A national diet company markets a special diet plan which requires dieters to use frozen meals prepared by the company. The company advertises that those who follow their plan for 10 weeks will lose, on the average, at least 10 lbs. A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less. If m represents the mean weight loss the population of all American adults would experience after 10 weeks on the plan, what is the appropriate alternative hypothesis that the consumer group wishes to test?a. Ha: mu < 10 b. Ha: mu > 10 c. Ha: mu (notequal)10 d. Ha: mu (notequal) 0

We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:

Step 1 - Picture a

Step 2 - Picture b

Step 3 - Picture c

Step 4 - Picture c.

Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.

The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.

A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

mean add upp all the numbers and divide by how many they are

Answer:

subtract 75 out of 636.75 then once you get that answer divided it by 100 to get the percentage

The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.

Therefore,

The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.

When we substitute the provided values, we get: ABCD perimeter = 9 units plus 5 units plus 9 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units As a result, the perimeter of ABCD is 28 units.

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The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Answer:

\( y= e^x\)

And we want to evaluate e^0 using the graph

And as we can see in the plot the y intercept is the blue point with y=0 and that correspond with:

\( y(0)= e^0 =1\)

Step-by-step explanation:

For this problem we know the following function:

\( y= e^x\)

And we want to evaluate e^0 using the graph

And as we can see in the plot the y intercept is the blue point with y=0 and that correspond with:

\( y(0)= e^0 =1\)

The distance between city A and city B is approximately 442.3 km.

What is the law of cosine?

The Law of Cosines, also known as the Cosine Rule, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, it states that:

c² = a² + b² - 2ab cos(C).

We can use the Law of Cosines to find the distance between City A and City B. Let's call this distance d.

From the information given, we know that:

The distance between the satellite and city A is 450 km.

The distance between the satellite and city B is 340 km.

The angle between city A, the satellite, and city B is 1.5 degrees.

Using the Law of Cosines, we have:

d² = 450² + 340² - 2(450)(340)cos(1.5)

d² = 202500 + 115600 - 2(450)(340)cos(1.5)

d² = 318100 - 122328.8

d² = 195771.2

d = √195771.2

d ≈ 442.3

Therefore, the distance between city A and city B is approximately 442.3 km (rounded to the nearest tenth).

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Answer:

\(\Large \boxed{\sf \ \ 7 \ \ }\)

Step-by-step explanation:

Hello, please consider the following.

The polynomial function is

\(x^3-5x^2-12x+14\)

The rational root theorem states that each rational solution

   \(x=\dfrac{p}{q}\)    

, written in irreducible fraction, satisfies the two following:

   p is a factor of the constant term

   q is a factor of the leading coefficient

In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.

Let's proceed with the prime factorisation of 14:

14 = 2 * 7

Finally, the possible rational roots of this expression are :

   1

   2

   7

   14

and we need to test for negative ones too

   -1

   -2

   -7

   -14

From your list, the correct answer is 7.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

the answer is C.) 7

9514 1404 393

Answer:

  consistent, independent

Step-by-step explanation:

Systems of equations are most easily classified these ways if the equations are in the same form. If we solve the second equation for y, we have ...

  y = x - 1

The x-coefficients of this and the first equation are different, so the system is consistent and independent.

__

A system is independent if the equations describe different lines.

A system is inconsistent if the equations describe parallel lines.

Here, the different lines are not parallel, so the system is independent and consistent.

Answer:

he domain of the composition is all real x values except for x = -1

In other words: \(\left \{ x \, |\, x \neq -1} \right \}\)

Step-by-step explanation:

Let's find the composition \(f(g(x))\) in order to answer about its domain (where on the Real number set the function is defined), give the two functions:

\(f(x)= \frac{1}{x+4}\)    and    \(g(x)=\frac{8}{x-1}\)  :

\(f(g(x))=\frac{1}{g(x)+4} \\f(g(x))=\frac{1}{\frac{8}{x-1} +4} \\f(g(x))=\frac{1}{\frac{8+4(x-1)}{x-1} }\\f(g(x))=\frac{x-1}{8+4x-4} \\f(g(x))=\frac{x-1}{4+4x} \\\)

This rational function is defined for every real number except when the denominator adopts the value zero. Such happens when:

\(4+4x=0\\4x=-4\\x=-1\)

So the domain of the composition is all real x values except for x = -1

Answer:

42/11

Step-by-step explanation:

11/7 = 6/v

cross multiply:

11v = 6x7 = 42.

v = 42/11 ≈ 3.81

Answer:

8units

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) y  = 3x + 1

When x = -1 ,   y = 3*(-1) + 1              

                          = -3 + 1

                        y = -2

(-1 , -2)

When x = 0 ,  y = 3*0 + 1

                      y = 1

(0 , 1)

When x = +1 , y = 3*1 + 1

                          = 3 + 1

                       y = 4

(1 , 4 )

Plot these points in the graph and join the points.

2) y = 2x -1

When x = -1 ,         y = 2*(-1) - 1

                                = - 2 - 1

                             y = -3

(-1 , -3)

When x = 0,      y = 2*0 - 1

                        y = -1

(0 , -1)

When x = +1 , y = 2*1 -1

                         = 2 - 1

                       y = 1

(1 , 1)

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

Answer:

∠ DCF = 45°

Step-by-step explanation:

given AB is parallel to CD , then

∠ BAF and ∠ AEC are alternate angles and are congruent , that is

∠ AEC = ∠ BAF = 75°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ AEC is an exterior angle of Δ CEF , then

∠ DCF + ∠ CFA = ∠ AEC

∠ DCF + 30° = 75° ( subtract 30° from both sides )

∠ DCF = 45°

Answer:

The first one

Step-by-step explanation:

She cant buy anything over $15, but she can buy something thats $15 :))

The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

The general form of linear equations is:

y = a + bx

Where:

a = intercept

b = slope

The form of the equation that models the cost is:

Total cost = cost of renting the van + [cost per mile x (m - 120 miles)

$598.74 = $183 + [$0.39 x (m - 120)

$598.74 = $183 + $0.39m - 46.80

$598.74 = 136.20 + $0.39m

Thus, they travelled 1186 miles.

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9514 1404 393

Answer:

  171° (angle) and 9° (supplement)

Step-by-step explanation:

If 'a' represents the measure of the angle then ...

  a = 19(180 -a) . . . . . the angle is 19 times its supplement

  20a = 19(180) . . . . add 19a

  a = 19(9) . . . . . . . . divide by 20

  a = 171 . . . degrees (the angle)

  180-a = 9 . . . degrees (the supplement)

Answer:

A proof for the statement by selecting the given sentences are as follows;

Suppose there is an integer m such that 7·m + 4 is divisible by 7

By definition of divisibility, 7·m + 4 = 7·k for some integer k

Subtracting 7·m from both sides of the equation gives 4 = 7·k - 7·m = 7·(k - m)

Dividing both sides of the equation by 7 results in 4/7 = k - m

But k - m is an integer and 4/7 is not an integer

Therefore, for every integer m, 7·m + 4 is not divisible by 7

Step-by-step explanation:

The given equation can be expressed as follows;

Where 7·m + 4 is divisible by 7, we have;

7·m + 4 = 7·k

Where 'k' is an integer

We have;

7·m + 4 - 7·m = 4 = 7·k - 7·m

∴ k - m = 4/7, where k - m is an integer

∴ k - m cannot be equal to 4/7, from which we have;

7·m + 4 cannot be divisible by 7.

Answer:

77

Step-by-step explanation:

dont use that

Answer: The number you reach would be -4

Step-by-step explanation:

The answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is 2/15 .

In the question ,

the expression is given as

=[2-|-2/3-2(-1/5)|] divided by 13

which means

= [2-|-2/3-2(-1/5)|] ÷ 13

Solving the terms inside [ ] first , we have

-2*(-1/5) = 2/5

Substituting the value of -2*(-1/5) in the expression , we get

= [2-|-2/3+2/5|] ÷ 13

Solving the norm(modulus) first

|-2/3+2/5| = |-10/15+6/15|  = |-4/15| = 4/15

Substituting the value of |-2/3+2/5| in the expression , we get

= [2-4/15] ÷ 13

Simplifying further we get ,

= [30/15-4/15] ÷ 13

= [26/15] ÷ 13

= \(\frac{\frac{26}{15} }{13}\)

= \(\frac{26}{15} \times \frac{1}{13}\)

= 2/15

Therefore , the answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is  2/15 .

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Answer:

it doesn't because there are places where there are two y values which just doesn't work out.

Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

\(m = -\frac{2}{3}\)

Step-by-step explanation:

Given

\(P_1 = (-1,3)\)

\(P_2 = (5,-1)\)

Required

Determine and interpret slope

Slope is calculated using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\((x_1,y_1) = (-1,3)\)

\((x_2,y_2) = (5,-1)\)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\) becomes

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

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

\(m = \frac{-4}{6}\)

\(m = -\frac{2}{3}\)

The above slope is negative and it implies that x increases when y decreases and vice versa.

Answer:

( − ∞ , ∞ ) hope i help

Step-by-step explanation:

First, solve each inequality. I'll solve the first one first.

7 ≥ 2 x − 5

12 ≥ 2 x

6 ≥ x

Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

( − ∞ , 6 ]

The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  

x

be any number less than 6, but it could also be 6.

Let's try the second example:

3 x − 2 4 > 4

3 x − 2 > 16    3 x > 18 x > 6

Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

( 6 , ∞ )  

The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either  x  is on the interval  ( − ∞ , 6 ] or the interval  ( 6 , ∞ )

. In other words,  x

is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  

x

could be any real number, since no matter what number  

x

is, it will fall in one of these intervals. The interval "all real numbers" is written like this:

( − ∞ , ∞ )