1. There were 45 more crossword puzzle books than jigsaw puzzles. 5/9 of the crossword puzzle books and 25% of the jigsaw puzzles were sold. Among the items sold, there were 91 more crossword puzzle books than jigsaw puzzles. How many crossword puzzle books and jigsaw puzzles remained in total?

2. In a warehouse, 60% of the table lamps were 30 more than 80% of the standing lamps. Given that there were a total of 155 table and standing lamps in the warehouse at first, how many table lamps were left if 30% of them were removed from the warehouse?

Answer:

Step-by-step explanation:

area of circle = pi*r^2

pi * 36 = 36pi = 113.04 which is about 113

Answer:

area= 39 square meters

Step-by-step explanation:

10×6=60m²

60m²÷2=30m² is the area of the bigger triangle

6×3=18m²

18m²÷2=9m²

9m²+30m²=39m²

Answer:2nd one

Step-by-step explanation:

For the given rectangular prism dimensions, the area of each base is obtained by multiplying the length and width.

1. Area of each base:

The area of a rectangular base is calculated by multiplying the length by the width. Therefore:

- The area of the base with dimensions 8 ft by 6 ft is 48 square feet.

- The area of the base with dimensions 10 ft by 15 ft is 150 square feet.

2. Lateral area:

The lateral area of a rectangular prism is the sum of the areas of all its sides, excluding the base areas.

- For the given dimensions, the lateral area would be (8 ft + 6 ft) × 2 + (10 ft + 15 ft) × 2 = 36 ft + 50 ft = 86 square feet.

The lateral area is calculated by adding the perimeter of the bases and multiplying it by the height of the prism, excluding the base areas.

For more questions on area, visit:

https://brainly.com/question/25292087

#SPJ11

Answer:

42/11

Step-by-step explanation:

11/7 = 6/v

cross multiply:

11v = 6x7 = 42.

v = 42/11 ≈ 3.81

To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.

First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):

W(y1, y2) = | y1 y2 |

| y1' y2' |

We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:

y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))

y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))

Substituting these values into the Wronskian:

W(y1, y2) = | sin(x) / √x cos(x) / √x |

| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |

Expanding the determinant:

W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))

Simplifying:

W(y1, y2) = -1 / (2√x)

Now, we can find the particular solution using the variation of parameters formula:

y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx

Here, g(x) = 3x√xsin(x). Substituting the values:

y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx

Simplifying the integrals:

y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)

Integrating:

y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C

Simplifying:

y_p(x) = 3x(sin^2(x) - cos^2(x)) + C

The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:

y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C

where C1, C2, and C are arbitrary constants.

Answer: 62.83

Step-by-step explanation:

The formula for the circumference of a circle is C = 2 π r

So, let’s set up our equation.
2 •π •10 (your radius is 10!)

Now just multiply it together.

2 • π • 10 = 62.83 ft^squared

Hopefully this is what you were looking for. :)

[tex]\frac{f(x)}{g(x)} =\frac{-10x}{x+3\\}\\ (\frac{f}{g} )(2)=\frac{-10(2)}{2+3}\\ \\\frac{-20}{5} =-4[/tex]

Answer is -4

The value of midpoint M of AB is,

⇒ M = (2, - 4)

Since, A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

Coordinates of A and B are,

A = (- 3, - 1)

B = (- 7 - 7)

Hence, By definition of midpoint we get;

M = (- 3 + (- 7))/2, (- 1 + (- 7))/2

M = (4/2, - 8/2)

M = (2, - 4)

Thus, The value of midpoint M of AB is,

⇒ M = (2, - 4)

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ1

The volume of a cone is given by the formula V = (1/3)πr²h, where "V" is the volume of the cone, "r" is the radius of the base, and "h" is the height of the cone.

If the cone is exactly half full of water by volume, then the volume of water is equal to half the volume of the cone. Let's call this volume "Vw".

So, Vw = (1/2) V

Substituting the formula for the volume of a cone, we get:

(1/3)πr²h(water) = (1/2) (1/3)πr²h(cone)

Simplifying, we get:

h(water) = (1/2) h(cone)

Therefore, the depth of the water in the cone is half the height of the cone.

Answer:

7 duckpin utuyuuuu I have no idea where to watch the video is not a good day at work now and

176° is the measurement of the angle asked.

From the Theorem,

An angle at the circumference of a circle is half the angle at the center subtended by the same arc.

The desired angle will be equal to twice the angle WYX

Thus,

Angle made by the arc = 2 * 88

Angle made by the arc = 176°

Learn more about the chord theorem here:

https://brainly.com/question/15298662

#SPJ1

Answer:

Step-by-step explanation:

10 : 25

then simplifies

2:5

The probability of this occurring is around 0.0714.

In order to determine the likelihood that an adolescent would play the lead role in each of Britney's four films, we must take into account both the total number of possible outcomes and the number of favourable possibilities.

There are 8 films scheduled in total.

Five films have had a teenager as the primary character.

Calculating the ratio of the number of favourable outcomes—all four films with teenagers—to the entire number of possible outcomes—any four films—will help us determine the probability.

The combination formula, sometimes referred to as "n choose r," shows how many different methods there are to choose 4 films from the available 8 options:

[tex]C(n, r) = n! / (r! * (n - r)!)[/tex]

In this case, we want to select 4 movies out of the 5 movies featuring a teenager:

[tex]C(5, 4) = 5! / (4! * (5 - 4)!) = 5[/tex]

The total number of ways to select any 4 movies out of the 8 total movies is:

[tex]C(8, 4) = 8! / (4! * (8 - 4)!) = 70[/tex]

Therefore, the likelihood that a teenager will play the lead role in each of the four films that Britney cleans up after is:

Probability is calculated as follows: 5 / 70 (rounded to four decimal places) = 0.0714 (Number of favourable outcomes / Total number of probable outcomes).

Therefore, the chance is around 0.0714.

For more such questions on deciaml places.

https://brainly.com/question/28393353

#SPJ8

The number of adult tickets sold were 80.

Let's denote the number of adult tickets sold as A and the number of student tickets sold as S.

The number of student tickets sold was two times the number of adult tickets sold:

S = 2A

We also know that the total number of tickets sold was 240:

A + S = 240

Substituting the value of S from the first equation into the second equation, we have:

A + 2A = 240

Combining like terms:

3A = 240

Divide both sides of the equation by 3:

A = 80

Therefore, 80 adult tickets were sold.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The value of x in the intersecting chords is determined as 5.

The value of x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

46 = ¹/₂ ( arc 21x - 5  -  arc x + box)

you will need to substitute the value of the box (what is inside the box?), that is the only you can solve it.

Let's say the box = 3

46 = ¹/₂ ( arc 21x - 5  -  (arc x + 3)

46 = ¹/₂ (21x - 5 - x - 3)

2(46) = 20x - 8

92 = 20x - 8

20x = 100

x = 100/20

x = 5

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

Answer:

dy/dx = 2x + 2

Step-by-step explanation:

the slope (gradient) is given by differentiating y = x² + 2x.

dy/dx = 2x + 2

Answer:

Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.

Step-by-step explanation:

To determine the percentage of the course Lucy has ridden so far, we can use the following formula:

Percentage = (Distance ridden / Total distance) * 100

Given that the total distance of the bike course is 88 miles and Lucy has

ridden 22 miles, we can substitute these values into the formula:

Percentage = (22 miles / 88 miles) * 100

Simplifying the equation:

Percentage = (1/4) * 100

Percentage = 25

Therefore, Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.

For more questions on total distance.

https://brainly.com/question/24479741

#SPJ11

Clearer image, please!

Check the picture below.

Answer:

These are all of the formulars for solving Trigonometry:

-sin θ = Opposite Side/Hypotenuse

-cos θ = Adjacent Side/Hypotenuse

-tan θ = Opposite Side/Adjacent Side

-sec θ = Hypotenuse/Adjacent Side

-cosec θ = Hypotenuse/Opposite Side

-cot θ = Adjacent Side/Opposite Side

Here is the visual edition below:

Angle x is 70 degrees, angle y is 110 degrees, and angle z is also 110 degrees.

When two lines intersect, they form four angles known as vertical angles. Given that one angle is 70 degrees, we can determine the degrees of angles x, y, and z.

Vertical angles are congruent, meaning they have the same measure. Thus, angle x is also 70 degrees.

Since angles x and y are linear angle pairs with 70 degrees, their sum is 180 degrees. Therefore, angle y can be calculated as 180 - 70 = 110 degrees.

To find the measure of angle z, we can use the fact that the sum of angles in a straight line is 180 degrees. Angle x and angle z form a straight line, so their sum is 180 degrees. Angle x is 70 degrees, so angle z can be found by subtracting 70 from 180: 180 - 70 = 110 degrees.

In summary, angle x is 70 degrees, angle y is 110 degrees, and angle z is also 110 degrees.

for such more question on Angle

https://brainly.com/question/25716982

#SPJ11

Hello !

28   23   18   13    8  ...

Para ir de izquierda a derecha, restamos 5 cada vez.

Using the sum and difference formula and trigonometric identities the value of tanθ and cosθ are cos(11π/12) = (-√6 + √2) / 4 and tan(11π/12) = 0 respectively.

The identity tan(α + β) = (tanα + tanβ) / (1 - tanα * tanβ) may be used to calculate tan using the sum method.

Here, we have θ = 11π/12, so we need to express it as the sum of two angles.

In this problem, we are given θ = 11π/12 and we can use the sum of two angles.

11π/12 = π/6 + 5π/6

putting the value of α = π/6 and β = 5π/6.

The sum formula of the tangent becomes;

tan(11π/12) = tan(α + β) = (tanα + tanβ) / (1 - tanα * tanβ)

Let's put in the values of α and β:

tan(11π/12) = (tan(π/6) + tan(5π/6)) / (1 - tan(π/6) * tan(5π/6))

The tangent of π/6 and 5π/6 will have values as;

tan(π/6) = √3/3

tan(5π/6) = -√3/3

Let's put in these values into the sum formula;

tan(11π/12) = (√3/3 + (-√3/3)) / (1 - (√3/3 * (-√3/3)))

tan(11π/12) = 0 / (1 - (-3/9))

= 0 / (1 + 1/3)

= 0 / (4/3)

= 0

Therefore, tan(11π/12) = 0.

Part B;

Using difference formula, the value of cosθ can be expressed using the trigonometric identity

cos(α - β) = cosα * cosβ + sinα * sinβ

Since we are given θ = 11π/12;

Let's express this as the difference of two angles

11π/12 = 3π/4 - π/6

Putting the value α = 3π/4 and β = π/6.

Using the difference formula for cosine;

cos(11π/12) = cos(α - β) = cosα * cosβ + sinα * sinβ

Let's plug in the values of α and β

cos(11π/12) = cos(3π/4 - π/6) = cos(3π/4) * cos(π/6) + sin(3π/4) * sin(π/6)

The known values of cosine and sine for 3π/4 and π/6 are;

cos(3π/4) = -√2/2

cos(π/6) = √3/2

sin(3π/4) = √2/2

sin(π/6) = 1/2

Plugging these values into the difference formula;

cos(11π/12) = (-√2/2 * √3/2) + (√2/2 * 1/2)

cos(11π/12) = -√6/4 + √2/4

Combining like terms:

cos(11π/12) = (-√6 + √2) / 4

Therefore, cos(11π/12) = (-√6 + √2) / 4.

Learn more on sum and difference formula here;

https://brainly.com/question/29164562

#SPJ1

Answer:

Apologies, but it seems that the table you mentioned is missing from your question. Could you please provide the table or the weights of the chicken in each package so that I can assist you further?

Step-by-step explanation:

7173 water bottles that can be produced at a production cost of $5,258.

To find the slope (m), we can use the formula:

m = (4582 - 885) / (6280 - 1200)

m = 3697 / 5080

m ≈ 0.7274

Now, let's find the y-intercept (b) using the equation:

b = y - mx

b = 885 - 0.7274 x 1200

b = 885 - 872.88

b ≈ 12.12

Therefore, the equation of line is

y = 0.7274x + 12.12

Now, the production cost of $5,258 means put y= 5258

5258 = 0.7274x + 12.12

5239.88 = 0.7274x

x= 7203

Thus, 7173 water bottles that can be produced at a production cost of $5,258.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ1

The critical value of the given data set is 3.42.

The two-way chi-square analysis is used to determine if there is a relationship between two categorical variables. In this case, the two variables are shiftwork availability and the union-management relationship.

To conduct the analysis, we need to calculate the expected frequencies for each cell in the table. We can do this by multiplying the row and column totals and dividing by the total number of observations.

For the cell in the top left corner (No Shiftwork/Good Relationship):

Expected Frequency = (36 × 33) / 100 = 11.88

We can then calculate the expected frequencies for the other cells in the same way.

Once we have calculated the expected frequencies, we can then calculate the chi-square statistic using the following formula:

Chi-square = Σ [(Observed Frequency - Expected Frequency)² / Expected Frequency]

Using this formula, we can calculate the chi-square statistic for the above example as follows:

Chi-square = (11 - 11.88)²/11.88 + (22 - 21.12)²/21.12 + (25 - 23.12)²/23.12 + (42 - 40.88)²/40.88 = 3.42

Finally, we can compare the chi-square statistic to the critical value of 3.84 at α = 0.05 (df = 1). Since our chi-square statistic is less than the critical value, we can conclude that there is no relationship between shiftwork availability and the union-management relationship.

Therefore, the critical value of the given data set is 3.42.

Learn more about the critical value here:

https://brainly.com/question/14508634.

#SPJ1