Question What is the value of the expression? 75÷5−[(9−7)×3]×2 Enter your answer in the box.

Answer:

12

Step-by-step explanation:

1+2=3 and 12 satisfied all the conditions

If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.

Divide its principal by the risk premium, the time period and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This process makes it easier to calculate interest. The most typical technique to figure out interests is as a portion of the principal sum. He will only pay his half of the 100% interest, for example, if he borrows $100 from a partner and agrees to repay the loan with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must pay the interest. Interest is often set as an annual percentage of the loan total.

given:

FV = 1000(1.06)²⁵

FV =  1000 × 4.2918

FV = 4291.8

If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.

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The value of x is 2 or 10 and the value of length RA is 96

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length. . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.

If RA = MA

x²-4x = 8x -20

x²-4x-8x +20 = 0

x²-12x +20 = 0

x²-10x -2x +20 = 0

(x²-10x)(-2x+20) = 0

x( x -10) -2(x-10) = 0

(x-2)(x-10) = 0

x-2 = 0

or x-10 = 0

x = 2 or 10

therefore RA = x²-4

when x = 2

RA = 0

when x = 10

RA = 100-4

= 96

therefore the value of length of RA is 96

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From the graph of system of linear inequality there may be other possible solutions, but (20, 100) is one that satisfies all the given constraints.

Let's first define our variables and their corresponding constraints:

Let a be the number of student tickets sold.

Let y be the number of adult tickets sold.

The total number of tickets sold cannot exceed 120, so we have the constraint

a + y ≤ 120 ...eq(i)

The minimum revenue required is $670, so we have the constraint          4a + 8y ≥ 670...eq(ii)

The drama club can sell at most 30 student tickets, so we have the constraint a ≤ 30.

The drama club must sell a minimum of 80 adult tickets, so we have the constraint y ≥ 80.

The last inequality is

y ≥ 80

To solve these inequalities graphically, we will plot the lines for each constraint on a coordinate plane and shade the region that satisfies all the inequalities. The shaded region will represent all possible combinations of student and adult tickets that meet the constraints.

First, let's plot the line for the a + y ≤ 120 constraint. We can rewrite this as y ≤ -a + 120 and plot the line y = -a + 120 on the coordinate plane:

The shaded region for this constraint is below the line and includes the origin.

Next, let's plot the line for the 4a + 8y ≥ 670 constraint. We can rewrite this as y ≥ (-1/2)a + 83.75 and plot the line y = (-1/2)a + 83.75 on the same coordinate plane:

The shaded region for this constraint is above the line.

Now, let's plot the constraint a ≤ 30. We can draw a vertical line at a = 30:

The shaded region for this constraint is to the left of the line.

Finally, let's plot the constraint y ≥ 80. We can draw a horizontal line at y = 80:

The shaded region for this constraint is above the line.

To find a possible solution, we need to find the point where all four shaded regions overlap. This point represents a combination of student and adult tickets that satisfies all the constraints. One such point is (20, 100), which means the drama club can sell 20 student tickets and 100 adult tickets to meet their requirements and raise at least $670 in revenue.

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Answer:

1.

a.

b. 115 feet.

c.  78.26feet.

Step-by-step explanation:

a.

some mathematical observations we can make about the path of the balloon based on the given equation:

b. The maximum height of the balloon occurs at the vertex of the parabola described by the function b(h). We can find the height of the vertex by using the formula h = -b/(2a), where b and a are the coefficients of the linear and quadratic terms in the equation, respectively.

In this case, a = -1/115 and b = 2, so the height of the vertex is:

h = -b/(2a) = -2/(2(-1/115)) = 115 feet

Therefore, the maximum height the balloon reaches is 115 feet.

c. To find the height of the balloon after 180 minutes, we can substitute h = 180 into the equation b(h) and simplify:

b(180) = 2(180) - 1/115(180)^2 = 360 - 281.73≈ 78.26

Therefore, when you have been on the ride for 180 minutes, the height of the balloon is approximately78.26feet.

Answer:

a) The balloon ride is 230 minutes long.

b) The maximum height the balloon reaches is 115 m.

c) The height of the balloon at 180 minutes is 78 feet.

Step-by-step explanation:

Given quadratic equation:

[tex]b(h)=2h-\dfrac{1}{115}h^2[/tex]

The height of the balloon at the start and end of the balloon ride is zero feet. Therefore, to determine how long the balloon ride is, set the given quadratic equation to zero and solve for h.

[tex]\begin{aligned}\implies2h-\dfrac{1}{115}h^2&=0\\\\h\left(2-\dfrac{1}{115}h\right)&=0\\\\2-\dfrac{1}{115}h&=0\\\\\dfrac{1}{115}h&=2\\\\h&=230\end{aligned}[/tex]

Therefore, the balloon ride is 230 minutes long.

To determine the maximum height the balloon reaches, find the y-value of the vertex of the given quadratic equation.

The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c. Therefore, the x-value of the vertex of the given equation is:

[tex]\implies -\dfrac{2}{2\left(-\frac{1}{115}\right)}=115[/tex]

To find the y-value of the vertex, substitute h = 115 into the given equation:

[tex]\begin{aligned}\implies b(115)&=2(115)-\dfrac{1}{115}(115)^2\\&=230-115\\&=115\; \sf ft\end{aligned}[/tex]

Therefore, the maximum height the balloon reaches is 115 ft.

To determine the height of the balloon when you have been on the ride for 180 minutes, substitute h = 180 into the equation:

[tex]\begin{aligned}\implies b(180)&=2(180)-\dfrac{1}{115}(180)^2\\\\&=360-\dfrac{6480}{23}\\\\&=78.260869...\\\\&=78\; \sf ft\end{aligned}[/tex]

Therefore, the height of the balloon at 180 minutes into the ride is 78 feet (rounded to the nearest foot).

Answer:

[tex]S_n= n^2+4n[/tex]

[tex]n=11[/tex]

Step-by-step explanation:

The given arithmetic series is 5 + 7 + 9 + ...

From inspection of the given series, we can see that the first term is 5.

The common difference is the difference between consecutive terms. Therefore, the common difference of the given series is 2.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

To determine an equation for the sum of the first n terms of the given series, substitute a = 5 and d = 2 into the formula.

[tex]\implies S_n=\dfrac{1}{2}n\left[2(5)+(n-1)(2)\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[10+2n-2\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[2n+8\right][/tex]

[tex]\implies S_n= n^2+4n[/tex]

To find the value of n, substitute Sₙ = 165 into the formula and solve for n:

[tex]\implies n^2+4n=165[/tex]

[tex]\implies n^2+4n-165=0[/tex]

[tex]\implies n^2+15n-11n-165=0[/tex]

[tex]\implies n(n+15)-11(n+15)=0[/tex]

[tex]\implies (n-11)(n+15)=0[/tex]

Apply the zero product property:

[tex](n-11)=0 \implies n=11[/tex]

[tex](n+15)=0 \implies n=-15[/tex]

Therefore, as the value of n is positive, the value of n for which the series has a sum of 165 is 11.

Using the Hamilton's method of apportioning of seats, the five countries will get the following number of seats:

Adams = 7

Grant =7

Colton= 11

Davis= 5

Hayes= 2

Total = 7+7+11+5+2 = 32 seats

To calculate the number of seats, first find the Standard Divisor (SD). That is: SD = Total population / Number of seats available

Total population = 213,000+225,000+351,000+158,000+70,000 = 1,017,000

Then divide the total population by number of seats available (32).

That is: SD = 1,017,000/32

SD = 31,781.25

Find the Standard Quota (SQ) for each county by using the formula;

SQ = County population / SD

Adam's SQ = 213,000/31,781.25 = 6.70

Grant's SQ = 225,000/31,781.25 = 7.08

Colton's SQ = 351,000/31,781.25 = 11.04

Davis's SQ = 158,000/31,781.25 = 4.97

Hayes's SQ = 70,000/31,781.25 = 2.20

Find the Lower Quota for each county and find the total number of occupied seats:

Adams = 7

Grant =7

Colton= 11

Davis= 5

Hayes= 2

Total = 7+7+11+5+2 = 32 seats

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Answer: y = 10/7 x= 26/7 so A (26/7 , 10/7)

Step-by-step explanation:

since an equation for x is already given, we can plug it in to the first equation to solve for y

3(4y-2) + 2y = 14

12y - 6 +2y = 14

14y -6 = 14

14y = 20

y = 20/14

simplify

y = 10/7

plug the y we just found into the equation for x to find the value of x

x = 4(10/7) -2

x= 40/7 - 2

make both fractions

x = 40/7 -14/7

x= 26/7

hope this helps!

Answer:

The probability that the couple have two girls and then a boy is 1/8 (12.5%).

Step-by-step explanation:

Tree diagrams show probabilities for sequences of two or more independent events.

To draw a tree diagram showing the given information:

See the attachment for the tree diagram.

To find the probability that the couple have two girls and then a boy, multiply along the branches representing those events.

Therefore, the probability that the couple have two girls and then a boy is:

[tex]\sf P(girl)\;and\;P(girl)\;and\;P(boy)=\dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{8}=12.5\%[/tex]

Answer:

1/8 or 0.125 (12.5%).

Step-by-step explanation:

Using the tree diagram, we can see that there are 8 possible outcomes for the gender of the three children: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG. Since each outcome is equally likely, the probability of any one outcome is 1/8.

The outcome we are interested in is GGB, which has a probability of 1/8. Therefore, the probability that the family has two girls, and then a boy is 1/8 or 0.125 (12.5%).

Answer:     b = 82°

To solve for angle b, calculate using the given angles and the straight angle theorem.

The straight angle theorem is a rule that says all straight lines are 180°.

Since the angle formed by XY is a straight line, it is also equal to 180°.

XY is divided into three separate angles, a, b and c.

If we add a, b, and c, it will equal to 180°.

XY = a + b + c                              XY is the sum of a, b, and c.

180° = 46° + b + 52°                     Substitute what we know.

To solve for b using this equation, isolate.

180° - 46° = 46° + b + 52° - 46°   Subtract 46° on both sides.

134° = b + 52°

134° - 52° = b + 52° - 52°             Subtract 52 on both sides.

82° = b                                         Keep the variable on the left.

b = 82°                                         Final answer.

Therefore, angle b is 82°.

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Answer:

Step-by-step explanation:

6 is the rate of change and 1/4 is the initial value

The size of the largest interior angle of the field is 69.86°

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

Given that, a triangular field has boundaries of lengths 170m, 195m and 210m, we need to find the size of the largest interior angle of the field,

We know that, angle opposite to the largest side is largest,

Therefore,

The largest angle is opposite is 210 m side, (say c)

Using the cosine rule,

210² = 170²+195²-2(170)(195)cosC

CosC = 170²+195²-210² / 2(170)(195)

CosC = 22825 / 66300

CosC = 0.344268477

C = 69.86°

Hence, the size of the largest interior angle of the field is 69.86°

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The probability that Winston makes exactly three mid-air catches in four tosses is 0.154, rounded to three decimal places.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.

This is a binomial distribution problem, where each toss is a Bernoulli trial with a probability of success of 0.4 (i.e., catching the ball mid-air) and a probability of failure of 0.6 (i.e., not catching the ball mid-air).

The number of successes (mid-air catches) in four tosses follows a binomial distribution with parameters n = 4 and p = 0.4.

The probability of getting exactly three mid-air catches in four tosses is:

P(X = 3) = (4 choose 3) * 0.4^3 * 0.6^1 = 4 * 0.064 * 0.6 = 0.154

where (4 choose 3) is the number of ways to choose 3 out of 4 tosses, and 0.4^3 and 0.6^1 are the probabilities of getting 3 mid-air catches and 1 miss, respectively, in any order.

Therefore, the probability that Winston makes exactly three mid-air catches in four tosses is 0.154, rounded to three decimal places.

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The age of Sadie is 6 years.

Two or more expressions with an Equal sign is called as Equation.

Let x be the age of Sadie

x+1 be the age of Guadalupe

The sum of the square of Sadie's age and 5 times Guadalupe's age is 71.

x² +5(x+1)=71

x² +5x+5=71

x² +5x-66=0

Factor out the expression.

x²+11x-6x-66=0

x(x+11)-6(x+11)=0

(x-6)(x+11)=0

x=6 and x=-11

Hence, the age of Sadie is 6 years.

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Answer:

Below

Step-by-step explanation:

See the image below :

Area of the ENTIRE rectangle would be: Area = Base * Height

I think you can see that  the triangle is 1/2 of the rectangle. so the

     Area of the right triangle would be: Area = 1/2 * base * height

For a game, Bob has a total of 60 adventure cards. The distribution of cards, c, to players, p, is shown in the table. c = 60 ÷ p

Probability defines the possibility of occurrence of an event. Probability is the unit of measurement for an event's likelihood. It represents the proportion of positive results to all results. For instance: Receiving the numbers 3 and 5 while rolling the dice, as well as getting both an even and an odd number.

The equation would read: c = 60 / 2, which implies c = 30 if p=2. The equation would read 12 = 60 / p, p = 5, 20 = 60 / 3, etc. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.

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We know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.

What are trigonometric ratios?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

We can use the following trigonometric ratios:

sin(A) = opposite/hypotenuse

cos(A) = adjacent/hypotenuse

In this case, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse:

opposite = BC = 9 units

adjacent = AB = 40 units

hypotenuse = AC = 41 units

Using these values, we can calculate the sine and cosine of angle A:

sin(A) = opposite/hypotenuse = 9/41

cos(A) = adjacent/hypotenuse = 40/41

Therefore, we know the lengths of the sides opposite and adjacent to angle A, as well as the length of the hypotenuse, then sin(A) = 9/41 and cos(A) = 40/41.

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Answer:

Step-by-step explanation:

The value of x is given as follows:

x = 24.75.

The value of x is obtained solving the proportion in the context of the problem.

The proportion is defined as follows:

sin(29º) = 12/x.

Applying cross multiplication, we can isolate the variable x as follows:

xsin(29º) = 12

x = 12/sin(29º).

Then a calculator is used to divide 12 by the sine of 29 degrees, and then the result is given as follows:

x = 24.75.

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Answer:16/10

Step-by-step explanation:

add 4/5+4/5=16/10

so the answer is 16/10

The solutions of the given system of linear inequalities are (0, 3) and (6, 2)

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

Given is a graph of a system of linear inequalities, we need to select the solutions of the following,

The solution of the system of linear inequalities, are given by the combined shaded reason of the graph,

Here, only points (0, 3) and (6, 2) are lies in the common combined part of the graph,

Hence, the solutions of the given system of linear inequalities are (0, 3) and (6, 2)

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The requried solution of the two linear equations is given as x = (b - d)/a-c and y = a (d - c)/(a-c).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

The question seems to be incomplete so the solution is a standard solution by assuming a standard linear equation.

The given equation,
ax + y = b - - - - - (1)
cx + y = d - - - - -(2)

Subtract equation 2 from 1
ax - cx + y - y = b - d

x(a - c) =  b - d
x = b - d / a - c

Now,
Put x in equation 1
a (b - d) / (a - c) + y = b
y = b - a(b - d)/(a - c)
y = ab - ac -ab + ad/(a - c)
y = a (d - c)/(a - c)

Thus, the requried solution of the two linear equation are given as x = (b - d)/a-c and y = a (d - c)/(a - c).

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The question seems to be incomplete,
The solution given is standard solution for the simultaneous equations.

1)

Area of a = 25 m²
2)

Length b = 5 m

3)

Length c = 7.94 m

4)

Area of d = 35.75 m²

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

1)

Figure a is a square:

Side = b

Area = b²

From (1),

Side = 5 m

Area of a = 5² = 25 m²

2)

Length b is in a triangle:

Using the Pythagorean theorem.

b² = 3² + 4²

b² = 9 + 16

b² = 25

b = 5 m _____(1)

3)

Length b is in a square:

From (2),

c = 7.94 m

4)

Figure d is a triangle.

Using the Pythagorean theorem.

c² + 9² = 12²

c² = 144 - 81

c² = 63

c = 3√7 m

c = 7.94 m _____(2)

Area = 1/2 x 9 x 7.94

Area =  35.73 m²

Thus,

Area of a = 25 m²
Length of b = 5 m

Length of c = 7.94 m

Area of d = 35.75 m²

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Answer:

(x - 1)^2 + (y + 3)^2 = 400.

Step-by-step explanation:

Your equation is correct.

The center of the circle is (1, -3), which is the midpoint of the diameter. The diameter is 20, so the radius is 10. The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values, we get:

(x - 1)^2 + (y + 3)^2 = 10^2

Simplifying the right side, we get:

(x - 1)^2 + (y + 3)^2 = 100

Therefore, the equation of the circle is (x - 1)^2 + (y + 3)^2 = 400.

Answer:

Step-by-step explanation:

To solve the polynomial P(m) = -m + 5m² - 8m + 4m⁵ - 8m⁰, we can simplify the expression by combining like terms:

P(m) = 4m⁵ + 5m² - 9m - 8

Therefore, the simplified form of the polynomial is P(m) = 4m⁵ + 5m² - 9m - 8.

Answer:p=\frac{4m^5+5m^2-9m-8}{m};\quad \:m\ne \:0

Step-by-step explanation:

According to the given information the Minimize equation is

Z = 110X11 + 120X12 + 120X21 + 130X22.

What is Statistics ?

Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It provides methods and techniques to make sense of complex data sets, to draw conclusions and make decisions based on the data. Statistics can be applied to a wide range of fields, including business, economics, social sciences, medicine, and many others. Some key topics in statistics include probability theory, hypothesis testing, regression analysis, and data visualization.

Minimize:

Z = 110X11 + 120X12 + 120X21 + 130X22

Subject to:

X11 + X12 ≤ 1500 (capacity constraint for Amarillo)

X21 + X22 ≤ 3300 (capacity constraint for Charlotte)

X11 + X21 ≥ 2100 (demand constraint for Detroit)

X12 + X22 ≥ 1000 (demand constraint for Atlanta)

where:

X11 = number of components produced in Amarillo and supplied to Detroit

X12 = number of components produced in Amarillo and supplied to Atlanta

X21 = number of components produced in Charlotte and supplied to Detroit

X22 = number of components produced in Charlotte and supplied to Atlanta

Therefore, according to the given information the Minimize equation is

Z = 110X11 + 120X12 + 120X21 + 130X22

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The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:

Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory

Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.

5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:

Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead

Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:

Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor

Without knowing the value for direct labor, we cannot compute the overhead cost.

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Therefore , the solution of the given problem of function comes out to be the number of tractors that  should be produced to incur minimum cost is 500.

The study of numbers and their variables, as well as our surrounds, structures, and both real and imagined locations, are all included in the mathematics curriculum. A function is a visual representation of the relationship between the quantities of inputs and the corresponding outputs for each. Simply described, a function is a collection of inputs that, when integrated, produce unique outputs for each input. Each role is given a country, city, or scope (also known as a realm).

Here,

The total cost function is:

C(x) = 23000 - 20x + 0.02x²

To find the minimum cost, we need to find the value of x that minimizes the total cost.

One way to do this is to find the vertex of the parabola that represents the total cost function.

The vertex of the parabola y = ax² + bx + c has an x-coordinate of -b/2a and a y-coordinate of c - b²/4a.

In this case, a = 0.02, b = -20, and c = 23000.

So, the x-coordinate of the vertex is:

x = -b/2a = -(-20)/(2 × 0.02) = 500

The minimum cost occurs at this x-value, so the number of tractors that should be produced to incur minimum cost is 500.

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