or Math Club (or both) is 5/12.

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--The given question is incomplete, the complete question is given

" The venn diagram shows the 12 students in Mr. Campbell's class. The diagram shows the memberships for the Volleyball Club and the Math Club. Note that "Ivanna" is outside the circles since she is not a member of either club. One student from the class is randomly selected. Let A denote the event "the student is in the Volleyball Club." LEt B denote the event "the student is in the Math Club." "--

Answer:

its 15.5 m

Step-by-step explanation:

The actual distance between City C and City D is approximately 647.06 miles.

We can use the given information to determine the scale of the map, which relates distances on the map to actual distances in the real world. Let x be the actual distance between City C and City D in miles. According to the map, the distance between City C and City D is represented by 4.42 feet. We can write this relationship as:

250 miles / 1.7 feet = x miles / 4.42 feet

Solving for x, we get:

x = (4.42 feet * 250 miles) / 1.7 feet = 647.06 miles

The key concept used in this problem is the idea of scale. Maps are often drawn to a specific scale, which allows us to relate distances on the map to actual distances in the real world. In this case, we used the scale of the map to convert the distance between City C and City D on the map (measured in feet) to the actual distance between the cities (measured in miles).

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An equation that could represent the graph of P(x) include the following: p(x) = -3/4(x - 2)²(x + 1).

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 2 at x = -1;

x = 2 ⇒ x - 2 = 0.

(x - 2)²

x = -1 ⇒ x + 1 = 0.

(x + 1)²

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 2)²(x + 1)²

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -3), we have;

-3 = a(0 - 2)²(0 + 1)²

-3 = a4

a = 3/4.

Therefore, the required polynomial function is given by:

p(x) = -3/4(x - 2)²(x + 1)

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Answer:

the answer is c

because when u add them that what it gives u

Answer:

A) m<L, m<K, m<J

Step-by-step explanation:

Triangle Congruence--

This means that the longest angle is always opposite the longest side,

and vice verse the shortest angle is always opposite the shortest side.

So in triangle JKL, the longest side is line KL (21).  This means angle J, which is opposite KL is the longest. Furthermore, angle L, opposite line JK (13), is the smallest. This also concludes angle K is in the middle of the two, forming the sequence L, K, and then J (ascending order).

The fraction is simplified to -2/3

A fraction can be defined as a mathematical expression representing a part of a whole number, element or variable.

There are different types of fractions. They are listed thus;

Examples of improper fractions are; 3/2, 4/3

Examples of proper fractions are; 1/2 3/4

From the information given, we have that;

7/12 - 5/12

Find the lowest common denominator

7 - 15/12

Subtract the values

-8/12

-2/3

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The net change in the value of this stock for the week is $2.12.

The total change in the value of the stock is  $4.38.

We have,

a)

The net change in the value of the stock for the week is the difference between the closing price on Monday and the closing price on Friday.

Net change expression.

= $6.40 - $4.28

= $2.12

b)

The total change in the value of the stock is the sum of the absolute changes from day to day.

Total change expression.

= |$5.17 - $4.28| + |$4.79 - $5.17| + |$7.15 - $4.79| + |$6.40 - $7.15|

= $0.89 + $0.38 + $2.36 + $0.75 = $4.38

Thus,

The net change in the value of this stock for the week is $2.12.

The total change in the value of the stock is  $4.38.

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Answer:

B. 46.

Step-by-step explanation:

First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.

To calculate the interest earned in 3 months, we need to first find the monthly interest rate.

The annual interest rate is 14%, so the monthly interest rate is:

14% / 12 months = 1.1667% per month

Next, we can calculate the interest earned in 3 months by multiplying the monthly interest rate by the principal (the amount in the savings account):

3 months * 1.1667% per month * $13,163 = $485.95

Therefore, Janelle will earn $485.95 in interest in 3 months.

Answer:

the depth of the pool, in feet, before Mr. Richardson started draining it

Step-by-step explanation:

y = -0.5x + 4 is the in the slope-intercept form, whose general form is

y = mx + b, where m is the slope of the line and b is the y-intercept.  The y-intercept is where the line intersects the x axis and in order to intercept the y-axis, x has to be 0.

Thus, when the y-intercept is 4, we know that x-value is automatically 4 and therefore Mr. Richardson's pool was already at a depth of 4 feet before the draining began.

After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.

To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.

The terms involved in this calculation are:
Time (t): 4.5 seconds.

Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
[tex]d = (1/2) \times g \times t^{2}[/tex]
Now, we will plug in the given values and solve for d:
Substitute the values
[tex]d = (1/2) \times 9.81 \times  (4.5)^{2}[/tex]
Calculate the square of time
[tex]d = (1/2) \times 9.81 \times 20.25[/tex]
Multiply the values
d = 99.3525.

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