An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 13 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 30 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds. The test statistic for this hypothesis would be __________.

The different statements and reasons to prove that −3(x + 8) = −21 are as detailed below.

Statement 1; −3(x + 8) = −21

Reason 1; Given

Statement 2; −3(x + 8)/-3 = −21/-3

Reason 2; Division property of Equality

Statement 3; x + 8 - 8 = 7 - 8

Reason 3; Subtraction Property of Equality

Statement 4; x = -1

Reason 4; Given

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Random note:}[/tex]

[tex]\large\textsf{(We will solve for your given question as well because it}\\\large\textsf{pops up in solving for your question.)}[/tex]

[tex]\huge\textbf{Solving for your original answer:}[/tex]

[tex]\mathbf{5 + 10x = 20}[/tex]

[tex]\mathbf{10x + 5 = 20}[/tex]

[tex]\huge\textbf{SUBTRACT 5 to BOTH SIDES:}[/tex]

[tex]\mathbf{10x + 5 - 5 = 20 - 5}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{10x = 20 - 5}[/tex]

[tex]\mathbf{10x = 15}[/tex]

[tex]\huge\textbf{DIVIDE 10 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{10x}{10}=\dfrac{15}{10}}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{x = \dfrac{15}{10}}[/tex]

[tex]\mathbf{x = \dfrac{15\div5}{10\div5}}[/tex]

[tex]\mathbf{x = \dfrac{3}{2}}[/tex]

[tex]\mathbf{x = 1 \dfrac{1}{2}}[/tex]

[tex]\mathbf{x = 1.5}[/tex]

[tex]\huge\textbf{Therefore, the overall answer should be:}[/tex]

[tex]\huge\boxed{\star\boxed{\mathsf{\ x= \dfrac{3}{2} \ }}\star}[/tex]

[tex]\huge\textbf{And to answer your question, the very}\\\\\huge\textbf{first step in solving for this equation}\\\\\huge\textbf{[5 + 10x = 20] is:}[/tex]

[tex]\huge\boxed{\textsf{Option D. Subtract 5 to both sides}}\huge\checkmark\\\\\\\\\\\large\text{Look at the explanation above to see how we chose that.}\\\\\large\text{Remember: addition opposite is subtration \& subtraction opposite}\\\large\text{is addition, whereas multiplication is division \& divsion is}\\\large\text{is multiplication.}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

The lines are given as:

y = -14x + 3 and y = -32x+3

Substitute y = -32x+3 in

-32x+3 = -14x + 3

Evaluate the like terms

-18x = 0

Divide by -18

x = 0

Substitute x = 0 in y = -14x + 3

y = -14(0) + 3

Evaluate

y = 3

Hence, the intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

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Answer:

Here you go with your correct answer

The only option that represents the correct repeating decimal is; Option C; 0.35 + 0.0035 + 0.000035

We want to find the option that is equal to the repeating decimal 0.353535.

Option A; 35 + 0.35 + 0.0035

When we add the above, we arrive at 35.3535 which is not equal to 0.353535. Thus, option A is incorrect.

Option B; 0.0035+ 0.000035 + 0.00000035

When we add the above, we arrive at 0.00353535 which is not equal to 0.353535. Thus, option B is incorrect.

Option C; 0.35 + 0.0035 + 0.000035

When we add the above, we arrive at 0.353535 which is not equal to 0.353535. Thus, option C is correct.

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Answer:

1.) C - 0.35+0.0035+0.000035+...

2.) The first term of the geometric series is 0.35.

3.) The common ratio of the geometric series is 0.01

4.) The simplified fractional representation of 0.353535... is 35 / 99

Step-by-step explanation:

Edge

Answer: 2.96% rounded

Step-by-step explanation: 10/30) x (9/29) x (8/28)  =  720 / 24,360 = 6/203 = 2.96%

Option 3 and 4. The two options that shows the correct representation of the inequality are:

–3(2x – 5) < 5(2 – x)

We have to open up the brackets by multiplying the sides

= -6x + 15 < 10 - 5x

Hence the  third option is certified to be correct.

Next this inequality has to be shown on a number line.

To do this we have to solve the inequality completely

From -6x + 15 < 10 - 5x

we have to take like terms

-6x+5x < 10 - 15

-x < -5

x<5

The sign of inequality has to be reversed given that the coefficient of x was negative.

Hence x>5. The number line would start from the right and it would move towards the right

From the solution here, we can see that the two correct options are

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Answer:

l = (S/pi)-r^2

Step-by-step explanation:

Just rearrange the equation.

S = pi*l + pi * r^2

S-pi*r^2 = pi*l

l = (S-pi*r^2)/pi

l = (S/pi)-r^2

1 gallon (gal) = 128 fluid ounce (fl oz)

1 hour (hr) = 60 minutes (min)

Convert 1 fl oz/min to gal/hr.

[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]

The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

Lets simplify the problem,

Let assume  the "tens" digit be x

Then the "units" difference =  (x-1), according to the condition.

Hence, the number itself is N = 10x + (x-1).

Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.

From the last statement of the problem, we have this equation

[tex]N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).[/tex]

Simplify and find "x"

[tex]11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3[/tex].

Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

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The  size of the sample should be obtained at 2401 in order to be 95% confident

Given that:

Margi of error, [tex]ME=0.02[/tex]

Population proportion, [tex]p=0.50[/tex]

To Find: The size of the sample that should be obtained in order to be 95% confident

Let the size of the sample be n

Using formula,

[tex]n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401[/tex]

Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident

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Answer:

The answer is C. U=3x and V=2y^3

Step-by-step explanation:

3x*3x=9x^2

2y^3*-2y^3=-4y^6

Other variables cancel each other out

The true statement about this information is that: A. It is both a relation and a function.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population.

In this context, we can infer and logically deduce that the true statement about this information collected by Jen is that it's both a relation and a function because it indicates a relationship between two variables.

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Answer:

It is both a relation and a function.

Step-by-step explanation:

The time taken to burn off the entire pizza by walking is 568.32 minutes.

2,368 = 125 × w

2,368 = 125w

w = 2,368 / 125

w = 18.944

Total time needed to burn all calories = 30 minutes × 18.944

= 568.32 minutes

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Answer:

56.8 m²

Step-by-step explanation:

This shape is clearly a trapezium / trapezoid. So :  

Area of a trapezium is given by the formula :

[tex]\frac{a+b}{2} h[/tex]

Substitute values given in diagram :

a = 4.2

b = 10

h = 8

[tex](\frac{4.2+10}{2} )8[/tex]

7.1 × 8 = 56.8

Units will be m² as this is area

Giving us our final answer of 56.8 m²

The angle through which ΔABC is rotated is; Option A: 48°

Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but preserves its length and shape. Thus, a rotational transformation is formed by two reflections.

In the given question, image ABCD is reflected over lines I, then m at an angle of 24° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 24 * 2 = 48°

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The computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.

It should be noted that the subtraction line is simply used to subtract numbers.

In this case, the computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.

When subtracting the numbers on the number line, we will move towards the left hand side of the number line.

An illustration of the number line is given.

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The value of a is (c) 86

The given parameter is:

Angle C = 86

By vertical angle theorem, we have:

Angle A = Angle C = 86

This implies that:

Angle A = 86

The arc A subtends angle A

This means that:

Arc A = 86

Hence, the value of a is (c) 86

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Answer:

b = 24 meter

Step-by-step explanation:

Using Pythagoras theorem:

a² + b² = c²

Here given: a = 10 m, b = ?, c = 26 m

Insert values

10² + b² = 26²

b² = 26² - 10²

b² = 676 - 100

b² = 576

b = √576

b = 24

Answer:24

Step-by-step explanation: i found the answer using the pythogaras theorem,the formula used is, h squared=b squared +p squared,formula used to find missing legnths of triangles such as hypotaneous and height.in this question you have to find the height,as you can see to the opposite of hypotaneous its height/perpendicular.

so according to formula,h squared=b squared+p squared

so,26 squared=10 squared+p squared.

in order to find p

p squared=26 squared -10 squared

which gives us 576

and p squared =576

the square on the p will go on the other side and become an underroot.

take the underoot of 576

which gives us p=24.

so the legnth is 24, found using pythogares theorem.by rearranging the formula and making p the subject in the formula

A scenario that would best model the graph on Holly, her home, and school is:

As Holly was heading to school, she felt uneasy and had to wait for 10 mins to catch her breath.

After doing so, she then continued to school which was 6 miles from her home. When she got there, she went to the nurse's office.

She waited in school for 15 minutes and was then told to go home to rest and recuperate. She then made the journey back home in a car and arrived in 10 minutes.

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The system of equation have one solution.

x² + y² = 25

x² - 6 = 0

x² = 6

x = √6

Therefore, let's substitute the value of x in equation (i)

x² + y² = 25

(√6)² + y² = 25

y² = 25 - 6

y² = 19

hence,

y = √19

Therefore, the system of equation have one solution.

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The equation of the trend line is y = 3x + 15

Start by entering the table of values in a graphing calculator.

From the graphing calculator, we have the following summary:

The equation of the trend line is represented as:

y = bx + a

Where

b = SP/SSX = 52.5/17.5 = 3

a = MY - bMX = 25.5 - (3*3.5) = 15

This gives

y = 3x + 15

Hence, the equation of the trend line is y = 3x + 15

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24.85

Step-by-step explanation:

First find the square root of 8.2 and subtract from the square root of 7.5. Multiply 3.5 by 0.71, the answer you get divide it by the answer you get after finding the square root.

The equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

We have:

x = -2 and x = 2

Rewrite as:

x + 2 = 0 and x - 2 = 0

Multiply both equations

(x + 2)(x - 2) = 0

This gives

x^2 - 4 = 0 --- option (a)

Add 4 to both sides

x^2 = 4

Multiply by 4

4x^2 = 16 --- option (d)

Hence, the equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

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30+20+50 = 100 ml total. 20 ml is orange juice.

So, 30/100 reduce by dividing top and bottom by 30 gives

3/10 is the proportion of orange juice in the fruit cocktail.

Hope this helps! :)

Answer:

3/10

Step-by-step explanation:

First, find the total amount of liquid for a drink with 30 mls of orange juice
Assume volumes can be added
30+20+50 = 100 ml
the percentage/proportion of orange juice in the drink is the number of mls of orange juice divided by the total volume
so
30/100
which can be reduced to 3/10

The least distance from point P to line l is approximately equal to 3.536 units.

There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:

Vector parallel to the line l

[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]

[tex]\overrightarrow{AB} = (3, - 3)[/tex]

A vector from one point on the line l to the point P

[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]

[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]

Now we proceed to find the vector distance by using the following vectorial formula:

[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]

[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]

[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]

[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]

[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]

The magnitude of the vector distance is determined by Pythagorean theorem:

[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]

d ≈ 3.536

The least distance from point P to line l is approximately equal to 3.536 units.

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Answer:

Slope=14.000/2.000=7.000

x-intercept = 300/-7 = -42.85714

 y-intercept = 300/1 = 300.00000

Step-by-step explanation:

Answer:

7x - 9x = 26

Step-by-step explanation:

9 times a number = 9x

7 times the number = 7x

=26 because it says so

and 9x subtracted from 7x is 7x - 9x

Answer:

Step-by-step explanation:

Since the new line is parallel to the one that has a slope of 1, we can write:

y = 1x + b for the new line

Remember that y=mx+b, where m is the slope and b the y-intercept, the value of y when x=0.

We need to find a value of b that forces the line through point (1,-1).  Use (1,-1) in the equation and solve for b:

y = 1x + b

-1 = 1*(1)+b

b = -2

The equation of the line parallel to one with slope of 1 and going through point (1,-1) is:

y = 1x - 2