y = -(x – 8)(x + 9)

HOW DO I MAKE THIS STANDARD FORM!!

Answer:100,000,000

Step-by-step explanation:

1,000,000 x 100 = 100,000,000

This is one-tailed test with such a left-tailed critical area since the inspector will only deny the null hypothesis if indeed the average is unquestionably less than $550.

Equal is indeed a noun, a verb, and an adjective in English. It indicates similarity in judgment, such as status, when used as a noun. It means the same thing in fact when used as a verb, such in a mathematical equation. It indicates being the same when used as an adjective, such as value.

The assumption we want to test is the null hypothesis, or H0. The assumption under consideration is that mean total amount of receivables is equal or greater to $550. Hence, we can say:

H0: 550 dollars, where is the demographic mean of any and all accounts receivable.

If you reject the null hypothesis, we will adopt the alternative hypothesis, represented by the symbol Ha. The alternate theory in this situation is that the average amount of all receivables is less that $550. Hence, we can say:

Ha: Where is the demographic mean of all receivable accounts, and is $550.

This is an each test with a moved critical area since the inspector will only deny the null hypothesis if somehow the average is unquestionably less than $550.

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The ratio of a pair of corresponding sides of the smaller triangle to the bigger triangle can be found by taking the square root of the ratio of their areas. In this case, the ratio would be √(36/72) or 1:√2.

When two triangles are similar, their corresponding sides are proportional to each other. In this scenario, we are given the areas of the two triangles, which are 72 and 36. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Let's denote the ratio of the corresponding sides as 'x'. According to this relationship, we have:

(area of smaller triangle) / (area of bigger triangle) = x^2

Plugging in the given areas, we get:

36 / 72 = x^2

Simplifying, we find:

1/2 = x^2

Taking the square root of both sides, we get:

x = √(1/2) = 1/√2

Rationalizing the denominator, we can express the ratio as 1:√2. Therefore, the ratio of a pair of corresponding sides of the smaller triangle to the bigger triangle is 1:√2.

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f(x)= -2x+1 {-2,0,2,4,6}

If x=-2, then -2(-2)+1 = 5

If x=0, then -2(0)+1 = 1

If x=2, then -2(2)+1 = -3

If x=4, then -2(4)+1 = -7

If x=6, then -2(6)+1 = -11

Answer:

B {5,1,-3,-7,-11}

Answer:

B

Step-by-step explanation:

-2(-2)+1

-2(0)+1

....

just plug the numbers in for x

Y=21

Step-by-step explanation:

The sum of the whole numbers from 1 to 680 is 231540.

Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant called the common difference.

The formula for sum of first n numbers can be expressed as;

Sₙ = (n/2)( a₁ + aₙ )

Where n is the number of terms, a₁ is the first term and aₙ is the nth term.

Given that,

The numbers are whole numbers from 1 to 680

Plug the given values into the equation above.

Sₙ = (n/2)( a₁ + aₙ )

S₆₈₀ = (680/2)( 1 + 680 )

S₆₈₀ = 340( 681 )

S₆₈₀ = 231540

Therefore, the sum of the whole numbers from 1 to 680 is 231540.

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The expectation of getting correct option out of total choice of 5 question.

Probability is the ratio of number of favorable outcomes to the total number of outcomes.It can not be more than 1.

we have five question each of them has four choice, two out of them are correct.

Number of correct choice in one question = 2

Total number of choice in a question = 4

probability to get correct option of one question = 2/4 = 0.5.

Then the probability of 5 question = 5(0.5) = 2.5

Thus, the expectation of correct choice is 2.5.

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Answer:

the answer is 130

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

when adding you positive number to a negative number you have to subtract. so to make it easier im going to change it from -240 +370 to

370-240 and solve

370-240=130

have a great day :D

\(y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

The probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7 is 28.43%. Correct option is D.

To calculate the probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7, we need to use the standard normal distribution and the z-score.

First, we can find the z-score for 82 using the formula:

z = (x - mu) / sigma

where x is the value of interest (in this case, 82), mu is the mean (78), and sigma is the standard deviation (7).

z = (82 - 78) / 7

z = 0.57

Next, we can use a z-table or a calculator to find the area under the standard normal curve corresponding to a z-score of 0.57. The area represents the probability that a score will be greater than 82.

Using a standard normal table, we find that the area to the right of z = 0.57 is 0.2843 or approximately 28.43%. Therefore , correct option is D.

In conclusion, by calculating the z-score and using a standard normal distribution table, we can find the probability that a score will be greater than a certain value in a normal distribution with a known mean and standard deviation.

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Complete question is:

A normal distribution with a mean of 78 and a standard deviation of 7, what is the probability that a score will be greater than 82?

group of answer choices

A. 23.89%

B. 26.11%

C. 76.11%

D. 28.43%

E. 52.22%

The value of y' of x³ + 3xy² + y = 15 when x = 1, are:

dy/dx (at x = 1) = -(3 + 3y²) / (1 + 6y)

The two equations of the tangent lines to the graph of x³ + 3xy² + y = 15 when x = 1 are:

y - 2 = -15/14 * (x - 1)

y + 7/3 = -1/14 * (x - 1)

Here, we have,

To find y' and the equations of the tangent line to the graph of x³ + 3xy² + y = 15 when x = 1, we will first find the derivative dy/dx and evaluate it at x = 1 to get the slope of the tangent line.

Then, we can use the point-slope form to write the equations of the tangent line.

Let's start by finding dy/dx:

Differentiating the equation x³ + 3xy² + y = 15 implicitly with respect to x:

3x² + 3y²(dx/dx) + 6xy(dy/dx) + dy/dx = 0

Simplifying the equation:

3x² + 3y² + 6xy(dy/dx) + dy/dx = 0

Rearranging to solve for dy/dx:

dy/dx = -(3x² + 3y²) / (1 + 6xy)

Now, we evaluate dy/dx at x = 1:

dy/dx (at x = 1) = -(3(1)² + 3y²) / (1 + 6(1)y)

= -(3 + 3y²) / (1 + 6y)

This gives us the slope of the tangent line when x = 1.

Now, let's find the y-coordinate corresponding to x = 1. We substitute x = 1 into the original equation and solve for y:

(1)³ + 3(1)y² + y = 15

1 + 3y² + y = 15

3y² + y = 14

This is a quadratic equation in terms of y. We can solve it to find the y-coordinate:

3y² + y - 14 = 0

Using factoring or the quadratic formula, we find that y = 2 or y = -7/3.

So, we have two points on the graph when x = 1: (1, 2) and (1, -7/3).

Now, we can write the equations of the tangent lines using the point-slope form:

Tangent line at (1, 2):

Using the slope dy/dx = -(3 + 3y²) / (1 + 6y) evaluated at x = 1:

y - 2 = dy/dx (at x = 1) * (x - 1)

Substituting the values:

y - 2 = (-(3 + 3(2)²) / (1 + 6(2))) * (x - 1)

Simplifying:

y - 2 = -15/14 * (x - 1)

This is the equation of the tangent line at (1, 2) in slope-intercept form.

Tangent line at (1, -7/3):

Using the slope dy/dx = -(3 + 3y²) / (1 + 6y) evaluated at x = 1:

y - (-7/3) = dy/dx (at x = 1) * (x - 1)

Substituting the values:

y + 7/3 = (-(3 + 3(-7/3)²) / (1 + 6(-7/3))) * (x - 1)

Simplifying:

y + 7/3 = -1/14 * (x - 1)

This is the equation of the tangent line at (1, -7/3) in slope-intercept form.

Therefore, the two equations of the tangent lines to the graph of x³ + 3xy² + y = 15 when x = 1 are:

y - 2 = -15/14 * (x - 1)

y + 7/3 = -1/14 * (x - 1)

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Perimeter is the sum of the length of the sides used to make the given figure. The length and the width of the rectangle are 60 meters and 20 meters, respectively.

Perimeter is the sum of the length of the sides used to make the given figure.

Let the width of the rectangle be represented by x.

Given that the pen should be three times as long as it is width. Therefore, the dimensions of the rectangle can be written as,

Width of the rectangle = x

Length of the rectangle = 3x

Also, it is given that the perimeter of the rectangle should be equal to 160 meters, therefore, we can write,

Perimeter = 2(Length + Width)

160 = 2(3x + x)

160 = 2(4x)

160 = 8x

x = 160/8

x = 20 meters

Now, the dimensions of the rectangle can be written as,

Length = 3x = 3 × 20 meters = 60 meters

Width = x = 20 meters

Hence, the length and the width of the rectangle are 60 meters and 20 meters, respectively.

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Answer:

B) 9

Step-by-step explanation:

x + 5 > 8      

x > 3

OR

5 + 8 > x

x < 13

possible values for third side of triangle:  4,5,6,7,8,9,10,11,12

The possible integer values of this scenario are A) 6

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

Given, the lengths of the sides of a triangle are x, 5, and 8.

x² + 5² < 8².

x² + 25 < 64.

x² < 39, now perfect squares less than 39 are 36, 25, 16, 9, 4, 1, 6 integer values.

x² + 5² = 8².

x² + 25 = 64.

x²  = 39, No integer values.

x² + 5² > 8².

x² + 25 > 64.

x² + > 39.

Here the possible integer values are infinite.

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Answer:

40

Step-by-step explanation:

20 - 40 = -20

Using zero as a reference point 20 is 20 units above zero and -20 is 20 units below zero.

20 + 20 = 40

-20 and 20 are 40 units away from each other.

-20 is 40 less than 20

Answer:

Ishaan is 21. Christopher is 7.

Answer:  Ishann is 21 years old.

Step-by-step explanation:

In this situation, we will represent Ishaan age by the variable  y and we will represent Christopher's age by x.

Ishaan is 3 times as old as Christopher and that can be represented by the equation,   y = 3x  

He is also 14 years older, and it can also be represented by the equation,  

y = x + 14.  

y= 3x

y = x + 14  

Using both equations, substitute the value of y in one of the equations into the other.

x + 14 = 3x                   Solve for x .

-x           -x

 14 = 2x  

  x = 7  

This means that Christopher is 7 years old.

To solve for Ishaan's age , input the value of x into one of the equations.

y = 3(7)

y = 21.

Answer:

-1,373

Step-by-step explanation:

a69 = -13 + (69-1)(-20)

= -13+(68)(-20)

= -13 - 1,360

= -1,373

Answer:

-1373

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

Lets say there's an A.P. whose :-

Formula for finding nth term of A.P. = aⁿ = a + (n - 1)d

SOLUTION :-

According to the question ,

By using the formula for finding nth term ,

69th term of A.P. = -13 + (69 - 1)×(-20) = -13 + (-1360) = -1373

The amount of Linus's money spent on 200 rounds of arcade game is   $55.

The given question is incomplete, so

Lets suppose that Linus has played 200 round of arcade game and now we will need to determine the amount of Linus's money spent on 200 rounds of arcade game.

Entrance fee of an arcade = $5

Additional cost to play one round = $0.25

With the help of given equation ( C=0.25r+5 )  we will determine the amount of Linus's money spent on 200 rounds of arcade game.

'C' = The relationship between the amount of Linus' money spent

'r'  = The number of rounds of arcade games played

Let's solve the equation now,

As we know that r is number of rounds Linus has played which is 200 rounds.

So,     C = 0.25r+5

          C = 0.25 × 200 + 5

          C = 50 + 5

          C =  $55

Hence, we got that Linus has spent total $55 on 200 rounds of arcade game.

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\(27x-18 = 9(3x-2)\\\\9~ \text{units} ~ \text{and}~ (3x-2)~ \text{units}.\)

Answer:

Una función se puede representar de

diferentes modos: mediante una ecuación,

en una tabla, con una gráfica o con

palabras.

Consideraremos los tipos principales de

funciones que se presentan en el cálculo y

describiremos el proceso de usarlas como

modelos matemáticos del mundo real-.

Step-by-step explanation:

Answer:

Quadratic functions look like a U. Increase exponentially to the right decrease exponentially to the left. Exponents on variables

Linear functions are straight and increase arithmetically. No exponents on variables.

Exponential functions increase exponentially in one direction. Looks like an L. X is the exponent.

Step-by-step explanation:

A small p-value provides strong evidence against the null hypothesis. The null hypothesis is the hypothesis that there is no significant difference or relationship between two variables.

The p-value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.
If the p-value is small, typically less than 0.05, it means that the observed result is unlikely to have occurred by chance alone if the null hypothesis is true. This suggests that there is strong evidence against the null hypothesis and that we should reject it in favor of the alternative hypothesis. .
For example, if we conduct a hypothesis test to determine whether a new drug is more effective than a placebo, a small p-value would indicate that the drug is indeed more effective. This is because the observed results are highly unlikely to occur if the drug is not effective.
In summary, a small p-value provides strong evidence against the null hypothesis and supports the alternative hypothesis. It suggests that the observed results are not due to chance and that there is a significant difference or relationship between the variables being studied.

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Answer: (a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ft

sin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned.

The given integral is ₁∫₀^(π/2) sin²(x)dx.

The trapezoidal rule is given by:(b - a) [(f(a) + f(b))/2]And, the Gauss-Quadrature formula for n = 2 is: ∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]

Here, a = 0, b = π/2, gp₁ = -0.5773, gp₂ = 0.5773, w₁ = w₂ = 1.

(i) Trapezoidal Rule: The trapezoidal rule with one interval is given by:(b - a) [(f(a) + f(b))/2] = π/4 [sin²(0) + sin²(π/2)] = 0.7854

(ii) Gauss-Quadrature: Using the Gauss-Quadrature formula with n = 2, we get:∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]= π/2 [ sin²( [ (π/2)/2 ] (-0.5773) + π/4 ) + sin²( [ (π/2)/2 ] (0.5773) + π/4 ) ]= 0.7853Comparing the above two methods, the trapezoidal rule and Gauss-Quadrature method are nearly the same and are close to the exact value.

Exact value = (π/2)/2 - sin(π)/4 = 0.7854Conclusion:Thus, it can be concluded that the given integral using the trapezoidal rule (using only one interval) and Gauss- Quadrature (n=2) is approximately equal to 0.7854.

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Answer:

The value of 9x - 5 is -41.

Step-by-step explanation:

-2x - 3 = 5

-2x = 5 + 3

-2x = 8

x = -4

9x - 5

= 9(-4) - 5

= -36 - 5

= -41

Answer:

The slope is \(\frac{3}{4} \\\)

Answer:

\(\frac{3}{4}\)

Step-by-step explanation:

\(m = \frac{5-2}{3-(-1)} = \frac{3}{4}\)

Answer:

F.

Explanation:

The number of quarts of cream Type A is x.

Type A cream has 18% butterfat, so the amount butterfat will be 0.18x

For type B, we know that the total amount of cream will be 90, so if cream type A is x, cream type B is 90 - x.

Type B crem has 24% butterfat, so teh amount in the mixture will be 0.24(90-x)

Then, the mixture will be 90 quarts of crean that is 22% butterfat, so the amount in the mixture will be 0.22(90)

Therefore, the table that represent this data is table F.

So, the answer is F.

The factory overhead efficiency variance for May is $480 unfavorable.

What is overhead efficiency variance ?

The overhead efficiency variance measures the difference between the actual hours worked and the standard hours allowed, multiplied by the standard overhead rate.

Step 1: Budgeted overhead at 90% capacity:

Budgeted overhead = 6,120 DLHs * $3.00 per DLH = $18,360

Step 2: Budgeted overhead at 70% capacity:

Budgeted overhead = $15,640

Step 3: Standard hours at 70% capacity:

Standard hours = 6,120 DLHs / 90% * 70% = 4,760 DLHs

Step 4: Variable overhead rate:

Variable overhead rate = ($18,360 - $15,640) / (6,120 DLHs - 4,760 DLHs) = $2.00 per DLH

Step 5: Variable overhead efficiency variance:

Variable overhead efficiency variance = (4,760 DLHs - 5,000 DLHs) * $2.00 = $480 unfavorable

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The required volume of the shape is \(\frac{850\pi}{3}$\) cubic units.

A measurement of three-dimensional space is volume. It is frequently expressed mathematically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are linked.

First, let's find the volume of the cylinder:

\($$V_{cylinder} = \pi r^2 h = \pi (5)^2 (8) = 200\pi$$\)

Next, let's find the volume of the hemisphere:

\($V_{hemisphere} = \frac{2}{3}\pi r^3 = \frac{2}{3}\pi (5)^3 = \frac{250\pi}{3}$$\)

To find the volume of the entire shape, we simply add the volume of the cylinder and hemisphere:

\($$V_{shape} = V_{cylinder} + V_{hemisphere} = 200\pi + \frac{250\pi}{3} = \frac{850\pi}{3}$$\)

Therefore, the volume of the shape is \(\frac{850\pi}{3}$\) cubic units.

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