heres your daily dos of math
y = -4 - (-11)

Answer:

0.3696 radian

21.178°

Step-by-step explanation:

Given :

Radius, r = 22 yards

Area of Sector = 89.45 yd²

Approximate angle of the sector :

Area of Sector = 1/2 * θ * r²

89.45 = 1/2 * θ * 22²

89.45 = 0.5 * 484 * θ

89.45 = 242θ

θ = 89.45 / 242

θ = 0.3696 radian

Radian to degree

0.3696 * 180 / π = 21.178°

Answer:

18

Step-by-step explanation:

Equation 9 x 4 / 2 = 18

First do 9 x 4 which is 36

Next do 36 / 2 which is 18

Also the "/" is another way to say to divide

The given statement "Customer arrivals per unit of time would tend to follow a binomial distribution" is False.

The probability distribution that models the number of successes in a fixed number of trials is called binomial distribution. It is used when we are conducting a fixed number of trials and the trials are independent of each other, the probability of success is constant throughout each trial, and there are only two possible outcomes. In the case of customer arrivals per unit of time, the binomial distribution may not be appropriate. Rather, a Poisson distribution is commonly used to model customer arrivals, which assumes that customer arrivals are random and occur at a constant rate.

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Answer:

48-6c = 0

Step-by-step explanation:

she has 48 total donuts. If she gives 6 away at every class, you would be subtracting 6 times the amount of classes. after giving them all away, she should have 0 donuts.

have a lovely day <3

The total cost of the ingredient is $0.84 for 6 ounces.

Define fixed cost.

The cost or expense known as fixed cost is unaffected by a short-term horizon's growth or reduction in the number of units produced or sold. To put it another way, it refers to a cost that is linked to a time period rather than a specific economic activity.

It can be viewed as costs that a business must pay regardless of the volume of business activity, such as the number of units produced or sales made. One of the two main parts of the overall manufacturing cost is the fixed cost.

Solution Explained:
Given,

1 pound = $2.25

Since 1 pound = 16 ounces

So, 16 ounces = 2.25

      1 ounce = 2.25/16 = 0.14

Therefore, 6 ounces = 0.14 X 6 = 0.84

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keeping in mind that in a rhombus the diagonals always meet at right-angles, Check the picture below.

Answer:

x =2.39

Step-by-step explanation:

;D

Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site

Probability: The chance that a given event will occur. The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes

given that the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0. 40

Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey

Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site

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Answer:

Because 0.40 represents likelihood over many visits to the site in the long term, Avery's interpretation of the probability is incorrect.

Step-by-step explanation:

What does the term probability mean?

Probability: The likelihood that a specific occurrence will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely outcomes that result in a specific event

Given that there is a 0. 40 percent chance that a randomly chosen website visitor will be requested to take an online survey

Avery asserts that of the following 5 site visits, 2 will be required to complete the survey.

Because 0.40 represents chance over the long term and several visits to the site, Avery's interpretation of the probability is incorrect.

Interior Angle is 180n = 375 - x in given question.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

To determine the number of sides in a convex polygon given the sum of all but one of its interior angles, we can use the formula:

Sum of interior angles = (n - 2) * 180 degrees,

where n represents the number of sides in the polygon.

In this case, the sum of all but one of the interior angles is missing, so we need to subtract one interior angle from the total sum before applying the formula.

Let's denote the missing interior angle as x. Therefore, the sum of all but one of the interior angles would be the total sum minus x.

Given that the stamina is 15, we can express the equation as:

(15 - x) = (n - 2) * 180

Simplifying the equation, we have:

15 - x = 180n - 360

Rearranging the terms:

180n = 15 - x + 360

180n = 375 - x

Now, we need more information or an equation to solve for the number of sides (n) or the missing interior angle (x).

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The probability that none are broken as calculated from the data given is 0.96.

No of eggs = 12

percentage of broken eggs = 4%

=4/100 * 12 = 0.48 eggs

therefore , probability of getting broken egg

= no of favorable outcome/ no of outcomes

=0.48/12

=0.04

hence probability of not getting any broken egg

= 1 - P(broken)

= 1- 0.04

= 0.96

There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.

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The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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Answer:

1.) Roses ; 2.) Alfalfa

Step-by-step explanation:

Given the graph below :

1 fruit = 5 ladybugs

Initial number of ladybugs on the roses = (7*5) = 35 lady bugs

Subtracting 10 ladybugs from lettuce and adding to the Alfalfa ;

Total number of ladybugs on the Alfalfa = (25 + 10) = 35 ladybugs

Hence, both the Roses and Alfalfa now have the same number of ladybugs.

Lettuce has 5 and grape has 10 Ladybugs

Hence, number of ladybugs on the Roses and Alfalfa are the same.

(a) No solutions when r ≠ 6 and s ≠ 5. (b) Exactly one solution when r = 6 and s = 5. (c) Infinitely many solutions when r = 6 and s is arbitrary.

For the system of equations to have (a) no solutions, both r and s must have values that do not satisfy the equations. For example, if r ≠ 6 and s ≠ 5, then the equations cannot both be true. For the system to have (b) exactly one solution, both r and s must have values that satisfy the equations. For example, if r = 6 and s = 5, then the equations are both true and have one unique solution. For the system to have (c) infinitely many solutions, one of the variables must have a value that satisfies the equations, while the other variable may take on any value. For example, if r = 6 and s is arbitrary, then the equations are both true and have infinitely many solutions.

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1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

2y^3x^7-3y

Step-by-step explanation:

I had the same problem on my test and got it right trust me

The expression 12(x⁷)(y³) divided by 6(x³)(y) is equal to 2x⁴y².

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

To simplify the expression, we can divide the coefficients and subtract the exponents of the variables with the same base.

Therefore:

12(x⁷)(y³) divided by 6(x³)(y)

= (12/6)(x⁽⁷⁻³⁾(y⁽³⁻¹⁾)

= 2x⁴y²

Therefore, 12(x⁷)(y³) divided by 6(x³)(y) is equal to 2x⁴y².

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Answer:

g(3) = 6

Step-by-step explanation:

The right side of the equation is the part with all the information for the doing of the math.

x^2 - 3 means square the number and then subtract 3.

On the left side of the equation is the g(x). g(x) or f(x) or k(x) is literally just y. Someone could ask what is f(x)? It is y.

What is g(x)? It is y.

What is g? It is the name of the function. So instead of saying ..."the thing where you square a number and then subtract 3..." you can just say "g". Now the (x) beside g DOESNOT mean times, bc sometimes parenthesis means times. THIS IS NOT TIMES!

The (x) is like a billboard. Tells you who will be starring as x in the work on the right side of the equation.

If you see g(x)=x^2-3

then whatever is in the ( ) on the left, put that in the place of x on the right.

g() = ^2 - 3

g(12) = 12^2 - 3

g(-7) = (-7)^2 - 3

or like your question

g(3) = 3^2 - 3

do the calculation

g(3) = 9 - 3

g(3) = 6

done! Hope this helps!

Answer:

x = 76

Step-by-step explanation:

Given

f(x) = \(\frac{1}{4}\) x + 5 and f(x) = 24, then equate the right sides

\(\frac{1}{4}\) x + 5 = 24 ( subtract 5 from both sides )

\(\frac{1}{4}\) x = 19 ( multiply both sides by 4 to clear the fraction )

x = 76

Answer:

2 gallons

Step-by-step explanation:

1 1/4 = 1 + 1/4 = 4/4 + 1/4 = 5/4

Then:

5/4 gallons ⇒ 5/8 fence

x  gallons ⇒ 8/8 fence

x = (5/4)(8/8) / (5/8)

x = ((5*8)/(4*8)) / (5/8)

x = (5/4) / (5/8)

x = (5*8)/(4*5)

x = 40/20

x = 2

Answer: 20

Step-by-step explanation:

The true statements about quadratic function are statement I and III.

We can use the discriminant of the quadratic equation to determine the validity of each statement:

The discriminant of the quadratic equation nx² + 7√n x + n = 0 is:

Δ = (7√n)² - 4n² = 49n - 4n².

I. For any n, the roots are distinct.

For the roots to be distinct, the discriminant Δ must be positive.

Therefore, we must have:

49n - 4n² > 0

n(49 - 4n) > 0

This inequality is satisfied when n < 0 or n > 49/4. However, n is a positive integer, so the only valid solution is:

n ≥ 13/4

Therefore, for any n ≥ 4, the roots are distinct. Statement I is true.

II. There are infinitely many values of n for which both roots are real.

For both roots to be real, the discriminant Δ must be non-negative.

Therefore, we must have:

49n - 4n² ≥ 0

n(49 - 4n) ≥ 0

This inequality is satisfied when 0 ≤ n ≤ 49/4. Since n is a positive integer, there are only a finite number of solutions for n, namely n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Therefore, statement II is false.

III. The product of the roots is necessarily an integer.

The product of the roots is given by:

n²/(nx² + 7√n x + n) = n/(x + 1/√n)

Since the roots are distinct, the product is:

n/(x1 + 1/√n)(x2 + 1/√n)

This expression simplifies to:

n/(nx² + 7√n x + n + 1) = 1/(x + 1/7√n)

Since x is a root of the quadratic equation, we have:

nx² + 7√n x + n = 0

Therefore, the product of the roots is:

n/(n + 1) = 1 - 1/(n + 1)

Since n is a positive integer, n + 1 is also a positive integer, and the product of the roots is an integer minus a fraction.

Therefore, statement III is true.

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The complete question is below:

Consider the quadratic equation nx² + 7√(nx) + n = 0,  where n is a positive integer.

Which of the following statements are necessarily correct?

I. For any n, the roots are distinct.

II. There are infinitely many values of n for which both roots are real.

III. The product of the roots is necessarily an integer.

GIven:

To Determine: The equivalent of the given expression

Distributing the sign outside as shown below:

Hence, the equivalent expression by distributing the sign outside the given expression is:

8.4n+1

Answer:

She should walk approximately 1,463.34369 feet along the sidewalk going to the east, then walk the remaining straight line distance along the grass.

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

Explanation:

Refer to the diagram below.

Alaina starts at point A. If she stays on the sidewalk the entire time, then she can go from A to C to D in that order.

If she takes the direct line route, then she would go from A to D across the grass entirely.

The two paths have pros and cons. The optimal solution is a mix of the two routes. This means she'll be on the sidewalk for some amount of time, and then cut along the grass once reaching a certain point.

Let's say point B is the point where she decides to cut along the grass. In the diagram below, I made \(\text{BC} = x\) so that I could find \(\text{BD} = \sqrt{x^2+600^2}\) through the pythagorean theorem fairly quickly.

If \(\text{BC} = x\), then the remaining bit of the east/west side walk is \(\text{AB} = 2000-x\) since the two portions must add to 2000 feet.

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

If she travels along the side walk at a rate of 6 ft/sec, and travels 2000-x feet (from A to B), then it will take her

time = distance/speed = \(\frac{2000-x}{6}\) seconds

Then if she cuts across the grass to follow path BD, then she'll take another

time = distance/speed = \(\frac{\sqrt{x^2+600^2}}{4}\) seconds since she's traveling 4 ft/sec here.

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

If Alaina goes from A to B to D in that order, then she takes a total of

\(\text{(time from A to B)}+\text{(time from B to D)}\\ = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\)

That represents the total time taken when following this path at those specified speeds mentioned.

The goal is to find the minimum of that function. So we'll need to compute the derivative.

\(f(x) = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\\\\ f \ '(x) = -\frac{1}{6}+2x*\frac{1}{2*4\sqrt{x^2+600^2}}\\\\ f \ '(x) = -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}}\\\\\)

Set the derivative equal to zero and solve for x

\(f \ '(x) = 0\\\\ -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}} = 0\\\\ \frac{x}{4\sqrt{x^2+600^2}} = \frac{1}{6}\\\\ 6x = 4\sqrt{x^2+600^2}\\\\ (6x)^2 = \left(4\sqrt{x^2+600^2}\right)^2\\\\ 36x^2 = 16(x^2+600^2)\\\\ 36x^2 = 16x^2+16*600^2\\\\\)

\(36x^2 = 16x^2+5,760,000\\\\ 36x^2-16x^2 = 5,760,000\\\\ 20x^2 = 5,760,000\\\\ x^2 = 5,760,000/20\\\\ x^2 = 288,000\\\\ x = \sqrt{288,000}\\\\x \approx 536.65631\)

If you were to perform the first derivative test, you should find that the local min occurs at roughly x = 536.65631

This means she must walk a approximately 2000-x = 2000-536.65631 = 1,463.34369 feet when going from A to B such that to minimize the walking time.

Side note: you can use the minimum feature on your calculator to confirm the answer

Answer:

  (b)  1 - x - 2 + 2 x = 10 x - 25 - x

Step-by-step explanation:

The distributive property tells you the factor outside parentheses multiplies each term inside parentheses.

__

  1 -(x +2) +2x = 5(2x -5) -x

The minus sign outside the parentheses on the left side of the equal sign represents a factor of -1. Using the distributive property there, we have ...

  1 +(-1)(x) +(-1)(2) +2x = 5(2x -5) -x

  1 -x -2 +2x = 5(2x -5) -x . . . . . . simplify a bit

The 5 outside parentheses on the right side of the equal sign similarly multiplies each of the terms inside those parentheses:

  1 -x -2 +2x = (5)(2x) +(5)(-5) -x

  1 -x -2 +2x = 10x -25 -x . . . . . . . . matches the second choice

_____

Additional comment

It might be helpful to think of parentheses as a "bag." The factor outside tells you how many bags you have. (All are the same.) When you eliminate the parentheses, you are essentially dumping the contents of the bags into one pile. Since all of the bags have the same contents, the total is the product of what's in a bag and the number of bags.

Answer:

1600

Step-by-step explanation:

(20 x 16)5

=320 x 5

=1600

Answer:

6.93

Step-by-step explanation:

formula to find height of equilateral triangle is \(\frac{\sqrt{3} }{2} *A\) A is the side of the equilateral triangle

Answer:

6.93 inches

(first option listed)

Step-by-step explanation:

we can find the height of this triangle by turning it into a right triangle, and then using the Pythagorean Theorem

(process shown in photo)

hope this helps!! have a lovely day :)

Answer:

7

Step-by-step explanation:

17 times 60 is 1020

1020 plus 30 is 1050

2 times 60 is 120

120 plus 30 is 150

1050 divided by 150 is 7

Answer:

B.7

Step-by-step explanation:

17.5 divided by 2.5 is 7

Answer:

x ≤ 4/7

Step-by-step explanation:

Simplify the given 2x ≤ -2/3 (4x + 4) by multiplying both sides by (3/2):

(3/2)(2x) ≤ (3/2)(-2/3)(4x + 4)

We get 3x ≤ -4x - 4

Solve for x by combining like terms.  Add 4x to both sides, obtaining

7x ≤ 4

and so the solution is the set

x ≤ 4/7

Answer: 10 miles.

Step-by-step explanation:

Let m the number of miles that each dog is walked.

It is given that Beth does not charge a registration fee for her dog-walking service, but she charges $5 per mile that each dog is walked.

Amount charged by Beth = 5m

Tonya’s dog-walking service charges a registration fee of $20, plus $3 per mile that each dog is walked.

Amount charged by Tonya = 20+3m

We need to find the number of miles m for which Tonya and Beth would charge the same amount.

\(5m=20+3m\)

\(5m-3m=20\)

\(2m=20\)

Divide both sides by 2.

\(m=10\)

Therefore, for 10 miles Tonya and Beth would charge the same amount.