Which system of linear inequalities is graphed?
y ≤3x-2
x+ 2y≥4

y≥3x-2
x+2y ≤4

y< 3x-2
x+2y>4

y>3x-2
x+2y <4

Use the given equation to write the compound inequality (this equation is going to be in the middle of the inequality)

The surface area is about 157.08 square feet. use formula for the surface area of a right cylinder  to get answer .

what is surface area ?

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object. Surface area is usually measured in square units

In the given question,

The formula for the surface area of a right cylinder is:

S = 2πr² + 2πrh

where r is the radius of the cylinder, h is its height, and π is a mathematical constant approximately equal to 3.14159.

Substituting the given values, we get:

S = 2π(2.5)² + 2π(2.5)(7.5)

S ≈ 2π(6.25) + 2π(18.75)

S ≈ 39.27 + 117.81

S ≈ 157.08

Rounding this to the nearest hundredth, we get:

The surface area is about 157.08 square feet.

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Answer:

Step-by-step explanation:

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

The results show that the most common response was access, with 27% of the respondents choosing it as the most urgent health problem.

Cost came in second place, with 20% of the respondents choosing it. Obesity and cancer followed closely behind, with 14% and 13% of the respondents choosing them, respectively. Government interference and the flu were the least common responses, with only 3% and less than 0.5% of the respondents choosing them, respectively.

The margin of sampling error for the poll is ±4 percentage points, which means that if the poll was conducted multiple times, 95% of the time, the results would be within 4 percentage points of the actual population values.

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Answer:

a = 3 yd

b = 4 yd

c = 5 yd

Step-by-step explanation:

We can use the Pythagorean Theorem to find the value of x as follows:

a² + b² = c²

(x)² + (x+1)² = (2x-1)²

x² + x² + 2x + 1 = 4x² - 4x + 1

2x² - 6x = 0

2x(x-3) = 0

x = 0 or x = 3

Since x cannot be 0, we have x = 3.

Now we can use x=3 to find the lengths of all sides:

a = x = 3 yd

b = x+1 = 4 yd

c = 2x-1 = 5 yd

Therefore, the length of all sides of the truss are:

a = 3 yd

b = 4 yd

c = 5 yd

Answer:

264

Step-by-step explanation:

volume = l x w x h

8 x 5 x 5 = 200

8 x 8 x 1 = 64

200 + 64 = 264

Given that Line a is parallel to Line b (Line a ║ Line b), the triangle that is similar to ΔJKH is 1. ΔMKN

Similar triangles are triangles that have congruent corresponding angles, and in which all three corresponding sides are proportional.

The given parameter is Line a is parallel to Line b, which gives: a║b

Two triangles are similar if they satisfy the following conditions:

According to alternate angles theorem, the angles ∠JHK in ΔJKH is congruent to the ∠KNM in triangle ΔMKN

Similarly, the angle ∠HJK in ΔJKH is congruent to the ∠KMN in ΔMKN

Therefore, ΔJKH is similar to ΔMKN by Angle-Angle, AA similarity postulate.

The correct option for the triangle similar to ΔJKH is option 1. ΔMKN

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Bank Reconciliation Statement:

Bank reconciliation statements are prepared to find out the facts behind the differences between the cash account balance and the balance shown by the bank statement. Periodical bank reconciliation helps to prevent frauds and rectify any accounting errors and mistakes.

Calculation of Cash Account Balance of Brentwood Bike Co. as of May 31:

1. Bank Reconciliation Statement of Bentwood Bike Co. as of May 31.

Balance as per cash account  $35,670

Add:  

Less:  

2. Journal Entries to be recorded:

3. Computation of cash account balance should be reported in the balance sheet on May 31:

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Answer:

48000dL

Step-by-step explanation:

hope it helped!~

have a nice day

Answer:

The answer is 48,000 DL

Answer:

x=5

Step-by-step explanation:

60+11x+13x =180° (sum of angles in a triangle )

60+24x=180

24x=180-60

24x=120

x=120/24

x=5

Therefore the angles are 60, 55, 65

Which shows that it is a scaleness triangle and an acute angle

We have the following system of equations:

To determine if it has one solution, infinitely many solutions or no solution, let's rewrite the equations in slope-intercept form:

*If the slopes are the same but the y-intercepts are different, the system has no solution.

*If the slopes are different, the system has one solution.

*If the slopes are the same and the y-intercepts are the same, the system has many solutions.

Then, in this case since their slopes are different and their y-intercept are different, the system of equations has exactly one solution.

The value of the expression \(2\cos(t) + \tan^2(t)\) is 4 and the exact value of \(\sin^{-1}(\sin(\frac{5\pi}{3}))\) is \(\frac{5\pi}{3}\)

The point on the unit circle is given as:

\(P = (\frac 12, \frac{\sqrt{3}}2)\)

A point on a unit circle is represented as: (x,y), such that:

cos(t) = x and sin(t) = y.

This means that:

\(\cos(t) = \frac 12\)

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

Calculate tan(t) using:

\(\tan(t) = \frac{\sin(t)}{\cos(t)}\)

So, we have:

\(\tan(t) = \frac{\frac{\sqrt 3}{2}}{1/2}\)

Evaluate

\(\tan(t) = \sqrt 3\)

The expression is then calculated as:

\(2\cos(t) + \tan^2(t) = 2 * \frac12 + (\sqrt 3)^2\)

Evaluate each term

\(2\cos(t) + \tan^2(t) = 1 + 3\)

Evaluate the sum

\(2\cos(t) + \tan^2(t) = 4\)

Hence, the value of the expression \(2\cos(t) + \tan^2(t)\) is 4

The expression is given as:

\(\sin^{-1}(\sin(\frac{5\pi}{3}))\)

As a general rule, the arc sine of sine x is x.

This means that:

\(\sin^{-1}(\sin(\frac{5\pi}{3})) = \frac{5\pi}{3}\)

Hence, the exact value of \(\sin^{-1}(\sin(\frac{5\pi}{3}))\) is \(\frac{5\pi}{3}\)

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Answer:

x = 9

Step-by-step explanation:

The easiest way you can do this is to set both expressions equal to each other and solve for x.

2x + 3 = 3x - 6 (subtract 2x from both sides to get x on one side)

3 = x - 6 (add 6 to both sides to get x by itself)

9 = x aka x = 9

You can double-check your answer by plugging in 9 for x in both expressions.

2(9) + 3 = 21

3(9) - 6 = 21

Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.

1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.

2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.

3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.

4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.

5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.

6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.

7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.

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Answer:

-4.25

Step-by-step explanation:

The given number is 4.25 and we have to find the opposite of this number.

Opposite of a number is also known as additive inverse and it is defined as "if the sum of two numbers is zero then two numbers are opposite or additive inverse of each other"

For example, if x is a number then its opposite is -x.

and hence, x + (-x) = 0

Using this fact, we can conclude that the opposite of 4.25 is -4.25 because

4.25 + (-4.25)

= 4.25 - 4.25

=0

Answer:

But -4.25

....................................................................................

Answer:

56°

Step-by-step explanation:

First, the measure of angle GHE is equal to DFH. This means that you can set 98-6x=63-x, which becomes 5x=35 so x=7. Substitute 7 for x and you'll get DFH =63-7, which is 56.

Thus, the cardinal number of the set E is found to be: N(E) = 6.

A cardinal number describes or expresses how many of anything are present.

So all natural numbers are often refereed to as cardinal numbers. Cardinal numerals have been used for counting. When an ordinal number is an integer that represents the location or place of an object.

The description of a cardinal number is really a number that is used to express quantity in whole numbers. Decimals and fractions are not regarded as cardinal numbers. Natural numbers and numbering numbers constitute cardinal numbers. Each of them is a positive integer.

Given data:

N(CxE) = 18

C = {4, 5, 6)

In which N is the cardinal number, that is the total elements present in the set.

So,

N(C) = 3

Given that: N(CxE) = 18

The formula for the Cartesian product is:

N(CxE) = N(C) * N(E)

18 = 3* N(E)

N(E)  = 18 /3

N(E) = 6

Thus, the cardinal number of the set E is found to be: N(E) = 6.

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Complete questions:

Find N(E), Given That N(CxE) = 18 And C = {4, 5, 6).

Α. 6

B. 9

C. 3

D. 5

Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

The increment in \(f\) is approximately \(-3.883\times 10^{-3}\).

The linear approximation is derived from definition of tangent, that is to say:

\(\Delta f \approx m_{x}\cdot \Delta x\) (1)

Where:

The slope is found by derivatives:

\(m_{x} = \frac{\pi}{5} \cdot \cos \frac{\pi\cdot x}{5}\)    (2)

If we know that \(x = 3\) and \(\Delta x = 0.02\), then the increment in \(f\) is:

\(\Delta f \approx \left(\frac{\pi}{5}\cdot \cos \frac{3\pi}{5} \right)\cdot (0.02)\)

\(\Delta f \approx -3.883\times 10^{-3}\)

The increment in \(f\) is approximately \(-3.883\times 10^{-3}\). \(\blacksquare\)

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:

1.6

Step-by-step explanation:

5 times 1.6 is 8.

answer

306.87 degrees and 666.87 degrees.

steps

4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Equation with tangent function.

Title: Solving an equation involving tangent function

Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).

Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).

Numbered list:

Start with the equation 4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

Take the arctangent (or inverse tangent) of both sides to find θ.

Specify the interval [0,360) when giving the solution.

Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.

One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).

To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.

Subtracting 5 from both sides gives us: 4tanθ = -5

Dividing both sides by 4: tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Sure, here's just the math:

4tanθ + 5 = 0

Subtracting 5 from both sides:

4tanθ = -5

Dividing both sides by 4:

tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides:

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

ChatGPT

Answer:

see explanation

Step-by-step explanation:

The most likely error is adding the exponents instead of multiplying them, that is

\((a^{m}) ^{n}\) = \(a^{mn}\) , then \((3^{3}) ^{1}\) = \(3^{3(1)}\) = 3³ = 27

However

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\) ← the student may have used this definition to obtain 81

Answer:

Area = π(13^2) = 169π = 530.9 ft^2

Since 3.14 is used for π,

Area = 3.14(13^2) = 530.7 ft^2

Answer:

what is the expressio

Step-by-step explanation:

Part A

For Todd's class, we have this given info:

Compute the z score for x = 74.6

z = (x-mu)/sigma

z = (74.6 - 70.6)/(11.9)

z = 0.34 approximately

Side note: Convention usually has z scores rounded to two decimal places. If your teacher instructs otherwise, then go with those instructions of course.

======================================================

Part B

For Garret's English class, we have:

Compute the z score for x = 68.8

z = (x-mu)/sigma

z = (68.8 - 63.7)/(8.6)

z = 0.59 approximately

======================================================

Part C

Garret has the higher z score, which means that Garret did relatively better to his classmates compared to Todd's performance (in relation to his classmates). The z score is the distance, in units of standard deviation, the score is from the mean. Positive z values are above the mean, while negative z values are below the mean.

Answer:

HEY

Step-by-step explanation:

Answer:

Thank you so much

God bless u

Step-by-step explanation:

The angle formed by the two hands have a measure less than 1/4 turn

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

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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