Subtract 9/10-2/5 what is the answer?

Answer:

a) 3 to 4

b) 3 : 4

\(\sf \dfrac{girls }{boys} = \dfrac{3}{4}\)

Notice that girls = 3, boys = 4

So, Ratio of girls to boys can be rewritten as 3 : 4 and 3 to 4

Fractions are usually represented in ratio like

So

here

Answer:

The nth term rule of the quadratic sequence is \(2n^{2} +5n-3\).

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by =  \(an^{2}+bn+c\)

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a  =  \(\dfrac{4}{2}\) = 2

SO, the first term of the nth term rule equation is \(an^{2}\) = \(2n^{2}\).

Now, in the term \(2n^{2}\), put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then \(2n^{2}\) = \(2 \times (1)^{2}\) = 2

If n = 2, then \(2n^{2}\) = \(2 \times (2)^{2}\) = 8

If n = 3, then \(2n^{2}\) = \(2 \times (3)^{2}\) = 18

If n = 4, then \(2n^{2}\) = \(2 \times (4)^{2}\) = 32

If n = 5, then \(2n^{2}\) = \(2 \times (5)^{2}\) = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is \(2n^{2} +5n-3\).

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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The probability that it weighs more than 51 pounds exactly 53 pounds.

Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.

We need to find the probability that it weighs more than 51 pounds,

P(X = 53) = 0

z = (51 - 50) / 0.5 = 2.00

P(X > 51) = P(z > 2.00) = 0.0228

z1 = (49 - 50) / 0.5 = -2.00

z2 = (51 - 50) / 0.5 = 2.00

P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544

Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.

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The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.

The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:

High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.

Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.

Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.

Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.

Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.

However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.

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Answer:7/12

Step-by-step explanation:

. Means x 6/

8

- 1/

6

= 6 · 3/

8 · 3

- 1 · 4/

6 · 4

= 18/

24

- 4/

24

= 18 - 4/

24

= 14/

24

= 2 · 7/

2 · 12

= 7/

1

Answer:

Step-by-step explanation:

D. No solution

This is simply because -3x-6 cannot equal -3x-7 because -6 and -7 are different numbers therefore x is a false statement.

Answer:

5 & -4

4 & -3

3 & -2

2 & -1

Step-by-step explanation:

5 + (-4) = 1

4 + (-3) = 1

3 + (-2) = 1

2 + (-1) = 1

Sheena receives change of $7.55 after paying $20 bill.

Information is graphically represented in a bar graph. To represent value, it makes use of bars that stretch to various heights. Vertical bars, horizontal bars, grouped bars (multiple bars that compare values in a category), and stacked bars can all be used to create bar graphs.

Therefore,

Sheena buys three items, one sandwich and two pretzels.

Given the rate of sandwich = $6.95

Rate of pretzels = $2.75 each

So rate of two pretzels = $2.75 x 2 = $5.5

Total amount paid = $20

To find the change she receives ,

Total payment paid - total amount of items

Total amount for items = $6.95 + $5.5

                                     = $12.45

Change receives = $20 - $12.45

                            = $7.55

Therefore the change Sheena receives is : $7.55.

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Using a scale factor of 3 to draw the diagram simply mean the length will be tripled. Let us use 3 of those boxes to represent 1 in our graph therefore tripled the the length can be represented below

The angles ∠DEF and ∠JKL are congruent , option(D) is correct .

Two or more angles are said to be Congruent , if they are identical to each other , OR in other words ,

the angles that have equal measure are said to be Congruent .

For Example : if ∠ABC = 60° and ∠DEF = 60°  then both the angles are congruent .

In the question ,

it is given that

the measure of ∠ABC = 120°

∠DEF = 45°

∠GHI = 30°

∠JKL = 45°

As we can see that ∠DEF and ∠JKL have equal measure of 45° , hence they are congruent .

Therefore , the angles ∠DEF and ∠JKL are congruent , option(D) is correct .

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The base price is $300 and $20 per guest, then the initial value will be equal to $300.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Base price = $300

Price per guest = $20 for up to 30 guests.

Then, the equation according to this will be,

$300 + $20(x)

Here, x is the number of guest, which is not more than 30.

Also, the initial value will be equal to the base value, which is 300.

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Answer:

The y-intercept is -4

y= -2/3 + (-4)

The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

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Answer:

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(30-30) = 40 RIGHT THE SIMILAR FROM 60 -40 AND CALCULATE ALL OF IT +4

ANSWER: 405

Where we used the rule

Similarly,

And

Therefore, the answers are options C and E

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer:

203/297 as a (Decimal: 0.683502)

Step-by-step explanation:

have a wonderful day <3

Answer:

203/297

Step-by-step explanation:

First we make both numbers into improper fractions

3 2/9 = 29/9

4 5/7 = 33/7

When you dividing fractions, you multiply the first fraction by the reciprocal of the second fraction.

29/9 * 7/33 =

203/297

Answer:

20 hours

Step-by-step explanation:

400 divided by 20 is 20

Answer:

Time taken = 20 hours

Step-by-step explanation:

Speed  = distance travelled / time taken

20 mi/hr = 400 mi / time taken

Time taken = 400 mi / 20

Time taken = 20 hours

Answer: C; 5.32

Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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For eliminate a variables we need addition method or elimination method.

In an equation or formula, a variable is a symbol or letter that stands in for an unknowable or varying quantity or value.

We can multiply the second equation by -2, so that the coefficient of x in both equations will be the same but with opposite signs:

⇒ 4x - 9y = 8

⇒ -4x - 6y = -48

Add the two equations together: ⇒ -15y = -40

⇒ y = 8/3

Substitute this value of y back into either equation to solve for x.

⇒ 4x - 9(8/3) = 8

⇒ 4x - 24 = 8

⇒ x = 8

Therefore, the steps to eliminate a variable in this system using the addition method are to multiply the second equation by -2, add the two equations together to eliminate the x variable, solve for y, and then substitute that value back into either equation to solve for x.

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a. The marginal profit function Py is Py = -30x + 47y - 915 and

b. Change in profit if price increase by 1 cent is 831 cents.

To find the marginal profit functions Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.

Given:

P(x, y) = (x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)

a. Marginal profit function Px:

To find Px, we differentiate P(x, y) with respect to x while treating y as a constant:

Px = ∂P/∂x = (∂/∂x) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Px = (55 - 4x + 5y) + (x - 40)(-4) + (70 + 5x - 7y)(5)

Simplifying further:

Px = 55 - 4x + 5y - 4x + 40 + 350 + 5x - 7y

Combining like terms:

Px = 355 - 3x - 2y

b. Marginal profit function Py:

Similarly, to find Py, we differentiate P(x, y) with respect to y while treating x as a constant:

Py = ∂P/∂y = (∂/∂y) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Py = (x - 40)(5) + (70 + 5x - 7y)(-7) + (y - 45)(5)

Simplifying further:

Py = 5x - 200 - 7y - 490 - 35x + 49y + 5y - 225

Combining like terms:

Py = -30x + 47y - 915

This is the profit function Py.

b. Estimating the daily change in profit:

To estimate the daily change in profit, we need to evaluate Px and Py at the given prices and calculate the change in profit when the prices are increased as specified.

Given initial prices:

First brand price (x) = 70 cents

Second brand price (y) = 73 cents

To estimate the change in profit, we substitute the initial prices into Px and Py and calculate the results:

Px(70, 73) = 355 - 3(70) - 2(73)

          = 355 - 210 - 146

          = -1

Py(70, 73) = -30(70) + 47(73) - 915

          = -2100 + 3431 - 915

          = 416

The daily change in profit can be estimated by multiplying the changes in price (1 cent for the first brand and 2 cents for the second brand) with the respective marginal profit functions:

Change in profit = ΔP ≈ Px(70, 73) * 1 + Py(70, 73) * 2

               ≈ -1 * 1 + 416 * 2

               ≈ -1 + 832

               ≈ 831 cents

Therefore, the estimated daily change in profit when the salesperson increases the price of the first label by 1 cent and the price of the second label by 2 cents is 831 cents.

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The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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Answer:

<3=75°

Step-by-step explanation:

Angle 3 and angle 2x+95 are supplementary( supplementary angles add up to 180°)

So <3+2x+95=180

<3+2x=180-95

<3+2x=85( let's call this equation 1)

Next, angle 5 and angle 8x+71 are opposite angles (opposite angles are equal) therefore <5=8x+71

Now, <3 and <5 are co-interior angles(co-interior angles are supplementary)

So <3+8x+71=180

<3+8x=180-71=109

Thus, <3+8x=109(let's call this equation 2)

Now solving equation 1 and 2 simultaneously:

Make <3 the subject of equation 1

<3=85-2x

Put <3=85-2x into equation 2

85-2x+8x=109

6x=24

x=24/6=4

Now, remember that angle 2x+95 becomes

2(4)+95

8+95=103°

Therefore<3=180-105=75°

Answer:

It can be written in interval notation as [-5,5)