There are 61 guests at a party. There are 17 more men than women. How many women are at the party?

Answer:

10x+15y-10

Step-by-step explanation:

5(2x+3y-2)

=10x+15y-10

Answer: Pretty much correct except one thing is wrong.

Step-by-step explanation:

In place of CB you should write AB because the sides doesn't match when you flip the triangle CED.

Hope it helps!

Answer:

Step-by-step explanation:

You want two integers with a product of 36 such that one is 3 less than 5 times the other.

Let x be "the other" integer. Then one is (5x-3), and the product is ...

  x(5x -3) = 36

  5x² -3x = 36 . . . . . . eliminate parentheses

  x² -0.6x = 7.2 . . . . . . . divide by 5

  x -0.6x +0.09 = 7.29 . . . . . add (0.6/2)² to complete the square

  (x -0.3)² = 7.29

  x = 0.3 +√7.29 = 0.3 +2.7 = 3

  5x -3 = 5·3 -3 = 12

The two integers are 12 and 3.

Answer:

To calculate the angle, you would need to use the tangent of an angle formula: tan(θ) = 107/260. Solving for θ yields an angle of 29.4 degrees. You would have to look up at an angle of 29.4 degrees to see the tip of the lighthouse.

To do trigonometry, you need to have a clear understanding of triangles and the relationships between their sides and angles. To do trigonometry without images or diagram, let's go straight to the explanation below.

When solving trigonometry word problems without a drawing/image, the following steps can be helpful:

It is important to note that in order to use trigonometry, you need to have a clear understanding of triangles and the relationships between their sides and angles.

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The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.

To find the dimensions of the wall find the dimensions of the rectangles given in the figure. Calculate the area of the rectangle and factorize the resultant equation for the value of 'x'. Calculate the dimensions of the wall by using the number of panels along the height and top.

Here we have  

A wall has paneling made up of rectangles

Area of the rectangle = 30 square feet  

Given that the edge of each rectangle in the paneling is (2x+3) feet in width and (4x+2) feet in height.  

Area of the rectangle = (2x + 3)(4x +2) = [ 8x²+ 16x + 6 ]  

Given that area of the rectangle = 30 ft²  

=> 8x²+ 16x + 6 = 30

=> 8x²+ 16x - 24 = 0  

=> x² + 2x - 3 = 0

=> x² + 3x - x - 3 = 0

=> x(x + 3) - (x + 3) = 0

=> (x + 3)  (x - 1) = 0

=> x = -3 and  x = 1  

We need to x = 1  [ since height can't be taken in negative ]

Dimensions of the rectangle,

Width, 2x + 3 = 2(1) + 3 = 5 feet

Height, 4x + 2 = 4(1) + 2 = 6 feet

Given that there are 4 rectangles along the height

Height of the wall = 4 × 6 = 24 feet

There are 3 rectangles along the top.

Width of the wall = 3 × 5 = 15 feet

Therefore,

The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.

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The amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:

$3,062.

The amount of tax is obtained identifying the correct position in the table in this problem.

The person in this problem is the head of the household, meaning that we should observe the last column of the table.

As income of $27,811 is between $27,800 and $27,850, hence, looking at the fourth-to-last row, the amount of tax owed by a head-of-household taxpayer with a taxable income of $27,811 is given as follows:

$3,062.

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Answer:

⁵/₄ or 1.25

Step-by-step explanation:

Firstly, represent the number as a fraction:

0.8 = ⁸/₁₀ = ⁴/₅

Then, simply flip the top and bottom:

The reciprocal of ⁴/₅ is ⁵/₄

⁵/₄ = 1.25

According to the random survey, the majors chosen by the freshmen of our university were:

To get a better understanding of the proportions of students choosing certain majors, universities can survey a sample of their entering freshmen. This survey should be representative of the population, so it should be conducted using a randomized sampling technique.

The survey should ask questions about the major the student is planning on pursuing and other relevant information, such as the student's interests and motivations.

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As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.

Given that it has three sections and three corners, a triangle qualifies as a polygon. It corresponds to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle only with vertices A, B, and C. Once the points are not collinear, a unique plane and triangular in Geometric forms are discovered. Triangles are polygon because they have three parts and three corners. The points where its three sides of the triangle converge are referred to as the triangle's corners. Three pyramid angles are multiplied ta yield 180 °.

given

Provided that segment AD is an altitude, AD in triangle ABC is perpendicular to hypotenuse BC.

Triangle DAC is a right triangle, as it should be. As the acute angles of a right triangle are complementary, the measures of angle C and angle DAC add up to 90 degrees.

The same holds true for angles C and CBA's measurements.

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The optimal solution amount will increase by the amount that the additional 10 units of the second constraint can be used to benefit the overall solution.

The optimal solution amount will increase with the addition of 10 units to the second constraint. This is because the additional 10 units can be used to benefit the overall solution by providing more of the resources that are necessary to reach the optimal solution. For example, if the second constraint is a limit on the amount of a certain resource that can be used, then the additional 10 units can be used to increase the amount of resources available, which can lead to a better overall solution. In addition, the additional 10 units can also be used to increase the efficiency of the solution, by allowing the solution to use the same amount of resources more efficiently.

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Answer: To calculate the amount of simple interest, we use the formula: I = P * r * t, where P is the principal amount (7500), r is the annual interest rate (5%) and t is the time in years (5).

So, the simple interest is: I = 7500 * 5 * 0.05 = 187.5

The total amount Susan will have to pay back to the bank is the principal amount plus the interest:

7500 + 187.5 = $76 87.5

Therefore, Susan will pay the bank back $76 87.5 after 5 years.

Step-by-step explanation:

Grace read 4/7 of the book at night.

To solve this problem, we need to use the fractions to calculate the amount of the book that Grace read in the morning and the amount of the book that she read at night.

The total amount of the book that Grace read in the day is 1/3 + 2/5 = 7/15.

Since she read 1/3 of the book in the morning, then the amount of the book that she read at night is 7/15 - 1/3 = 4/15.

To calculate the amount of the book that she read at night as a fraction of the total book, we need to divide 4/15 by 7/15.

4/15 ÷ 7/15 = 4/7

Therefore, Grace read 4/7 of the book at night.

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Answer: 0.73

Step-by-step explanation: Because finding the absolute value only means finding how far away a number is from 0 on a number line, the answer is 0.73.

The water level in the tank will take x = 30 minutes to decrease from 15 inches to 9 inches deep. It will take 6 minutes for the water level to decrease by 0.5 inches.

The water level in the tank is currently 15 inches deep and is decreasing by 0.5 inches every minute. In order to determine how many minutes, x, it will take for the water level to measure 9 inches deep, we will need to calculate the difference between the current water level and the desired water level. To do this, we need to subtract 9 inches from 15 inches, and this will give us a difference of 6 inches. Now, since the water level is decreasing by 0.5 inches per minute, we need to divide 6 inches by 0.5 inches, which will give us 12 minutes. Since 12 minutes is equal to 2 intervals of 6 minutes, the water level will take x = 30 minutes to decrease from 15 inches to 9 inches deep.

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The repairs and maintenance charges for this vehicle are 207 dollars and 0 cents.

Operating costs are continuous expenses paid as a result of the usual day-to-day operations of an organization. Operating costs comprise both the cost of goods sold and additional operating expenditures, which are sometimes referred to as selling, general, and administrative costs.

here, we have,

From the data provided in the table, we can deduce the repair and maintenance charges of the vehicle.

The name of Car 8 implies that they are talking about Version V-8 of the Sedan Car.

Year-driven third implies the third year which alludes to the 6th column of the table.

Number of miles driven = 9000

From the repair and maintenance cents per mile in the table:

The total cost for this service = number of miles driven × repair and maintenance cost

The total cost for this service = 9000 × 2.3

The total cost for this service = 20700 cents

The total cost for this service in dollars and cents  

= $207.00

The total cost for this service is 207 dollars and 0 cents.

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As per arithmetic progression the value of 15th term is 0.

An arithmetic progression, or A.P., is a sequence of numbers in which the difference between consecutive terms is constant.

To start, let's call the common difference "d" and the first term "a". We can use the formula for the nth term of an A.P., which is Tn = a + (n-1)d, where Tn is the nth term and n is the position of the term in the A.P.

Using this formula, we can find the 6th term and 9th term. For the 6th term, T6 = a + (6-1)d = a + 5d. For the 9th term, T9 = a + (9-1)d = a + 8d.

Now, using the information given, we can create an equation: 6(a + 5d) = 9(a + 8d). Expanding both sides and simplifying, we get:

6a + 30d = 9a + 72d

Subtracting 9a from both sides, we get:

-3a + 30d = 72d

Subtracting 30d from both sides, we get:

-3a = 42d

Dividing both sides by -3, we get:

a = -14d

Now that we have found the value of "a", we can use the formula for the nth term again to find the 15th term. T15 = a + (15-1)d = -14d + 14d = 0.

So, the 15th term of the A.P. is 0.

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Answer:

D. [tex]56.25 mm^{2}[/tex]

Step-by-step explanation:

A = [tex]\frac{A + 2}{2}[/tex]h =

[tex]\frac{16 + 9}{2}[/tex]x4.5

Thus,

=56.25

Option D.

Answer: 2,4,6

Step-by-step explanation: All of these have x=3 as a solution.

Answer:

Step-by-step explanation:

6=2x

x^2=9

x-3=0

The conditional probability that the previous state was state 2 given that the chain is currently in state 1 is equal to the probability of transitioning from state 2 to state 1.

The conditional probability of transitioning from one state to another in a Markov Chain is dependent on the transition probabilities between the states. In this case, the conditional probability of transitioning from state 2 to state 1 is equal to the probability of transitioning from state 2 to state 1. This probability can be determined by looking at the transition matrix of the Markov Chain. The transition matrix specifies the probability of transitioning from one state to another. Therefore, the conditional probability of transitioning from state 2 to state 1 given that the chain is currently in state 1, is equal to the probability of transitioning from state 2 to state 1 as specified in the transition matrix.

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Step-by-step explanation:

Assuming it is a constant speed of 50km/h

So you travel 50km in one hour

So if you want to go 100km traveling at the constant speed of 50km it will take two hours as you are going 50km for one hour it will take two hours to go 100km.

The steps to conduct a statistical survey are given below.

A statistical survey is any structured inquiry designed to obtain aggregated data, which may be qualitative or quantitative where the individual or corporate identities of the respondents are in themselves of little significance.

Given is to conduct a statistical survey.

The steps to conduct a statistical survey are given below -

Therefore, the steps to conduct a statistical survey are given above.

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{Question in english -

How to conduct a statistical survey}

Answer:

2.44π cm²

or

7.68 cm²

Since the choices are not shown, I do not know whether the choices are in terms of π or totally numeric Choose one of the two above. They are both the same value

Step-by-step explanation:

Area of a circle of radius r is  A = πr²

An entire circle encompasses 360°

If a sector of the circle has an angle of Фat the center, the area of the sector is Ф/360 x πr²

Given r = 4 and Ф = 55°

Area of this sector = 55/360 x π (4)² = 55/360 x 16 x π = 2.44π

2.44π = 7.68 cm²

From the given triangle, the lengths of AB and PB becomes: 9 cm and 4 cm respectively.

Tri-, which means "three," and angulus, which means "angle or corner," are the origins of the Latin word triangulus, which means "three-cornered" or "having three angles." A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. 180 degrees is the summation of the triangle's three angles.

In ΔAPC and ΔABC

∠ABC = ∠ACP and ∠BAC = ∠CAP

∴ ΔABC ≅ ΔACP

Because ∠ABC = ∠ACP, thus ∠A = ∠A, so, ∠ABC = ∠ACP

As, ΔABC ≅ ΔACP

∴ AB = BC = AC = CP  (the corresponding sides of a similar triangle are proportional)

∵ BC = 12, AC = 6, CP = 8

∴ AB = (6/8) × 12

or, AB = 9 cm

as, ΔABC ≅ ΔACP

∴ AP : AC = AC : AB

or, AP = (6/9) × 6

or, AP = 4 cm

next, PB = AB - AP

PB = 9 - 4 cm

PB = 5 cm

Thus, the lengths of AB and PB becomes: 9 cm and 4 cm respectively.

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The complete question is as follows:

The new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero.

When a problem is in canonical form and the associated basic feasible solution is degenerate, this means that one of the basic variables has a value of zero. If the pivot operation is then performed with the basic variable with a value of zero extracted from the basis, the new basic feasible solution will have x\ as a non-basic variable and a new basic variable with a value not equal to zero. This is because the pivot operation involves exchanging the extracted basic variable with one of the non-basic variables. Therefore, the new basic feasible solution will not be degenerate, as the new basic variable will have a value not equal to zero.

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Answer & Step-by-step explanation:

To simplify the expression 3a + 6b - 8a + 9b, we can combine the like terms (terms with the same variable).

First, we can combine the 3a and -8a terms since they have the same variable 'a'. When we subtract 8a from 3a, we get -5a.

Then, we can combine the 6b and 9b terms since they have the same variable 'b'. When we add 6b and 9b, we get 15b.

Putting it all together, we get:

3a + 6b - 8a + 9b = -5a + 15b

Therefore, the simplified expression is -5a + 15b.

3a+6b-8a+9b

9b+6b-8a+3a

15b-5a

5(3b-a)

Answer:

Step-by-step explanation:How do you find the gradient and y-intercept?The equation y = mx + c is the general equation of any straight line where m is the 

The cost for sending the parcel with each company is £72 via WeGoFast and £80 by ParcelsFly.

In product, exploration, retail, and account, a cost is the value of plutocrat that has been used up to produce commodity or deliver a service, and hence isn't available for use presently. In business, the cost may be one of accession.

Hector needs the parcel to be send.

Dimension for his cuboid parcel is given by 10 cm by 10 cm by 40 cm.

10cm x 10cm x 40cm

Sum of the three dimension in cm

= (10 + 10 + 40) cm

= 60 cm.

Volume of the parcel in  = (10 × 10 × 40)  = 4000 cm³

Price charge by WeGoFast

= Sum of the three dimensions in cm × £1.20

= £ (60 × 1.20) = £72.

Price charged by ParcelsFly

= Volume measured in  × £0.02

= £ (4000 × 0.02) = £80

Therefore, The cost of sending the parcel with each company is £72 by WeGoFast and £80 by ParcelsFly.

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The quadratic equation has the following three features:

B. 7 is the coefficient of one term of the expression.

C. x is a variable in the expression.

D. The expression has three terms.

In this question we have the case of a quadratic equation in standard form, whose features must be understood by direct inspection. At first sight we get the following conclusions:

Lastly, we get the following roots from the quadratic equation:

x² + 7 · x + 6 = 0

(x + 1) · (x + 6) = 0

x = - 1 or x = - 6

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