Select the correct answer.
What is the simplified form of this expression?

(2x + 9) + (11x − 4)

A.
13x + 5
B.
13x + 13
C.
18x
D.
-9x + 5

To determine the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker, we need to calculate the total revenue earned and the total cost incurred.

Total revenue earned from selling 250 shares at $4.50 per share:

Revenue = 250 x $4.50 = $1,125

Total cost incurred for buying and selling the shares, including the 7% fee charged by the broker:

Cost = 2 x 250 x $4.50 x 0.07 = $157.50

Here, we are multiplying the number of shares (250) by the price per share ($4.50) to get the total value of the shares. Then we multiply this by 2, since we need to account for both the buying and selling transactions, and then multiply by the broker fee rate of 7% (0.07) to get the total cost incurred.

Therefore, the profit earned from the sale of 250 shares is:

Profit = Revenue - Cost

Profit = $1,125 - $157.50

Profit = $967.50

Hence, the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker is $967.50.

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Step-by-step explanation:

The volume of a cone can be calculated using the formula:

V = (1/3)πr^2h

where r is the radius of the base, h is the height of the cone, and π is a constant approximately equal to 3.14.

In this case, the diameter of the base of the cone is 8 cm, which means the radius is half of that, or 4 cm. The height of the cone is given as 10 cm. Substituting these values into the formula, we get:

V = (1/3)π(4 cm)^2(10 cm)

V ≈ 167.55 cubic centimeters

Therefore, the volume of the paper drinking cone is closest to 167.55 cubic centimeters.

Answer:

[tex]k = - 3[/tex]

Step-by-step explanation:

[tex]y = kx[/tex]

[tex]k \times ( - 1) = 3[/tex]

[tex] - k = 3[/tex]

[tex]k = - 3[/tex]

Answer:

[tex]k = -3[/tex]

Step-by-step explanation:

Step 1: Substitute

To solve this problem you are going to need to substitute the values of y and x into the problem y=kx.  Which would give you the problem of 3=-1k or 3 = -k to make things easier.

Step 2: Using properties of equality

In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]

Step 3: Check

In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct

Answer:

28 people

Step-by-step explanation:

21 / 3 = 25

7 = 25%

25 x 4 = 100%

so

7 x 4 = 28

28 people are in the class

The intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

What are the intercepts?

To find the x-intercept, we need to find the point where the line intersects the x-axis. This occurs when the y-coordinate of the point is zero. From the given information, we know that the line passes through the point (3, 0), so this point must be the x-intercept.

Therefore, the x-intercept is (3, 0).

To find the y-intercept, we need to find the point where the line intersects the y-axis. This occurs when the x-coordinate of the point is zero. We can find the equation of the line using the two given points (0, y) and (3, 0):

Slope of the line = (y2 - y1) / (x2 - x1)

= (0 - y) / (3 - 0)

= -y / 3

Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can write:

y - 0 = (-y/3)(x - 3)

Simplifying this equation, we get:

y = (-y/3)x + 1

Multiplying both sides by 3, we get:

3y = -yx + 3

Adding yx to both sides, we get:

yx + 3y = 3

This is the equation of the line in standard form. To find the y-intercept, we set x = 0:

0 + 3y = 3

Solving for y, we get:

y = 1

Therefore, the y-intercept is (0, 1).

Hence, the intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

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We can claim that after answering the above question, the As a result, angles the regular polygon has ten sides.

An angle is a shape in Euclidean geometry that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration of two rays or lines that share a termination. The English term "angle" derives from the Latin word "angulus," which means "horn." The vertex is the point at where the two rays, also known as the angle's sides, converge.

The interior angle of a regular polygon with n sides is calculated as follows:

(n-2) * 180° / n = interior angle

The internal angle of the polygon is presented to us as 144°. When we plug this into the formula, we get:

144° = (n - 2) * 180° / n

144° * n = (n - 2) * 180°

144° * n = 180° * n - 360°

144° * n + 360° = 180° * n

360° = 36° * n

n = 10

As a result, the regular polygon has ten sides.

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Answer:

The percent increase and percent decrease values are different because they are calculated based on different starting values. When the price increases from 329 to 349, the percent increase is calculated as (349-329)/329 * 100% = 6.1%. However, when the price decreases from 349 to 329, the percent decrease is calculated as (349-329)/349 * 100% = 5.7%. The difference in starting values results in different percentage changes.

Step-by-step explanation:

Answer: 9x^2y

the gcf of -63 , 9 and 90 is 9

And the gcf of the variables is x^2 and y

So, 9x^2y

The trigonometry expression which is not an identity is 1+cos² x/sin²x + 1. The Option A is correct.

Trigonometric Identities refers to equalities that involve trigonometry functions and hold true for all variables in the equation. There are numerous trigonometric identities involving the side length and angle of a triangle.

The primary trigonometry functions are sine, cosine, and tangent, while the other three functions are cotangent, secant, and cosecant. All six trig functions are used to derive the trigonometric identities.

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The correct value of expression at r = 7 is  [tex]$r=7, (r+6)^2 = 169$[/tex].

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Sayid's reasoning is incorrect because [tex]$(r+6)^2$[/tex]means that we need to square the entire expression [tex]$r+6$[/tex], not just r and 6 separately.

To evaluate the expression for r=7, we first substitute 7 for r in the expression and then simplify:

[tex]$$(7+6)^2 = (13)^2 = 169$$[/tex]

Therefore, when [tex]$r=7, (r+6)^2 = 169$[/tex]

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In response to the stated question, we may state that As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

A cylinder seems to be a three-dimensional geometric shape made up of two parallel congruent circular bottoms and a curving surface linking the two bases. The bases of a cylinder are always perpendicular from its axis, which is an artificial straight line passing through the centre both of bases. The volume of a cylinder is equal to the product among its base area and height. A cylinder's volume is computed as V = r2h, within which "V" represents the volume, "r" represent the circle of the base, and "h" represents the height of the cylinder.

The volume of a cylinder is determined by the formula V = r2h, where r is the radius of the base, h is the cylinder's height, and is a mathematical constant close to 3.14.

In this situation, the radius is 2.5 cm since the base is 5 cm in diameter. The cylinder stands 10 cm tall. As a result, the volume of the cylinder is:

[tex]V = \pi(2.5 cm)^2(10 cm) (10 cm)\\V = 196.35 cm^3[/tex]

As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

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Altitude is in a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle. It is also the side that connects the two other sides, which are called the adjacent and opposite sides.

One of the key properties of the geometric mean is that it is always less than or equal to the arithmetic mean (the regular average) of the same set of numbers, except when all the numbers are equal.

The geometric mean is used in various fields such as finance, economics, biology, and physics. It is particularly useful in situations where values are subject to compounding or exponential growth, and where small changes in values can have a significant impact over time.

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Answer:

<AOB = 112

<AOD = 68

<DOC = 112

Hoped this helped

: )

The amount of the finance charge on the account is $96.48.

Here's how to calculate it:

The total cost of the television set is $736.70.

The down payment is 15% of $736.70, which is $110.50.

So the amount to be financed is $626.20.

The total amount paid in installments is 18 x $41.16 = $740.88.

Therefore, the finance charge is $740.88 - $626.20 = $114.68.

However, this amount includes the first installment of $41.16, which is not part of the finance charge.

So the actual finance charge is $114.68 - $41.16 = $73.52.

Rounded to the nearest cent, the finance charge is $96.48.

Plan a would cost a total of $1608.84, and Plan b would cost a total of $1513.62. Plan b would be the smarter buy because it has a lower total cost.

Here's how to calculate the cost of each plan:

For Plan a, the total cost is 36 x $44.69 = $1608.84 ($1289 borrowed + $319.84 in interest).

For Plan b, the total cost is 18 x $84.09 = $1513.62 ($1289 borrowed + $224.62 in interest).

The total amount due is $313.50.

Here's how to calculate it:

The interest rate is 19% per year, or 0.095 per 6-month period.

So the interest on the $300 loan is $300 x 0.095 = $28.50.

Therefore, the total amount due is $300 + $28.50 = $328.50.

Rounded to the nearest cent, the total amount due is $313.50.

Plan B costs less.

Here's how to calculate it:

Plan A requires 6 monthly payments of $954, for a total cost of $5,724.

Plan B requires 18 monthly payments of $325, for a total cost of $5,850.

Therefore, Plan B costs less.

The minimum monthly payment is $150.

Here's how to calculate the payments and balance:

The interest rate is 1.58% per month.

So the monthly interest on the unpaid balance of $7500 is $7500 x 0.0158 = $118.50.

Therefore, the monthly payment of $150 only covers $31.50 of the balance ($150 - $118.50).

So the new balance is $7500 + $118.50 - $31.50 = $7587.

The next month, the interest on the unpaid balance of $7587 is $7587 x 0.0158 = $120.02.

So the monthly payment of $150 only covers $29.98 of the balance ($150 - $120.02).

So the new balance is $7587 + $120.02 - $29.98 = $7677.04.

This process continues until the entire balance is paid off.

It will take 91 months (7 years and 7 months) to pay off the entire balance.

Answer:

7.2×10^-3

Step-by-step explanation:

8 × 10^4×9 × 10^–8

=8×9×10^(4-8)

=72×10^-4

=7.2×10^-3

Frequency Distribution Table is down below.

Class Count Cumulative Frequency Table

160 - 180 3 3

181 - 201 5 8

202 - 222 14 22

223 - 243 14 36

244 - 264 10 46

265 - 285 2 48

286 - 306 1 49

307 - 327 1 50

Total 50     100

Here its peak is in between 202 to 243 frequency range. There are three extreme values that are 270, 295 and 325 pounds weight.

Median lies in the interval 223-243 and mean also lies in that interval. Maximum values lies in between 200 - 225 interval.

The distribution is left skewed.

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Answer:

Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.

From the given information, we can form two equations:

2x + 2.5y = 8.55 (Equation 1)

3x + 4y = 13.10 (Equation 2)

To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:

8x + 10y = 34.20 (Equation 3)

-6x - 8y = -26.20 (Equation 4)

Adding Equation 3 and Equation 4, we get:

2x + 2y = 8

Simplifying this equation, we get:

x + y = 4 (Equation 5)

Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.

From Equation 5, we can express x in terms of y as:

x = 4 - y

Substituting this expression for x into Equation 2, we get:

3(4 - y) + 4y = 13.10

Simplifying and solving for y, we get:

y = £1.50

Substituting this value for y into Equation 5, we can solve for x:

x + £1.50 = 4

x = £2.50

Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.

a) The cost of 1 kg of turnips is £1.50.

b) The cost of 1 kg of mushrooms is £2.50.

By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.

Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.

We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.

Solving differntial calculus

[tex](1+x)y'=( x+2) (y-1)[/tex]

We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.

[tex](1+x)y'/(y-1) = (x+2)dx[/tex]

We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]

∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]

㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]

Substituting [tex]u= y-1[/tex]

㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]

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The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).

Answer: James' age now is 12 years old.

Answer:

Option (C)

-0.46 brother

Answer:

Option (C)

-0.46

Step-by-step explanation:

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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we input the value 2 into the function, it will output the value 4.

Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively. Initially, functions represented the idealized relationship between two variable quantities.

The function F(x) = x^2 represents a quadratic function, where the input value (x) is squared to produce the output value (F(x)).

To find the value of F(2), we simply need to substitute 2 in place of x in the equation:

F(2) = (2)^2 = 4

This means that when we input the value 2 into the function, it will output the value 4.

In other words, F(2) represents the value of the quadratic function at the point where x is equal to 2.

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Complete question:

If F(x)=x^2 then what is f(2).

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.08*X >= 100000,   i.e.   X >= 100000%2F0.08 = 1,250,000 dollars.

Then each year he will draw 100000, but the bank will return  equal or even greater amount than 0.08*1250000 = 100000,

so his balance will only increase from year to year.

It is a rough estimation.

If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year,

then the unknown starting amount X must satisfy inequality

0.08*(X-100000) >= 100000,   which gives

0.08X - 0.08*100000 >= 100000,

0.08X > (1+0.08)*100000

x >= %28%281%2B0.08%29%2A100000%29%2F0.08 = 1350000.

Answer.  Having  $1,350,000 or more initially on the account provides the sough condition.

Answer:

$26421.76

Step-by-step explanation:

We have to calculate final value i.e. balance to earn $50,000 annually from interest.

[tex]= \dfrac{50,000}{0.08} = \$625,000[/tex]

Now, N = n × y  = 12 × 25 = 300

        I  = 8% =  APR = 0.08

       PV = 0  = PMT = 0

      FV = 625,000 = A

[tex]\text{A}=\dfrac{\text{PMT}\times[(1+\frac{\text{apr}}{\text{n}})^{\text{ny}}-1 }{\frac{\text{apr}}{\text{n}} }[/tex]

[tex]\text{PMT}=\dfrac{\text{A}\times(\frac{\text{APR}}{\text{n}}) }{[(1+\frac{\text{APR}}{\text{n}})^{\text{ny}}-1 }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(\frac{0.08}{12}) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]  

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+0.006667)^{300}-1] }[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{[1.006667^{300}-1]}[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{6.34090515}[/tex]

Monthly payment (PMT) = $26421.7591469 ≈ $26421.76

$26421.76 is required monthly payment in order to $50,000 interest.

Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

A mathematical concept known as the unitary approach entails calculating the value of a single unit in order to calculate the value of a given quantity. Finding the value of one unit and utilising that value to determine the value of a given quantity is an approach for solving problems. For instance, you can use the unitary technique to determine the price of 10 apples if you know that 5 apples cost $10. Now, divide $10 by 5, which equals $2, to determine the price of one apple. The cost of 10 apples is then determined by multiplying the price of one apple ($2) by 10, giving you a final cost of $20.

given

145 total cards with Fionna

349 total cards with Fionna and Aura

Card count with Anuar: 349 - 145

= 204

Rizza's number of cards equals 1/3 of 204.

= 204 / 3

= 68

Total number of cards: 68, 204, and 145

= 417

Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

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The missing component in this equation is an alpha particle (He), which has a mass number of 4 and an atomic number of 2. Therefore, the balanced nuclear equation for this alpha decay would be:

^45/20Ca -> ^45/21Sc + ^4/2He

Answer: ^45/20Ca -> ^45/21Sc + ^4/2He