Jesse has 414 inches of ribbon for making bows. She uses 3 inches of ribbon for each bow. How many bows can she make?
Write a division expression that can be used to answer this question.

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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Answer:

  94.3

Step-by-step explanation:

You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"

The diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.

The solution is found by multiplying both sides by 82:

  (x/82)·82 = (115/100)·82

  x = 94.3

The question can also be written as a statement:

  "what" is 115% of 82

When written as an equation, "is" means "equals", and "of" means "times":

  what = 115% × 82

Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...

  x = 115/100 × 82 = 1.15 × 82

All that remains is to evaluate this expression.

  x = 1.15 × 82 = 94.3

So, the answer to the question is ...

  94.3 is 115% of 82.

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

the bottom faded looking one

Step-by-step explanation:

Answer:

$66.57

Step-by-step explanation:

Cost of one DVD = $19.99

Cost of 3 DVDs = $19.99*3 =$59.97

Rate of GST = 5%

Amount of GST

= 5%* $59.97

= 0.05*59.97

= $2.9985

Rate of PST = 6%

Amount of PST

= 6%* $59.97

= 0.06*59.97

= $3.5982

Total cost of DVDs

= $59.97 + $2.9985 + $3.5982

= $66.5667

= $66.57

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

\( \: :\implies \) 500000 /170

\( :\implies \: \) 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

\( \: :\implies \) 1000/0.21

\( \: :\implies \) 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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The reason for each of the statements are given below;

40. Given

41. Linear pair of angles are supplementary.

42. Supplementary angles.

Supplementary angles add up to 180 degrees.

3204:119=

=26,92

=27/10

Answer:

The **Gross Domestic Product (GDP)** is the total value of goods and services produced in a country in a year. According to the World Bank, the GDP of the United States was **$22.67 trillion** in 2020.

If the U.S. economy grows by 1%, the GDP would increase by **$226.7 billion** (1% of $22.67 trillion). If the U.S. economy contracts by 1%, the GDP would decrease by **$226.7 billion**.

The average American output is measured by Gross Domestic Product per capita (GDP per capita). According to the World Bank, the GDP per capita of the United States was **$68,309** in 2020.

If we assume that the population of the United States is 340 million people, then each person's share of GDP would be approximately **$201** ($68,309 divided by 340 million).

Therefore, if the U.S. economy grows by 1%, each person's share of GDP would increase by approximately **$0.67** ($201 times 1% growth rate). If the U.S. economy contracts by 1%, each person's share of GDP would decrease by approximately **$0.67** ($201 times 1% contraction rate).

Answer:

S(a) = 27,5036  squared units

Step-by-step explanation:

Shaded area is :

S(a)  =  Area of the circle  - area of the regular pentagon      (1)

A(c) = area of the circle

A(c) = π*(r)²    ⇒  A(c) =  π*(6)²     ⇒   A(c) =  36*π   ⇒ A(c) = 113,0976 squared units

Area of a regular pentagon:

a) If we draw a straight line between the center and each vertex we get  5 triangles, and if we draw the apothem for each side, we get 10 triangles. We will calculate the area of one  of these triangles

The first 5 triangles has a central angle equal to 72⁰ according to:

360/5  =  72

When we divide these triangles in two triangles by means of the apothem, each central angle will be of 36⁰, then

sin 36⁰  =  0,58778  and cos 36⁰ = 0,809017    and   sin 36⁰ =  x/6      here x is half of the side of the regular pentagon. Then

0,58778  =  x/6

x = 6*0,58778

x =  3,52668 units of length  

and cos 36⁰ = a/6      where a is the apothem, then

0,809017  = a / 6     ⇒   a  = 6*0,809017

a =  4,8541 units of length

Now we are in conditon to calculate area of the triangles as:

A(t) = (1/2)*b*h

A(t) = (1/2)*x*a     ⇒ A(t) = 0,5* 3,52668*4,8541

A(t) = 8,5594 squared units

Finally we have 10 of these triangles, then

Area of regular pentagon is : 10*A(t) squared units

A(p) = 85,594 squared units

Now plugging these values in equation (1) we get the shaded area

S(a) =  113,0976 - 85,594

S(a) = 27,5036  squared units

Answer:

um

Step-by-step explanation:

I guess 1 and a half?? i dont quite understand

Answer:

They can vary. Why? Look at the picture

Answer:

Degrees of freedom for independence  in chi-square statistic

ν = ( r-1) (s-1) =6

Step-by-step explanation:

Explanation:-

Given data  chi-square test for independence is being used to evaluate the relationship between two variables

Given "A" is classified into 3 categories

Second 'B' is classified into 4 categories

In this chi-square test, we test if two attributes A and B under consideration are independent or not

We will assume that

Null Hypothesis : H₀: The two variables are independent

Degrees of freedom in chi-square test for independence

ν = ( r-1) (s-1)

Given data 'r' = 3  and  's' = 4

Degrees of freedom for independence

ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6

Test statistic

                       χ ²  =  ∑  \(\frac{(O-E)^{2} }{E}\)

This question is based on Chi-square test. Therefore, the chi-square statistic for this test would have df equal to \(X^{2} = \sum \dfrac{(O-E)^2}{E}\).

Given:

Chi-square test for independence is being used to evaluate the relationship between two variables . Given "A" is classified into 3 categories . Second 'B' is classified into 4 categories

According to the question,

In this chi-square test, we would be test if two attributes A and B under consideration are independent or not.

Let assumed that,  null Hypothesis : H₀: The two variables are independent

Now, degrees of freedom in chi-square test for independence is,

 ⇒ ν = ( r-1) (s-1)

It is given that, 'r' = 3  and  's' = 4.

Thus, degrees of freedom for independence is,

ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6

Therefore, test statistic be,

\(X^{2} = \sum \dfrac{(O-E)^2}{E}\)

Therefore, the chi-square statistic for this test would have df equal to \(X^{2} = \sum \dfrac{(O-E)^2}{E}\).

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Answer:

C

Step-by-step explanation:

Answer:

A x√2/2

hope it helps and your day will be full of happiness

No, we cannot prove that war is near based on these propositions only.

In logic and mathematics, a proposition is a statement or assertion that is either true or false. It is also referred to as a declarative sentence. Propositions are often used as the building blocks for logical reasoning and mathematical proofs.

Here,

The given propositions are a chain of conditional statements, also known as if-then statements. To prove that war is near, we would need a statement or evidence that directly supports this claim. None of the given propositions directly state or imply that war is near. Even if we assume that all the given propositions are true, the only thing we can conclude is that Notre Dame de Paris cathedral started burning. We cannot make any conclusions about whether war is near or not.

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Answer:

1. 2 subtracted from x² equals 5

2. The product of x and 5 subtracted from 3 is -10

Step-by-step explanation:

1.) x² - 2 = 5

2 subtracted from x² equals 5

2.) 3 - 5x = -10

The product of x and 5 subtracted from 3 is -10

The linear equation that fits the data for tree y = 0.3X + 18.3

Given that data :

x = year.

y = trunk diameter, in inches

Year trunk diameter

1-18.6, 3-19.2, 5-19.8, 7-20.4, 9-21.0, 11-21.6, 13-22.2

As per the question, we have the points:

(x₁,y₁)=(1,18.6)

(x₂,y₂)=(3,19.2)

First, we calculate the slope (m):

m=y₂-y₁/x₂-x₁

So, we have:

m=19.2-18.6/3-1

m=0.6/2

m=0.3

The equation is then calculated as:

y=m(x-x₁)+y₁

So, we have:

y=0.3(x-1)+18.6

y=0.3x-0.3+18.6

y=0.3x+18.3.

So, the linear equation that fits the data for tree 1 is y=0.3x+18.3.

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Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

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The unknown angle measures are d = 76, c = 53, a = 51 and b = 76

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

The lines

The sum of angles on a line is 180

So, we have

b = 180 - 51 - 53

b = 76

By vertical angle theorems, we have

d = 76

c = 53

a = 51

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Answer:

it's a 0.1 seconds per copy

B) 15 hours, 34 minutes

2:12 + 15 hours = 5:12 A.M

5:12 + 34 minutes = 5:46 A.M

Answer:

82991 employees

Step-by-step explanation:

One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that

28300 = 34.1%

If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get

829.912 = 1%

Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get

100% = 82991

Answer:

a triangle that may not have the same dimensions as the bases

Step-by-step explanation:

The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.

Answer:

c

Step-by-step explanation:

A Roth 401(k) plan takes money after tax has been removed from gross income, and has a contribution limit, but withdrawal is tax free.

Answer:

its c

Step-by-step explanation:

Answer:

B. Share them with the office to celebrate a job well-done.

Step-by-step explanation:

This is a question about ethics.

There are 3 dozen doughnuts, which is equal to 36 doughnuts, probably enough to go round the office of the newsroom.

The feature profile from yesterday was a team work, you were not the only one involved, since the doughnut was brought to the newsroom, it is ethical that you share them with the office to celebrate a job well-done. This shows that you appreciate the team work put together by the whole office.

As noble and benevolent as taking the doughnut to the homeless center, it wont be ethical in this situation.