Which domain restriction would allow you to define the inverse of the tangent function?\((-(\pi )/(2), -(\pi )/(2))\)(-π, π)\(-(\pi )/(2),0\)\(0,(\pi )/(2)\)

The correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200, option A is correct.

We have two carriers: land carriers and air carriers.

The land carriers can transport 1500 pieces of mail per load, and the air carriers can transport 1250 pieces of mail per load.

The loading equipment at the distribution center can handle up to 200 loads per day.

To represent this situation using a system of inequalities, we can define the variables x and y as the number of loads by land carriers and air carriers, respectively.

The first inequality, 1500x + 1250y ≥ 175,000, represents the total number of pieces of mail transported per day.

The second inequality, x + y ≥ 200, represents the total number of loads.

Hence,  the correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200.

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To complete the job in 12 days, they need 100 workers.

We know that 30 workes can complete 1 job in 40 days, then if each worker works at a rate R, then we can write:

30*R*40 days = 1 job

R = (1/1200) job/day

Then if they need to complete the job in 12 days, the number N of workers needed is:

N*(1/1200)*12 = 1

N = (1200/12) = 100

100 workers are needed.

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Answer:

P(A) = 0.57 (rounded to two decimal places).

Step-by-step explanation:

The probability of selecting a red marble from the hat can be found by dividing the number of red marbles by the total number of marbles:

P(red) = number of red marbles / total number of marbles

P(red) = 20/35

We can simplify this fraction by dividing both the numerator and denominator by 5:

P(red) = 4/7

So the probability of selecting a red marble from the hat is 4/7, or approximately 0.57 when rounded to two decimal places.

Therefore, P(A) = 0.57 (rounded to two decimal places).

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Answer: I don’t really know

Step-by-step explanation:

The arc length EF of the circle is 2π. Therefore, option C is the correct answer.

The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference.

The formula to find the arc length of a circle is θ/360° ×2πr.

Given that, ∠EDF=π/2= 90° and radius of a circle = 4 units.

Here, arc length = θ/360° ×2π×4

= 90°/360° ×2π×4

= 1/4 ×2π×4

= 2π

Therefore, option C is the correct answer.

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According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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The numeric values of the piecewise function in this problem are given as follows:

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

A piecewise function is a function that has different definitions, based on the input x of the function.

For values of x that are of 1 or less, the function is defined as follows:

f(x) = x.

Hence the numeric values in this interval are given as follows:

For values of x that are greater than 1, the function is defined as follows:

f(x) = -x + 4.

Hence, at x = 3, the numeric value of the function is given as follows:

f(3) = -3 + 4 = 1.

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Answer:

55*5=275

Step-by-step explanation:

Answer:

275 miles

Since the car travels 55 miles per hour then you would multiply 55 times 5 to get the answer, which is 275.

Answer:

Yes

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

She received $5 back

Step-by-step explanation:

Answer:

170

Step-by-step

Add 5 27 times count by 5s and you will get the answer.

Answer; 0 ,2?

Step-by-step explanation:

im not so sure tbh its a lil confusing dont they tell how many years its been?

9514 1404 393

Answer:

  (a) x = 22

  (b) 46°

  (c) 44°

  (d) 180°

Step-by-step explanation:

Because the sum of the interior angles of a triangle is 180°, we know that the sum of the acute angles in a right triangle is 90°.

The sum of the marked acute angles is 90°.

  2x +(3x -20) = 90

  5x = 110 . . . . . . . . . . add 20, collect terms

  x = 22 . . . . . . . . . divide by 5

__

∠CBA = (3x -20)° = (3·22 -20)° = 46°

__

∠CAB = 2x° = 2(22)° = 44°

__

The sum of a triangle's interior angles is 180°.

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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Answer:

it takes 3 hour

Step-by-step explanation:

ypir welcome

This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex Algebraic equations and expressions.

The algebraic expression ÷ 8 can be written in a variety of ways depending on the context and the specific operation being performed. However, in general, the phrase "divided by 8" or "the quotient of x and 8" can be used to represent this expression.

For example, if we have an algebraic expression such as 24 ÷ 8, we can write it as

24 divided by 8

the quotient of 24 and 8

24/8

In each case, the idea is the same: we are dividing 24 into 8 equal parts, or finding how many groups of 8 are contained in 24.

In the context of an algebraic equation or expression, the phrase "divided by 8" is often used to indicate that the variable or expression preceding it is being divided by 8. For example:

3x ÷ 8

(2y + 5) ÷ 8

In these cases, we are dividing the value of 3x or the sum of 2y and 5 by 8. The quotient of these expressions will depend on the specific values of x and y."divided by 8" is a commonly used phrase to represent the algebraic expression ÷ 8. This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex algebraic equations and expressions.

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Answer:

13 ingredients

Step-by-step explanation:

The number of different recipes that can be made from 2 ingredients = 78

Since there are no two recipes that share the exact same two ingredients ;

The number of recipes in Mark's kitchen is:

nCk = 78

k = Number of ingredients per recipe = 2

n = total number of ingredients in kitchen

Total recipes made = 78

n! / (n-r)!r! = 78

n! / (n - 2)!2! = 78

n(n-1)(n-2)! / (n-2)! * 2 * 1 = 78

n(n - 1) / 2 = 78

n(n-1) = 156

n² - n = 156

n² - n - 156 = 0

Factorize :

n² - 13n + 12n - 156 = 0

n(n - 13) +12(n-13) = 0

(n-13) = 0 ; (n+12) = 0

n = 13 or n = - 12

n cannot be negative

Hence, n = 13

Number of ingredients is 13

Answer:

84 square inches

Step-by-step explanation:

First, separate this shape into two shapes you can easily find the area of. You can do this by turning it into a rectangle and a rhombus.

Say the rectangle has measurements of 5 by 6 inches. The area of that rectangle will be 30 square inches. Save this value to add on later.

The rhombus now has a height of 4 (because the side length 10 minus the side length 6 equals 4), and two bases by the values of 12 and 15. The area of a rhombus can be found with the equation:

a = 1/2(b1 + b2) x h

Simply plug in those values to find the area of the rhombus, 54. Now add the area of the rhombus and the area of the rectangle to get 84 square inches as your final area.

The sec 132 degrees 15 minutes in degrees is approximately -1.638 degrees.

The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).

In other words,

sec(x) = 1 / cos(x)

The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.

To convert sec(132 degrees 15 minutes) to degrees, we first need to convert the angle to decimal degrees.

We know that 1 degree is equal to 60 minutes, so 15 minutes is equal to 15/60 = 0.25 degrees.

Therefore, the angle 132 degrees 15 minutes is equal to 132 + 0.25 = 132.25 degrees.

Now we can find the secant of this angle:

sec(132.25 degrees) = 1/cos(132.25 degrees) ≈ -1.638

So the answer is approximately -1.638 degrees.

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We have to find the 2nd derivative of the function:

We would need to know the product rule of derivatives, which is:

If u and v are two functions, then the derivative of u*v is:

So, we have:

Remember, the derivative of e^x is e^x and the derivative of "x" is 1.

Thus, we have:

To get the 2nd derivative, we again have to use the product rule of differentiation on xe^x and just do the differentiation of e^x and sum it. Thus, the process is shown below:

The 2nd derivative of the function shown is:

Answer: c

Step-by-step explanation:

Just took the test

Explanation:

Most states (but not all) require liability insurance at minimum. This covers injury and property damage to the person you accidently hit. It likely does not cover you personally so you'd need other insurance for that.

States like Iowa, New Hampshire, and Ohio offer exemptions from insurance if you can show you are responsible with money. Meaning that if you have a steady income and are smart with money, then you likely would be able to pay off any future accident without needing insurance. Though the damages might get wildly expensive, so a liability policy isn't always a bad thing.

The area of the triangle, Rounded to the nearest hundredth, is approximately 132.02 cm².

The area of a triangle with the given measurements, we can use the formula for the area of a triangle using side lengths and an included angle. The formula is:

Area = (1/2) * a * c * sin(B)

where a and c are the side lengths, B is the included angle between those sides, and sin(B) represents the sine of angle B.

Let's calculate the area using the given measurements:

B = 103° (included angle)

a = 12 cm

c = 22 cm

First, we need to convert the angle from degrees to radians, as the sine function operates on radians. We can use the conversion: radians = degrees * (π/180).

B in radians = 103° * (π/180) ≈ 1.8 radians

Next, we can substitute the values into the formula:

Area = (1/2) * a * c * sin(B)

     = (1/2) * 12 cm * 22 cm * sin(1.8 radians)

Using a calculator, we can evaluate sin(1.8 radians) ≈ 0.9833.

Area ≈ (1/2) * 12 cm * 22 cm * 0.9833

       ≈ 132.02 cm² (rounded to the nearest hundredth)

Therefore, the area of the triangle, rounded to the nearest hundredth, is approximately 132.02 cm².

Among the given options, the closest match is:

b) 132 cm² (rounded to the nearest whole number)

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The zeros of g(x) = (x + 2)(x − 1)(x − 2) are x = -2, 1 and 2

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

The 5 functions of g(x)

To determine the key features of the function g(x), we make use of the first

g(x) = (x + 2)(x − 1)(x − 2)

So, we have

Zeros

This is when the function equals 0

(x + 2)(x − 1)(x − 2) = 0

Evaluate

x = -2, 1 and 2

The y-intercept

This is when the value of x in the function equals 0

g(0) = (0 + 2)(0 − 1)(0 − 2)

Evaluate

g(0) = 4

End behaviour

This is the behavior of the graph of the function as it approaches the ends of the x-axis

So, we have

\(\mathrm{as}\:x\to \:+\infty \:,\:g\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:g\left(x\right)\to \:-\infty \:\)

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Answer:

14 or 14(unit)^2

Step-by-step explanation:

Area of a triangle = (base × height)/2

2--5 = 7

2--2 = 4

(7 × 4)/2 = 28/2 = 14

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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Step-by-step explanation: To shift the graphs up and down on the coordinate system, you need to manipulate or change the y-intercepts.

The y-intercept is just the constant term in the equation.

As long as the slopes remain the same, the graphs can be

translated up or down by changing the constant value.

Take a look at these lines graphed below.

Notice that y = x + 11 is the same as y = x + 4 but

y = x + 11 is translated 7 units down to get y = x + 4.

Answer:

\(t_{n-1,\alpha/2}=3.59114678\)

Therefore we do not have sufficient evidence at \(1\%\) level that the true mean diameter has moved away from the target

Step-by-step explanation:

From the question we are told that:

Sample size \(n=36\)

Mean diameter \(\=x=1.4\)

Standard deviation \(\sigma=0.5cm\)

Null hypothesis \(H_0 \mu=1.5\)

Alternative hypothesis \(\mu \neq 1.5\)

Significance level \(1\%=0.001\)

Generally the equation for test statistics is mathematically given by

\(t=\frac{\=x-\mu}{\frac{s}{\sqrt{n} } }\)

\(t=\frac{1.4-1.5}{\frac{0.5}{\sqrt{36} } }\)

\(t=-1.2\)

Therefore since this is a two tailed test

\(t_{n-1,\alpha/2}\)

 Where

   \(n-1=36-1=>35\)

   \(\alpha=/2=0.001/2=>0.0005\)

From table

\(t_{n-1,\alpha/2}=3.59114678\)

Therefore we do not have sufficient evidence at \(1\%\) level that the true mean diameter has moved away from the target