Evaluate `int cosec^(2)(7-5x)dx​

Answer:

The nth term of this sequence is \(a_{n} = -2n + 2\)

Step-by-step explanation:

In this sequence we keep adding -2 on to get the next term. This sequence is called an arithmetic sequence, a sequence that uses addition to keep increasing.

The formula for the nth term of an arithmetic sequence is

\(a_{n} = d\) · \(n + a_{1} - d\)

\(a_{1}\) stands for the first term in the sequence, and \(d\) stands for the difference between each number in the sequence.

\(a_{1} = 0\) and \(d\) = -2, so :

\(a_{n} = -2\) · \(n + 0 - (-2)\\\)

\(a_{n} = -2n + 2\)

Therefore, to find the nth term in this sequence you would use the formula

\(a_{n} = -2n + 2\)

The best assessment of the linearity of the relationship between the day of the month and account balance would be "Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month."The correct answer is option C.

When assessing linearity, it is important to examine both the scatterplot and the residual plot. The scatterplot is used to visualize the relationship between the variables, while the residual plot helps us assess the appropriateness of a linear model by examining the pattern of the residuals (the differences between observed and predicted values).

If the scatterplot appears reasonably linear, it suggests that there is a linear relationship between the variables. In this case, since the scatterplot appears linear, it supports the use of a linear model to predict the account balance based on the day of the month.

Furthermore, the residual plot is used to check for any patterns or systematic deviations from the line of best fit. If the residual plot exhibits no obvious pattern and the residuals appear randomly distributed around zero, it indicates that the linear model captures the relationship adequately.

Therefore, if the residual plot shows no obvious pattern, it provides further evidence in favor of using the line of best fit to predict the account balance based on the day of the month.

In conclusion, when the scatterplot appears linear and the residual plot shows no obvious pattern, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.

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Answer:

person above

Step-by-step explanation:

the obvious

If the length of the leg of the isosceles triangle is 17 cm and the base is 16 cm then the length of altitude to the base is  15cm .

An Isosceles triangle is defined as a triangle in which any two side are of  equal length .

The Length of the leg is = 17cm ,

the base of the triangle is = 16cm ;

let the length of the altitude to the base be = x cm ,

The altitude to the base of the triangle divides it into two right angle triangle.

So , in one of the right angle triangles, Base = 16/2 = 8 cm

the Hypotenuse of triangle = length of the leg = 17 cm

By Applying Pythagoras theorem,

we get ,

17² = 8² + x²   ,

289 = 64 + x² ,

x² = 289 - 64

x² = 225 ,

taking Square root(√) on both the sides ,

we get , x = 15 .

Therefore , the length of the altitude to the base is = 15 cm .

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To find the altitude of an isoceles triangle with a base length of 16 cm and a leg length of 17 cm, use the Pythagorean Theorem. Calculate 17² + 16² = c², then solve for c² to get c = √545 = 23.3 cm.

The altitude of the triangle can be found using the Pythagorean Theorem.

a² + b² = c²

17² + 16² = c²

289 + 256 = c²

545 = c²

c = 23.3 cm

(or)

17² + 16² = c² => 289 + 256 = c²

=> 545 = c²

=> c = √545 = 23.3 cm

The altitude of an isoceles triangle can be found by using the Pythagorean Theorem. The formula for the theorem is a² + b² = c², where a and b are the two sides and c is the hypotenuse, which is the altitude. In this situation, a is the leg length of 17 cm and b is the base length of 16 cm. Substituting these values into the equation gives 17² + 16² = c². Solving for c² gives c = √545 = 23.3 cm, which is the length of the altitude.

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Step-by-step explanation:

Using the trigonometric identity

sin(a - b) = sin a cos b - cos a sin b

So sin 79° cos 19° - cos 79° sin 19° can be written as

sin ( 79 - 19) = sin 60

And

\( \sin(60) = \frac{ \sqrt{3} }{2} \)

Hope this helps you

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

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The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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The given  expression √(a³-7)+ | b |, when a = 2 and b = -4, the value of the expression is, 5

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

√(a³-7) + | b |

where, a = 2

b = -4

Now, by putting values of a and b in the given equation,

⇒ √(a³-7) + | b |

⇒ √(2³-7) + | -4 |

For whatever value of x, |x| will give always positive value

So, now it can be further written as,

⇒   1  + 4

⇒   5

Hence, the value is 5

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The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

we have the system

2x - 4y = 6 -------> equation A

-5x - 20y = - 15 -----> equation B

Solve by elimination

so

Multiply equation A by -5 both sides

-5*[2x - 4y = 6] -----> -10x+20y=-30 -------> equation C

step 2

Adds equation C and equation B

-10x+20y=-30

-5x - 20y = - 15

------------------------

-15x=-45

Find out the value of y

substitute the value of x in any equation

2(3) - 4y = 6

6-4y=6

-4y=6-6

-4y=0

therefore

Answer:

A=3

4a2=3

4·362≈561.18446

Step-by-step explanation:

Answer:

a) 0.025£ b)3825£

Step-by-step explanation:

a) 5200-200=5000 - of the value will be lost after reaching the milleage of 200000 miles

200000-5000

1-x

200000=5000/x

x=5000/200000= 5/200=1/40=0.025£- the depreciation cost per mile

b)0.025*55000= 1375- the decreasing of the price

5200-1375=3825£- the book value of the car after it has driven 55000 miles

Answer:

x = 2

Step-by-step explanation:

8 = 6x + -2x

8 = 4x

8 = 4x

4 4

2 = x

Answer:

1.8 gallons

SEE NOTE BELOW*

Step-by-step explanation:

2x10x16=320

2x20x10=400

400+320=720

720÷400=1.8 gallons

NOTE* This would be painting the four walls.  If you include the floor and ceiling:

2x16x20=640

720+640=1360

1360÷400=3.4 gallons

The least amount of paint needed to paint the walls of a room in the shape of a rectangular prism is 1.8 gallons (2 gallons approx).

Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.

The formula to calculate the total surface area of a rectangular prism is given as,

TSA of rectangular prism = 2(lb + bh + lh)

Where, l is length, b is breadth and h is the height of the rectangular prism.

Calculation for the paint required for rectangular prism:

The area of the sides of prism to be painted is

Area A = 2×(length×height) + 2×(breadth×height)

Length = 20 feet

Breadth = 16 feet

Height = 10 feet

A = 2×(20×10) + 2×(16×10)

A = 720 sq. feet

Now, the paint need for painting 400 sq. feet is 1 gallon.

Thus, paint required for 720 sq. feet is,

=> 720 ft² / 400 ft² /gal = 1.8 gal  

Therefore, for painting rectangular prism, the amount of paint required is 1.8 gal.

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Answer:

48

Step-by-step explanation:

About 40 millions of aluminum cans can be recycled each month in the US. A quarter of these aluminum cans are used to make one aluminum boat. How many aluminum boats can be made in one year in the US?

Given that:

Approximate Number of cans that can be recycled per month in the US = 40 million

Fraction of recycled cans that can be used to make an aluminum boat = 1/4

The number of aluminum boats that can be made in the US in one year :

If about 40 million cans are recycle per month :

The number of boat that can be made from each monthly recycled aluminum cans will be :

Number of monthly recycled can needed to make one boat:

1/4 * 40 million = 10 million cans

Hence, 40,000,000 / 10,000,000 = 4

4 aluminum boats can be made in one month :

Number of months in a year = 12

Number of aluminum boats that can be made in a year :

4 per month * 12 = 48 aluminum boats

The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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Step-by-step explanation:

13. 15² = 12² + ?²

225 - 144 = ?²

? = √81

? = 9 feet

16. D. Regular Hexagon

The exact value of the inverse-trigonometric expression arccos( \(cos\frac{\pi }{2}\) ) is found to be  \(\frac{\pi }{2}\).

These are also called as arc functions. These trigonometric functions are inverse operations of given trigonometric functions. The cosine of the angle indicates the ratio of base of right triangle and hypotenuse of the same triangle and the inverse of the cosine is the ratio of base and hypotenuse will give the respective angle. Inverse functions can be used to unknown angles, angle of elevation or depression in any right triangle.

The given expression is arccos( \(cos\frac{\pi }{2}\) )

we know that arc cosine or inverse cosine= \(cos^{-1}(-x)\) = \(\pi - cos^{-1} - (x)\)

also we know that cos(-x)=cosx

arccos( \(cos\frac{\pi }{2}\) ) = arccos( \(-cos\frac{\pi }{2}\) )

                    = \(\pi - cos^{-1} (cos \frac{\pi }{2})\)

                    = \(\pi - \frac{\pi }{2}\)

                   = \(\frac{\pi }{2}\)

∴ The value of arccos( \(cos\frac{\pi }{2}\) ) is  \(\frac{\pi }{2}\).

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Answer:

The numbers are 6 and 7.

Step-by-step explanation:

4² = 16

5² = 25

6² = 36

7² = 49

√36 = 6

√42 = ?

√49 = 7

The numbers are 6 and 7.

The required slope-intercept form of equation is y = 45x/12 - 20.

The slope-intercept form of a line's equation is represented by the equation y = mx + b. This version of the equation places the y-intercept at b and the slope of the line at m. For instance, a line with the equation y = 2x Plus 4 has a y-intercept of 4, and its slope is 2.

We have two points from the graph

They are (0, -20) and (12, 25)

By using two points formula, we get

y - 25 = \(\frac{(-20-25)}{0-12}\)(x - 12)

y - 25  =\(\frac{45}{12}\) (x - 12)

y = \(\frac{45x}{12}\) - 45 + 25

y = 45x/12 - 20

Thus, required equation is y = 45x/12 - 20.

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Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

Answer:

\(-12w + x\)

Step-by-step explanation:

question:

\(-3w - 3x - 7w + 4x - 2w\)

first you add all the 'w' together.

(-3)+(-7)+(-2) = -10+(-2)=-12

so, \(-12w - 3x + 4x\)

second you add all the 'x' together

(-3)+(4) = 1

so, \(-12w+1x\)

then simplify:

\(-12w + x\) <--answer

hope this helps!

Answer:

So what's the Question ?????????

Answer:

each shirt 15 dollars each

Step-by-step explanation:

subtract 72 minus 12 since we know how much the hat is (12 dollars)

your answer should be 60

you will now divide, 60 divided by 4 is 15

and that is the answer

hope I helped you

This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

\(\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} \)

Now, check the triangle, sin 37° = 3/5

therefore,

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) \)

[ convert degrees on right side to radians ]

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) \)

There are three more possible values as :

\(\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} \)

or in decimals :

\(\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167\)

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

\(\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 2.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = -5.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 8.385\)

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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Answer:

A) - Value that corresponds to surviving the year would be: $-197

- Value Corresponding to not surviving = $98803

B) $-88.1

C) Yes, because the insurance company expects to make an average profit of $88.1 on every 29 year-old male that it insures for 1 year.

Step-by-step explanation:

A) We are told that the life insurance company charges $197 for insuring that the male will live through the year.

Thus, the value that corresponds to surviving the year would be: $-197 since amount that's paid out is $-197

We are told that the policy pays out $100,000 as a death benefit.

Therefore, the value that corresponds to not surviving the year is:

$100000 - 197 = $98803

B) From complement rule in probability;

P(not surviving) = 1 - P(surviving) = 1 - 0.9989 = 0.0011

Expected value would be;

μ = Σx•P(x) = (98803 × 0.0011) + (-197 × 0.9989) = $-88.1

C) Yes, because the insurance company expects to make an average profit of $88.1 on every 29 year-old male that it insures for 1 year.

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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