A doctor claims that the mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night. To investigate, he selects a random sample of 50 high school seniors from all high schools in his county. He also selects a random sample of 50 seniors from the colleges in his county. He constructs a 95% confidence interval for the true mean difference in the number of hours of sleep for seniors in high school and seniors in college. The resulting interval is (0.57, 1.25). Based upon the interval, can the doctor conclude that mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night?

yes because 1 is in the confidence interval
yes because 0 is not in the confidence interval
no because 1 is in the confidence interval
no because 0 is not in the confidence interval

The graph is showing the equation of circle x²+y²=4

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.

The equation will be as follows:-

x²+y²=4

Hence the graph is showing the equation of circle x²+y²=4

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The option (A) 63 inches to 81 inches is correct after using the empirical Rule.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

We have:

The mean height of the population is 72 inches and the standard deviation is 3 inches, 99.7% of the population will have a height

99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean.

The lower range = 72 – 3(3) = 63 inches

The upper range = 72 + 3(3) = 81 inches

Thus, the option (A) 63 inches to 81 inches is correct after using the empirical Rule.

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Answer:

Using 22/7 as pi, the area of a circle with a diameter of 14 metres is:

154 m²

Step-by-step explanation:

To solve, use the formula for the area of a circle.

Remember the formula for area of a circle. Be careful not to mix up the formula for area with the formula for circumference!

[tex]A = \pi r^{2}[/tex]

From the question, we know:

To use the formula, we need the radius ("r").

The radius is a line that goes from the centre point of the circle to the circle outline. It is half the length of the diameter.

The diagram shows the diameter ("d"), which goes through the centre point of the circle. It is twice the length of the radius.

Solve for "r".

r = d/2

r = (14 m)/2

r = 7 m

Substitute r = 7 m and π = 22/7  into the formula for the area of a circle.

[tex]A = \pi r^{2}[/tex]                         Start with the formula and substitute.

[tex]\displaystyle{A = \frac{22}{7} (7\ m)^{2}}[/tex]                Square "7" and the "m".

Remember that the answer for area is always squared units.

[tex]\displaystyle{A = \frac{22}{7} (49\ m^{2})}[/tex]      

Multiplying a fraction and whole number is the same as multiplying the whole number in the numerator (top of the fraction).

[tex]\displaystyle{A = \frac{22*49}{7}m^{2}}[/tex]              Simplify the numerator.

[tex]\displaystyle{A = \frac{1078}{7}m^{2}}[/tex]                  Divide.

[tex]A = 154\ m^{2}[/tex]                   Final answer

∴ The area of the circle is 154 m².

Answer:

448 fl oz/week

Step-by-step explanation:

1 week = 7 days

4 pints per day × 7 days/week = 28 pints per week

1 pint = 16 fl oz

28 pints/week × 16 fl oz/pint = 448 fl oz/week

Answer: The formula for area of a triangle is area equals base times height divided by 2. the height is 5 units.

Step-by-step explanation:

The equation that can be used to find out the total time it will take to William to mow the lawn is (75n) / 100=33.

This is a mathematical expression that represents a situation including a value that is not known.

In this case the best equation would be 75n / 100=33 as this is the only one that includes all the factors:

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Since the variable x is the numerator of the fraction, we first need to multiply each side by 6, since the denominator is 6. After doing this, the equation should now look like this: [tex]18 = x + 31[/tex]. Next, we subtract 31 from 18 following the rule. 18 - 31 = -13. x is equal to -13.

For shown work in order:

[tex](6) 3 = x +31[/tex]

[tex]18 = x + 31[/tex]

[tex]18 - 31 = x[/tex]

[tex]x = -13[/tex]

Answer:

20%

Step-by-step explanation: I took the test

It is a quadrilateral, parallelogram, and a rhombus

Answer:

quadrilateral, parallelogram, and rhombus.

Step-by-step explanation:

All quadrilaterals have 4 sides, all parallelograms have 2 sets of parallel sides, and a rhombus has diagonals that bisect each other perpendicularly.

Answer:

Step-by-step explanation:

An coincident system of equations means that it has infinite solutions, because one line is on the other one. This happens when their equation are the same, or their "parent" line is the same.

So, given equations are:

6x + 4y = 2 and 3x + 2y = 1

Observe that if we divide the first by 2, we have

[tex]\frac{6x+4y}{2} =\frac{2}{2}[/tex]

[tex]\frac{6x}{2}+\frac{4y}{2} =1[/tex]

[tex]3x+2y=1[/tex]

As you can see, using the first equation, we found that it has the same "parent" equation than the second equation. In other words, they are basically the same. This means that they represent the same line, so, the system is coincident and they have infinite solutions.

The answer is coincident :)

Answer:

  14 donuts

Step-by-step explanation:

Packing circles in a rectangular space is always an interesting problem. Sometimes, it works well to put them on a grid. Other times, more circles can be packed in if they are somewhat off-grid. The details depend on the specific dimensions.

The attached shows a way to fit 14 donuts in the box.

_____

Additional comment

Packing them on a square grid allows only 12 donuts to be put in the box.

The possible number represented by the 9 counter is 27

The counters are given as:

12 counters and 15 counters

When added, we get a number that can be represented by 9 counters.

This means that:

12 + 15 = 9x

Evaluate the sum

27 = 9x

Divide by 9

x = 3

When subtracted, you need more than 9 counters.

This means that:

x = 15 - 12 = 3

So, we conclude that the number is a multiple of 3 and 9

In other words, the decimal number is a multiple of 9 (i.e. 27)

Hence, the possible number is 27

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Answer:

B

Step-by-step explanation:

2.

what is the middle between 2 numbers (any numbers, really) ?

you add both numbers and divide the result by 2.

the same here :

(-3 + 24) / 2 = 21/2 = 10 1/2

proof :

what is the distance from -3 to 10 1/2 ? it is 10 1/2 from 0 to 10 1/2 plus 3 from -3 to 0 = 10 1/2 + 3 = 13 1/2.

what is the distance from 10 1/2 to 24 ? it is 13 from 11 to 24, and another half from 10 1/2 to 11. so, in total 13 1/2.

both distances are equal, so it is proven for 10 1/2 to be the midpoint.

Answer:

The answer is The function h because the graphs of f and h are symmetrical about the line y = x.

Step-by-step explanation:

A function and its inverse function become symmetrical across the line y = x.  

Answer:

Center = (-4, 5)

Radius = 5

Step-by-step explanation:

Equation of a Circle :

Finding the center :

Finding the radius :

Step-by-step explanation:

the area of a triangle is always

baseline × height / 2

where baseline and height are perpendicular (at a 90° angle) to each other.

so, in our case the area is

7 × 2 / 2 = 7 × 1 = 7 units²

Answer:

Step-by-step explanation:

Two legs of a right triangle measure 3 inches and 4 inches. Which of the following choice for the length of the third side will make the triangle a right triangle?

x = √(3²+4²)

x = √(9 + 16)

x = √25

The expression for the perimeter of the pool is 8x + 20 and the cost of fencing the pool is 27.76x + 69.4

There are two missing sides in the figure, and they can be calculated using the subtraction operation.

The equations to calculate the missing sides are:

Missing side 1 = 5x - 2 - (-6 + 4x)

Missing side 2 = 12 - x - (3x - 3)

Evaluate the equations

Side 1 = x + 4

Side 2 = 15 - 4x

Hence, the missing sides are x + 4 and 15 - 4x

This is the sum of the side lengths of the pool.

So, we have:

Perimeter = 5x - 2 + 12 - x - 6 + 4x + 3x - 3 + x + 4 + 15 - 4x

Collect like terms

Perimeter = 5x - x + 4x + x - 4x + 3x - 2 + 12 - 6  - 3  + 4 + 15

Evaluate

Perimeter = 8x + 20

Hence, the perimeter of the pool is 8x + 20

In (b), we have:

P = 8x + 20

Where P represents the perimeter of the pool

The cost of fencing the pool is the product of the perimeter and the unit cost per foot.

So, we have:

C = (8x + 20) * 3.47

Expand

C = 27.76x + 69.4

Hence, the cost of fencing the pool is 27.76x + 69.4

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Answer:

Step-by-step explanation:

4x + 2 = 11

4x = 9

x = 9/4

2(9/4) - 1

9/2 - 2/2= 7/2

Answer:

what is this question man .......

Answer:

24 ft

Step-by-step explanation:

to find the perimeter of rug is you have to add 9+9+3+3= 24

Step-by-step explanation:

If you agree that increasing age (for elementary school children) causes increasing foot size, and therefore increasing shoe size, then you expect a correlation between age and shoe size. Correlation is symmetric, so shoe size and age are correlated.

Answer:

D. 60

Step-by-step explanation:

210 baseballs divided evenly between 7 trash bins = 30 balls per bin

2 trash bins multiplied by 30 balls per bin = 60 balls in two bins

Hope this helps!

Answer:

[tex]\huge\boxed{\sf x > -1.25}[/tex]

Step-by-step explanation:

0.2 (x + 20) - 3 > -7 - 6.2x

Distribute

0.2x + 4 - 3 > -7 - 6.2x

0.2x + 1 > -7 - 6.2x

Add 6.2x to both sides

0.2x + 6.2x + 1 > -7

6.4x + 1 > -7

Subtract 1 to both sides

6.4x > -7 - 1

6.4x > -8

Divide 6.4 to both sides

x > -8/6.4

x > -1.25

[tex]\rule[225]{225}{2}[/tex]

Answer:

x > -1.25

Step-by-step explanation:

Using the distributive property: a(b + c) → ab + ac

1. Distribute '0.2'

0.2(x) + 0.2(20) - 3 > -7 - 6.2x

0.2x + 4 - 3 > -7 - 6.2x

0.2x + 1  > -7 - 6.2x

2. Add '6.2x' to both sides

0.2x + 6.2x + 1  > -7 - 6.2x + 6.2x

6.4x + 1 > -7

3. Subtract '1' from both sides

6.4x + 1 - 1 > -7 - 1

6.4x > -8

4. Divide both sides by '6.4' to isolate the variable

6.4x ÷ 6.4 > -8 ÷ 6.4

x > -1.25

Final answer: x > -1.25

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Answer:

The value of the rational expression when x = -3 is undefined.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Rational Functions

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{x}{x^2 - 9} ,\ x = -3[/tex]

Step 2: Find Value

∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.

___

Topic: Algebra II

Answer:

288 m^3

Step-by-step explanation:

V=(1/3)Bh, where B is base, and h is height

The base will use the equation A=(1/2)bh

B = (1/2)12x9

B = 54

the height is given: 16m

substitute into Volume equation:

V=(1/3)54x16

V=288

Answer:

  x = -47.1

  x = -3.35454... (2-digit repeat)

Step-by-step explanation:

Each of the absolute value functions causes the overall behavior of the equation to change where that absolute value function's argument is zero. Those values of x are -7, -5/2, -2/5.

These breakpoints cause the domain of the equation to be divided into 4 parts. A graphing calculator shows us that solutions exist only in the two regions ...

In those regions, the equation simplifies to ...

  2(-(x +2/5)) -2(-(x +7)) = 2/3x +(-(x +5/2))

  x(-2 +2) -4/5 +14 = x(2/3 -1) -5/2 . . . . collect terms

  15.7 = -1/3x . . . . . . add 5/2

  x = -47.1 . . . . . . . multiply by -3

__

  2(-(x +2/5)) -2(x +7) = 2/3x +(-(x +5/2))

  x(-2 -2) -4/5 -14 = x(2/3 -1) -5/2 . . . . collect terms

  (-3 2/3)x = 12.3 . . . . . . . . add 1/3x +14.8

  x = -36.9/11 = -369/110

  x = -3 39/110 ≈ -3.35454... (2-digit repeat)

Answer:

so first do nothing and just fail health class

The value of y that satisfies given conditions is y = - 8.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

We also know that slope(m) = (y₂ -y₁)/(x₂ - x₁).

So, lines parallel to each other have the same slope hence to find the value of y we'll equate their slopes.

∴ (3 - 9)/(4 + 4) = (y - 1)/(4 + 8).

-6/8 = (y - 1)/12.

-3/4 = (y - 1)/12.

-36/4 = y - 1.

- 9 = y - 1.

 y = - 8.

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