What is the measure of SRT?
R
S
53°
48°
[Not drawn to scale]
T

The minimum value of the function is -5 and the maximum value of the function is 15.

The minimum and maximum value of the given trigonometric function f(x)=10sin(2/5x)+5 can be determined by analyzing the amplitude and period of the sine function. The amplitude of the sine function is 10, which means that the maximum value of the function is 10+5=15 and the minimum value is -10+5=-5.

The period of the sine function is given by 2π/2/5=5π. This means that the function completes one full cycle every 5π units. To find the minimum and maximum values of the function, we need to evaluate it at the critical points of the function, which occur at intervals of 5π.

At x=0, the function has a value of 5+10sin(0)=15, which is the maximum value of the function. At x=5π/2, the function has a value of 5+10sin(2π/5)=5, which is the minimum value of the function.

At x=[tex]5π[/tex], the function has a value of 5+10sin(4π/5)=-5, which is the maximum value of the function. At x=15π/2, the function has a value of 5+10sin(6π/5) =5, which is the minimum value of the function.

Learn more about trigonometric function here:

https://brainly.com/question/28483432

#SPJ4

Answer:

The total area of the "i" figure is 5.33 square units.

The figure is made up of a square with side length 4 units, a triangle with base 4 units and height 3 units, and a semi-circle with radius 2 units.

The area of the square is 4^2 = 16 square units.

The area of the triangle is (1/2)(4)(3) = 6 square units.

The area of the semi-circle is (1/2)(pi)(2^2) = 2pi square units.

The total area of the figure is 16 + 6 + 2pi = 5.33 square units (to the nearest hundredth of a unit).

Here is a diagram of the figure with the areas of each shape labeled:

[Image of the "i" figure with the areas of each shape labeled]

The art studio can offer a maximum of 8 painting classes and 5 pottery classes per week, while still meeting the time constraint and earning at least $1000 per week.

To find the maximum number of classes the art studio can offer per week, we need to set up an equation based on the time constraint.

Let's assume that the studio offers x painting classes and y pottery classes per week. Since each painting class is 1 hour long and each pottery class is 1.5 hours long, the total time spent on classes can be represented by the equation:

1x + 1.5y ≤ 40

This equation states that the total number of hours spent on painting classes (1x) plus the total number of hours spent on pottery classes (1.5y) must be less than or equal to 40 hours per week.

To find the minimum revenue the art studio can earn per week, we can set up another equation based on the cost of each class and the minimum revenue requirement.

Let's assume that each painting or pottery class costs $35. Then the total revenue earned per week can be represented by the equation:

35x + 35y ≥ 1000

This equation states that the total revenue earned from painting classes (35x) plus the total revenue earned from pottery classes (35y) must be greater than or equal to $1000 per week.

Now we have two equations:

1x + 1.5y ≤ 40

35x + 35y ≥ 1000

We can use these equations to find the maximum number of classes the art studio can offer per week.

To do this, we can graph the two equations on the same coordinate plane and find the point where they intersect.

When we do this, we get the point (x, y) = (8, 16/3).

This means that the art studio can offer a maximum of 8 painting classes and 16/3 (or approximately 5.33) pottery classes per week, while still meeting the time constraint and earning at least $1000 per week.

Note that since the studio can only offer one class at a time, they would need to round down the number of pottery classes to 5 in order to offer a whole number of classes per week.

To learn more about graphs

https://brainly.com/question/23956559

#SPJ11

Katy and Colleen each choose a number from 3, 6, or 8. If the sum is even, Katy pays Colleen the sum in dimes, and if odd, Colleen pays Katy the sum in dimes. There are 9 possible outcomes with payments ranging from 3 to 16 dimes.

If Katy writes down 3, then Colleen has two choices, either write down 3 to make the sum even or 6 to make it odd. If Colleen writes down 3, the sum is even, and Katy pays Colleen 6 dimes. If Colleen writes down 6, the sum is odd, and Colleen pays Katy 3 dimes.

If Katy writes down 6, then Colleen has two choices, either write down 3 to make the sum odd or 8 to make it even. If Colleen writes down 3, the sum is odd, and Colleen pays Katy 6 dimes. If Colleen writes down 8, the sum is even, and Katy pays Colleen 14 dimes.

If Katy writes down 8, then Colleen has two choices, either write down 3 to make the sum odd or 6 to make it even. If Colleen writes down 3, the sum is odd, and Colleen pays Katy 8 dimes. If Colleen writes down 6, the sum is even, and Katy pays Colleen 14 dimes.

Therefore, the possible outcomes and their corresponding payments are

3 + 3: odd, Colleen pays Katy 3 dimes

3 + 6: even, Katy pays Colleen 6 dimes

3 + 8: odd, Colleen pays Katy 8 dimes

6 + 3: odd, Colleen pays Katy 6 dimes

6 + 6: even, Katy pays Colleen 14 dimes

6 + 8: even, Katy pays Colleen 14 dimes

8 + 3: odd, Colleen pays Katy 8 dimes

8 + 6: even, Katy pays Colleen 14 dimes

8 + 8: even, Katy pays Colleen 16 dimes.

To know more about possible outcomes:

https://brainly.com/question/27292589

#SPJ4

The money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

The money multiplier represents the amount of money the banking system can create through the lending process for every dollar of reserves held by the central bank. It is inversely related to the reserve requirement, which is the percentage of deposits that banks are required to hold as reserves.

When the reserve requirement is low, su

The money multiplier is given by the formula:

Money multiplier = 1 / Reserve requirement

(a) When the reserve requirement is 0.040, the money multiplier is:

Money multiplier = 1 / 0.040 = 25.000

(b) When the reserve requirement is 0.125, the money multiplier is:

Money multiplier = 1 / 0.125 = 8.000

(c) When the reserve requirement is 0.400, the money multiplier is:

Money multiplier = 1 / 0.400 = 2.500

(d) When the reserve requirement is 0.200, the money multiplier is:

Money multiplier = 1 / 0.200 = 5.000

Therefore, the money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

Learn more about money multipliers

https://brainly.com/question/14986591

#SPJ4

Answer:

pls mrk me brainliest (⁠´⁠(⁠ｪ⁠)⁠｀⁠）

The area of the surface is [tex]\sqrt{\frac{15}{4}}\times \pi[/tex]  unit square.

To find the area of the surface, we need to first find the intersection curve between the plane and the cylinder.
From the equation of the cylinder, we know that [tex]x^2 + y^2[/tex] = 9200.

We can substitute [tex]x^2 + y^2[/tex] for [tex]r^2[/tex] and rewrite the equation as [tex]r^2[/tex] = 9200.
Next, we can rewrite the equation of the plane as

z = 12 - 4x - 3y.
Now, we can substitute 12 - 4x - 3y for z in the equation [tex]r^2[/tex] = 9200, giving us:
[tex]x^2 + y^2[/tex] = 9200 - [tex](12 - 4x - 3y)^2[/tex]
Expanding and simplifying, we get:
[tex]x^2 + y^2[/tex] = [tex]16x^2 + 24xy + 9y^2 - 24x - 36y + 884[/tex]
Simplifying further, we get:
[tex]15x^2 + 24xy + 8y^2 - 24x - 36y + 884 = 0[/tex]
We can recognize this as the equation of an ellipse:

To find the area of the surface, we need to find the area of this ellipse that lies within the cylinder.
To do this, we can first find the major and minor axes of the ellipse.

We can rewrite the equation as:
[tex]15(x - \frac{4}{5})^2[/tex] + 8([tex]y[/tex] - [tex]\frac{9}{10}[/tex][tex])^{2}[/tex] = 1

So the major axis has length [tex]2/\sqrt{15}[/tex] unit and the minor axis has length [tex]\frac{2}{\sqrt{8} }[/tex] unit.
The area of the ellipse is then given by:
A = π x ([tex]\frac{1}{2}[/tex] x [tex]\frac{2}{\sqrt{15} }[/tex] x ([tex]\frac{1}{2}[/tex] x [tex]\frac{8}{\sqrt{8} }[/tex])
Simplifying we get:
A = π x ([tex]\sqrt{\frac{2}{15} }[/tex]) x ([tex]\sqrt{\frac{2}{8} }[/tex])
A = π x ([tex]\sqrt{\frac{1}{60} }[/tex])
A = [tex]\sqrt{\frac{15}{4}} \times \pi[/tex] unit square

For similar questions on area

https://brainly.com/question/10026601

#SPJ11

The perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.

Given that, an isosceles right triangle whose short sides have that length 0.75 units.

Let the longest side be x.

Here, x²=0.75²+0.75²

x²=1.125

x=√1.125

x=1.06 units

Now, the perimeter = 0.75+0.75+1.06

= 2.56 units

Therefore, the perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.

To learn more about the perimeter visit:

https://brainly.com/question/6465134.

#SPJ1

The coordinates of the point are (7,0).

distance from (-3,-5) to (x,y) = 2 * distance from (x,y) to (9,-8)

Using the distance formula, we can write this equation as:

√[(x - (-3))^2 + (y - (-5))^2] = 2 * √[(9 - x)^2 + (-8 - y)^2]

Simplifying this equation, we get:

[tex](x + 3)^2 + (y + 5)^2 = 4[(9 - x)^2 + (-8 - y)^2][/tex]

Expanding and simplifying further, we get:

[tex]17x + 16y = 119[/tex]

So the coordinates of the point on the directed line segment from (-3,-5) to (9,-8) that partitions the segment into a ratio of 2 to 1 are:

x = (119 - 16y)/17

y = any value (since we can choose any value of y and then calculate x using the equation above)

For example, if we choose y = 0, then we get:

x = (119 - 16(0))/17 = 7

So the coordinates of the point are (7,0).

Read more on coordinates of a point here:https://brainly.com/question/12160473

#spj1

To do this, we can use the Pythagorean theorem and trigonometric ratios instead.

1. Determine the coordinates of the given point, let's call it P(x, y), and the center of the circle, let's call it O(h, k). Also, note the radius, r.

2. Calculate the distance between point P and the center O using the Pythagorean theorem: d^2 = (x-h)^2 + (y-k)^2, where d is the distance.

3. Set d equal to the radius of the circle: r^2 = (x-h)^2 + (y-k)^2.

4. Now, let's find the angle θ between the x-axis and the line OP without using arctan. To do this, we'll use the sine and cosine ratios:

sin(θ) = (y-k) / r and cos(θ) = (x-h) / r

5. To eliminate the need for arctan, we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1. Substitute the sine and cosine ratios we found earlier:

((y-k) / r)^2 + ((x-h) / r)^2 = 1

6. Simplify the equation by multiplying both sides by r^2:

(y-k)^2 + (x-h)^2 = r^2

You'll notice that this equation is the same as the one we found in step 3, confirming that the point P lies on the circle. You've now solved the point circle problem without using arctan, by employing the Pythagorean theorem and trigonometric ratios instead.

To know more about pythagoras theroem refer here:

https://brainly.com/question/343682#

#SPJ11

The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces.

The sample mean weight of grapes is the midpoint of the confidence interval, which is given by:

sample mean = (lower bound + upper bound) / 2

sample mean = (15.875 + 16.595) / 2

sample mean = 16.235

Therefore, the sample mean weight of grapes is 16.235 ounces.

The margin of error is half the width of the confidence interval, which is given by:

margin of error = (upper bound - lower bound) / 2

margin of error = (16.595 - 15.875) / 2

margin of error = 0.360

Therefore, the margin of error is 0.360 ounces.

The correct answer is: The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces.

Learn more about weight

brainly.com/question/10069252

#SPJ11

If each of the 3 friends orders a veggie mushroom cheddar burger for 11%, the cost of each burger would be:

11% of $1.00 = $0.11

Since the prices are listed in fractions of a dollar, we can express the cost of each burger as 11/100 of a dollar.

So, the total cost of 3 veggie mushroom cheddar burgers would be:

3 x 11/100 = 33/100 = $0.33

Assuming that the glass of water is free, the total bill before taxes would be $0.33 for the 3 burgers. However, it's important to note that this calculation is based on the assumption that the prices are listed in fractions of a dollar, which may not be the case. If the prices are listed in a different unit, the calculation would need to be adjusted accordingly.

The interval 4:00-4:59 represents the most number of cars.

How to determine the interval with the most number of cars based on the given time ranges?

To determine the interval that represents the most number of cars, we need to analyze the given options and find the one with the highest number of cars.

Unfortunately, we don't have any data about the actual number of cars during those intervals. Therefore, we cannot provide a definitive answer to this question. We could only make an educated guess based on certain assumptions.

For instance, if we assume that the traffic is usually higher during rush hour, we could say that the intervals between 4:00-4:59 and 3:00-3:59 are more likely to have the highest number of cars. However, without additional information or data, we cannot provide a more accurate answer.

Learn more about interval

brainly.com/question/13708942

#SPJ11

.m The correct equation to determine the amount of material used, m, to construct the fully enclosed tent is:

                         c. =2(8∙9)+2(7.5∙8)+(12∙9∙6)

To determine the amount of material used to construct the fully enclosed tent, we need to consider the surface area of the tent. The tent is fully enclosed, so we need to calculate the area of all the sides.

Option a. =(8∙9)+2(7.5∙8) calculates the area of the top and two sides of the tent. This does not include the front and back of the tent, so it is not the correct equation.

Option b. =(8∙9)+2(7.5∙8)+2(12∙9∙6) calculates the area of the top, two sides, front and back of the tent, but it also includes an extra term of 2(12∙9∙6) which is not necessary for a fully enclosed tent. This option overestimates the amount of material used.

Option c. =2(8∙9)+2(7.5∙8)+(12∙9∙6) calculates the area of the top, bottom, and all four sides of the tent. This is the correct equation to determine the amount of material used in a fully enclosed tent.

Option d. =3(8∙9)+2(12∙9∙6) overestimates the amount of material used because it includes an extra term of 3(8∙9) which is not necessary for a fully enclosed tent.

To know more about equation refer here

https://brainly.com/question/24791936#

#SPJ11

The searchlight should be 1/3 feet deep at the edge of the opening. Since the paraboloid is a continuous surface, the depth will increase gradually from the edge of the opening to the vertex at (0,0,1).

Determine the depth of the searchlight shaped like a paraboloid of revolution, we need to use the equation for the standard form of a paraboloid of revolution:
z = (x^2 + y^2) / (4f)
where z is the depth, x and y are the horizontal and vertical coordinates, and f is the focal length of the paraboloid.
We know that the light source is located 1 feet from the base along the axis of symmetry, which means that the vertex of the paraboloid is at (0,0,1).
We also know that the opening is 6 feet across, which means that the horizontal distance from one side of the opening to the other is 3 feet.
Using this information, we can find the value of f:
f = (d/2)^2 / 2r
where d is the diameter of the opening (6 feet), and r is the radius of curvature at the vertex (1 foot).
f = (6/2)^2 / 2(1) = 4.5 feet
Now we can plug in the values for x, y, and f to solve for z:
z = (x^2 + y^2) / (4f)
z = (x^2 + y^2) / (4(4.5))
z = (x^2 + y^2) / 18
Since the opening is 6 feet across, we know that the maximum value of x is 3 feet. Therefore, we can use the maximum value of y (also 3 feet) to find the depth at the edge of the opening:
z = (3^2 + 3^2) / 18
z = 6/18
z = 1/3 feet
So the searchlight should be 1/3 feet deep at the edge of the opening. However, since the paraboloid is a continuous surface, the depth will increase gradually from the edge of ×the opening to the vertex at (0,0,1).

Read more about paraboloid.

https://brainly.com/question/18850313

#SPJ11

Using the identity: sin(A + B) = sin A cos B + cos A sin B, we can rewrite the expression as follows:

Sin 7A * Cos 3A = (sin 4A + sin 10A)/2 * (cos 2A + cos A)/2

Expanding this expression using the same identity, we get:

= (sin 4A * cos 2A + sin 4A * cos A + sin 10A * cos 2A + sin 10A * cos A)/4

Now, using the identity sin 2A = 2 sin A cos A, we can simplify further:

= (1/2) sin 2A * cos 2A + (1/2) sin 2A * cos 8A + (1/2) sin 6A * cos 2A + (1/2) sin 6A * cos 8A

Therefore, Sin 7A * Cos 3A can be written as:

(1/2) sin 2A * cos 2A + (1/2) sin 2A * cos 8A + (1/2) sin 6A * cos 2A + (1/2) sin 6A * cos 8A

To know more about conversions , refer here :

https://brainly.com/question/30386474#

#SPJ11

The probability of having at least one failure in five trials is approximately 0.83193 or 83.193%.

To calculate the probability of at least one failure, we first need to find the probability of having zero failures in five trials, which is equal to (0.3)^5 or 0.00243. Then, we subtract this value from 1 to obtain the probability of having at least one failure. This is because the sum of the probabilities of all possible outcomes should be equal to 1.

In this case, we can see that the probability of having at least one failure in five trials is quite high, at approximately 83%. This means that it is more likely than not that there will be at least one failure in a series of five trials with a success rate of 30%.

The probability of having at least one failure in five trials of a binomial experiment with a success rate of 30% can be calculated as follows:

1 - (probability of having zero failures in five trials)

= 1 - (0.7)^5

= 1 - 0.16807

= 0.83193

Therefore, the probability of having at least one failure in five trials is approximately 0.83193 or 83.193%.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

The angle measure is given as follows:

θ = 1/3 radians.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius is half the diameter, hence it is given as follows:

r = 27 ft. (half the diameter).

Hence the circumference is given as follows:

C = 54π cm.

The fraction represented by a distance of 9 ft is given as follows:

9/54π = 1/6π

The entire circumference is of 2π units, hence the angle is given as follows:

1/(6π) x 2π = 1/3 radians.

More can be learned about the circumference of a circle at brainly.com/question/12823137

#SPJ1

The closest answer to the amount that the account is worth after 15 years is $2,812.19, Therefore Option 3 is correct

The formulation for calculating the future value (FV) of an investment with compound interest is:

[tex]FV = P * (1 + r/n)^{(n*t)}[/tex]

Wherein P is the primary (the initial amount invested), r is the once a year interest rate, n is the variety of times the interest is compounded per year, and t is the term in years.

In this case, P = $2,000, r = 2.5% = 0.0.5, n = 4 (for the reason that interest is compounded quarterly), and t = 15. Plugging those values into the formulation, we get:

[tex]FV = $2,000 * (1 + 0.1/2/4)^{(4*15)}[/tex]

FV ≈ $2,812.19

Therefore, the closest answer to the amount that the account is worth after 15 years is $2,812.19.

Learn more about future value (FV):-

https://brainly.com/question/30390035

#SPJ4

The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.

To model the total amount of money Victoria will have in her bank account as interest accrues after depositing her $200, you can combine the two functions h(x) and s(x). The given functions are h(x) = 200 and s(x) = (1.05)^x−1.

First, note that s(x) represents the growth factor of the interest, which is 5% (1.05) compounded annually. To find the total amount after x years, you need to multiply the initial amount by the growth factor raised to the power of x.

So, the combined function T(x) can be written as T(x) = h(x) * s(x).

Substitute the given functions into the combined function:

T(x) = (200) * ((1.05)^x−1)

This function, T(x), models the total amount of money Victoria will have in her bank account after x years with interest accrued on her $200 deposit. The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.

To learn more about Interest

https://brainly.com/question/30819806

#SPJ11

The number of minutes you can use the card is 9 minutes

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

Using the above as a guide, we have the following:

f(x) = 0.25x + 0.75

If the total cost of the card is $5.00, the number of minutes you is

0.25x + 0.75 = 5

So, we have

0.25x = 4.25

Divide by 0.25

x = 9

Hence, the number of minutes is 9

Read more about proportion at

https://brainly.com/question/1781657

#SPJ1

The required answer is a possible scenario where BC (c) is less than AC * sin(angle A)

To justify if it is possible to have BC < AC sin(angle A) for an acute triangle ABC, let's consider the sine formula for a triangle.

The sine formula for a triangle states that:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite to those sides, respectively.

Now let's isolate side BC (b) in the equation:

b = c * sin(B) / sin(C)

Since triangle ABC is acute, all angles A, B, and C are less than 90°. Therefore, sin(B) and sin(C) will be positive values between 0 and 1.

Let's now compare BC (b) to ACsin(angle A):

b < AC * sin(A)

c * sin(B) / sin(C) < AC * sin(A)

We can rewrite the inequality in terms of angle C:

sin(B) / sin(C) < (AC * sin(A)) / c

Now let's recall that angle C is the angle opposite to side AC (c), and angle B is the angle opposite to side BC (b). Since sine is a positive increasing function for acute angles (0° to 90°), it follows that the sine of a larger angle will result in a larger value.

As angle C is opposite to the longer side (AC), angle C > angle B. Therefore, sin(C) > sin(B), and their reciprocals will have the opposite relationship:

1 / sin(C) < 1 / sin(B)

Now, let's multiply both sides of the inequality by c * sin(B):

c < AC * sin(A)

This inequality represents a possible scenario where BC (c) is less than AC * sin(angle A), justifying the initial claim. So, yes, it is possible to have BC < AC sin(angle A) for an acute triangle ABC.

To know more about  acute triangle. Click on the link.

https://brainly.com/question/1311149

#SPJ11

Based on the given information, Yasmina should use Sally's Saddles if she expects to give 200 rides and wants to make the most profit.

To determine which company Yasmina should use to offer horseback rides at her school's Spring Fair, we need to compare the costs and revenues associated with each option.

First, let's consider Polly's Ponies. They charge $100 for a small pony and Yasmina can charge children $2 for a ride. To break even with this option, Yasmina would need to give 50 rides ($100 / $2 per ride). If she expects to give 200 rides, she would earn $400 in revenue ($2 per ride x 200 rides) and have a profit of $300 ($400 revenue - $100 rental fee).

Next, let's consider Sally's Saddles. They charge $240 for a larger horse and Yasmina can charge children $3 for a ride. To break even with this option, Yasmina would need to give 80 rides ($240 / $3 per ride). If she expects to give 200 rides, she would earn $600 in revenue ($3 per ride x 200 rides) and have a profit of $360 ($600 revenue - $240 rental fee).

Therefore, if Yasmina wants to make the same amount of profit regardless of which company she uses, she would need children to take a total of 125 rides ((($240 rental fee for Sally's Saddles - $100 rental fee for Polly's Ponies) / ($3 per ride - $2 per ride)). If she expects to give 200 rides, she should use Sally's Saddles since she will make a higher profit of $360 compared to $300 with Polly's Ponies.

Know more about profit here:

https://brainly.com/question/15699405

#SPJ11

After 8 years, Devon's account balance will be approximately $4,551.24.

In this case, Devon's principal amount is $2,750, his annual interest rate is 6.5%, and the interest is compounded once per year. we can see that we made a mistake in our calculation of the final amount. The correct calculation is:

A = $2,750(1 + 0.065/1)¹ˣ⁸

A = $2,750(1.065)⁸

A = $2,750(1.614)

A = $4,434.49

Since the question provides answer choices that are rounded to the nearest cent, we can see that the closest answer choice to our calculated amount is $4,551.24 (answer choice 1).

To know more about Compound interest here

https://brainly.com/question/29335425

#SPJ4

The mathematical phrase 5 + 2 × 18 is an example of an arithmetic expression.

To solve this expression, follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets (P/B)
2. Exponents/Orders (E/O)
3. Multiplication and Division (M/D)
4. Addition and Subtraction (A/S)

Your expression: 5 + 2 × 18

Step 1: No parentheses/brackets to solve.

Step 2: No exponents/orders to solve.

Step 3: Solve multiplication: 2 × 18 = 36

Step 4: Solve addition: 5 + 36 = 41

So, the value of the expression 5 + 2 × 18 is 41.

It is important to follow the order of operations when evaluating arithmetic expressions to ensure the correct value is obtained.

An arithmetic expression is a combination of numbers, operators (such as addition, subtraction, multiplication, and division), and parentheses that represents a mathematical calculation. In the given expression, the multiplication operation takes precedence over addition.

According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition. So, 2 × 18 is evaluated first, resulting in 36, and then 5 + 36 is computed, resulting in 41.

Therefore, the value of the expression is 41. Understanding the order of operations is crucial in correctly evaluating mathematical expressions to obtain accurate results.

To know more about arithmetic expressions refer here:

https://brainly.com/question/17722547

#SPJ11

Answer: 720

Step-by-step explanation: 1800 x 40%

Answer:

720 math books

Step-by-step explanation:

1800×40%= 720

there are 720 math books

The value of b in the parallel line is 93 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as alternate interior angles, alternate exterior angles, corresponding angles, same side interior angles, vertically opposite angles, adjacent angles etc.

Therefore, let's use the angle relationship to find the angle b as follows:

Alternate interior angles are the angles formed when a transversal intersects two parallel lines. Alternate interior angles are congruent.

Using the alternate interior angle theorem,

b = 180 - 65.5 - 21.5

b = 93 degrees.

Learn more on angles here: https://brainly.com/question/29719855

#SPJ1

The conjecture "X, Y, Z and W are noncolinear" is always true when given that line segments XY and ZW intersect at point A. So option D is the correct answer.

When line segments XY and ZW intersect at point A, it means that X, Y, Z, and W do not all lie on the same line. Since they do not all lie on the same line, they are considered non-collinear.

So the correct answer is option D. X, Y, Z and W are noncolinear. ​

To learn more about intersect : https://brainly.com/question/11006922

#SPJ11

The equation that could be used to calculate the average speed of each vehicle is C. 140x = 95x + 40, where x represents the average speed of the helicopter in miles per hour and 140x represents the distance traveled by the small private airplane.

The equation that can be used to calculate the average speed of each vehicle is:

C. 140x = 95x + 40

Let's break it down:

Since the time taken by both vehicles is the same, the distances covered by each vehicle can be equated, giving us the equation 140x = 95x + 40.

Learn more about time,

https://brainly.com/question/26502542

#SPJ11

To find the rate of change of the volume of the cone, we need to use the formula for the volume of a cone:

V = (1/3)πr^2h

Taking the derivative of both sides with respect to time, we get:

dV/dt = (1/3)π[2rh(dr/dt) + r^2(dh/dt)]

Substituting the given values:

r = 40 in (radius is increasing at a rate of 4 in/s)
h = 20 in (height is decreasing at a rate of 3 in/s)
dr/dt = 4 in/s
dh/dt = -3 in/s

Plugging these into the formula:

dV/dt = (1/3)π[2(40)(20)(4) + (40)^2(-3)]

dV/dt = (1/3)π[3200 - 4800]

dV/dt = (1/3)π(-1600)

dV/dt = -1681.99 in^3/s

Therefore, the volume of the cone is decreasing at a rate of approximately 1681.99 cubic inches per second when the radius is 40 inches and the height is 20 inches.
To find the rate at which the volume of the cone is changing, we can use the formula for the volume of a cone (V = (1/3)πr^2h) and differentiate it with respect to time (t).

Given:
dr/dt = 4 inches per second (increasing radius)
dh/dt = -3 inches per second (decreasing height)
r = 40 inches
h = 20 inches

First, let's differentiate the volume formula with respect to time:
dV/dt = d/dt[(1/3)πr^2h]

Using the product and chain rules, we get:
dV/dt = (1/3)π(2r(dr/dt)h + r^2(dh/dt))

Now, plug in the given values:
dV/dt = (1/3)π(2(40)(4)(20) + (40)^2(-3))

Simplify:
dV/dt = (1/3)π(6400 - 4800)

dV/dt = (1/3)π(1600)

Finally, calculate the rate:
dV/dt ≈ 1675.52 cubic inches per second

So, the volume of the cone is changing at a rate of approximately 1675.52 cubic inches per second.

Learn more about radius here: brainly.com/question/13449316

#SPJ11