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Answer:

The approximate p-value for the suitable test

0.05 < p < 0.1

|t| = |-1.5806| = 1.5806

t = 1.5806 < 2.009 at 0.05 level of significance

Carisoprodol, a generic muscle relaxer, claims to have, on average, is equal to 120 milligrams of active ingredient.

Step-by-step explanation:

Step(i):-

Given mean of the Population 'μ' = 120 milligrams

Given random sample size  'n' = 50

Given mean of the sample x⁻ = 116.2 milligrams

Standard deviation of the sample 'S' = 17 milligrams

Null hypothesis :  'μ' = 120

Alternative hypothesis : 'μ' < 120

Step(ii):-

Test statistic

\(t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)

\(t = \frac{116.2 - 120}{\frac{17}{\sqrt{50} } } = \frac{-3.8}{2.404} = -1.5806\)

Degrees of freedom

ν = n-1 = 50 -1 =49

t₀.₀₅ = 2.009

|t| = |-1.5806| = 1.5806

t = 1.5806 < 2.009 at 0.05 level of significance

Null hypothesis is accepted

Carisoprodol, a generic muscle relaxer, claims to have, on average, is equal to 120 milligrams of active ingredient.

P- value:-

The test statistic |t| = 1.5806 at 49 degrees of freedom

The test statistic value is lies between 0.05 to 0.1

0.05 < p < 0.1

Answer:

0.0602

Step-by-step explanation:

jus took the test

Answer:

{6, 8, 10, 12, 14, 16, 18, 20, ...}

Step-by-step explanation:

even natural numbers >/= 6.

Thus this has no upper limit and the set is thus infinite.

The set of even natural numbers greater than or equal to 6 is

" The natural numbers are those numbers used for counting and ordering. Numbers used for counting are called cardinal numbers."

We know the natural numbers are:

{1, 2, 3, 4, 5, 6, 7,..........}

Now, the set of even natural numbers are:

{2, 4, 6, 8, 10...........}

Therefore, the set of even natural numbers greater than or equal to 6 is

{6, 8, 10, 12,..............}

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Answer:

Step-by-step explanation:

30

Square Area = side x side = 3x3 = 9

Rectangle Area = side x side= 7x3= 21

9 + 21 = 30 square inches

Answer:

30 square inches

Step-by-step explanation:

   \(\boxed{\text{\bf Area of rectangle = length *width}}\)

Rectangle1:

     Area = 6 * 3

              = 18 square inches

Rectangle2:

Area = 4 * 3

          = 12 square inches

Area of the figure = area of rectangle1 + area of rectangle2

                             = 18 + 12

                             = 30 square inches

The largest possible total area of the three pens is 15312.5sq.units.

What is a rectangular area?

The quantity of space occupied by a flat surface with a specific shape is referred to as the area.

Area of a Rectangle = (Length × Breadth) square units.

Here,

We let x be the length and y be the breadth of a rectangle area.

Given equation : 2y + 4x = 700

y + 2x  = 350

y = 350 - 2x .......(1)

Area of rectangular field (A)= xy

A = x(350 - 2x)

A = 350x - 2x²

Differentiating w.r.t x we get,

A' = 350 - 4x

Again, differentiating w.r.t x we get,

A" = -4

Let A' = 0

350 - 4x = 0

4x = 350

x = 87.5

A is maximum at 87.5feets.

Hence, the largest possible total area of the three pens = XY = 87.5×175 = 15312.5 sq. units.

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9514 1404 393

Answer:

Step-by-step explanation:

Each root r gives rise to a binomial factor (x-r). Each complex root also has a conjugate root, so roots ±ri give rise to a binomial factor (x^2 +r^2).

__

1. p(x) = (x -(-6))(x -3)(x -5)

  p(x) = (x+6)(x-3)(x-5)

__

2. p(x) = (x -2)(x -(-2))(x^2 +6^2)

  p(x) = (x -2)(x +2)(x^2 +36)

__

If you want standard form, you can start with factored form, then multiply it out.

3. p(x) = (x -1)(x +1)(x -7) = (x^2 -1)(x -7) = (x^2 -1)x +(x^2 -1)(-7)

  p(x) = x^3 -7x^2 -x +7

__

4. p(x) = (x -3)(x +3)(x^2 +2^2) = (x^2 -9)(x^2 +4)

  p(x) = x^4 -5x^2 -36

Answer:

Option A: $44746

Step-by-step explanation:

Step 1:

6.95% of $51000 = 3544.5

Federal & state Tax = $2250 + $460 = $2710

Total tax deducted = 3544.5 + 2710 = $6254.5

So,

$51000 - $6254.5 = $44,746.

Answer:

Area = 4x^2 + 12x + 9

Perimeter = 8x + 12

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

1 foot = 12 inches                          Find 1/4 foot in inches

1/4 a foot = 1/4 * 12 = 3 inches

6 1/4 feet = (6 + 1/4) * 12

=72 + 3

75 inches

Answer:

This mistake has no effect on the median and IQR, since it will be an outlier.

Step-by-step explanation:

xth percentile:

If a measure is said to be in the xth percentile, it means that x% of the measures are smaller than it, and (100-x)% are larger.

Median:

The 50th percentile is called median.

Interquartile Range:

Difference between the 75th and the 25th percentile.

In this question:

Tallest student measures 71 inches, but with a mistake, it was accidentaly entered 711.

However, since the mean and the median are related to the percentiles, in the middle of the distribution, they wont be affected by an outlier such as this.

Answer:

a-2 / a - 1

Step-by-step explanation:

Answer: 2 1/2y

Step-by-step explanation:

This is correct because y is not a number it is a variable. This is y get it. That this is correct. Hope this helps ;)

Answer:

C i think but I could be wrong

Step-by-step explanation:

Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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Since EM is an altitude of triangle EAT, it forms a right angle with AT. So

25x - 10 = 90

Solve for x :

25x = 100

x = 4

Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

The last one , because I will now solve it for you and prove therefore.

x²–4x+5=0;

D=(–4)²–4•5=16–20= –4= (2i)².

So:

x1= (4–2i)/2= 2–i

x2= (4+2i)2= 2+i.

This is the whole answer....

Three other u will solve by yourself and have roots which will not be suitable.

Answer:

14

Step-by-step explanation:

6(2)

12

4÷2

2

12+2

pemdas

Answer:

14

Step-by-step explanation:

first u multiply 6 and 2 to get 12 because u always start with parenthesis or squares, then you divide 4 and 2 to get 2 because afterwards u play around with the multiplication and division. finally u add both answers u got to get 14

Yes, when given angle measures of 25 degrees, 65 degrees, and 90 degrees, it is possible to draw a triangle.

The above is possible because the sum of angles in a triangel must always be 180 degree.

Since we have 90, 65, and 25, and

90 + 65+25 = 180 degrees.

This means that we can get a traingle with those dimensions.

A s a matter of fact, the triangle that will be generated is  right angled triangle.

A right triangle or right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides.

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Given:

Solve the equation for y,

Answer: y = -2x +4

Answer:

The longest length of carpet is 160 cm.

Step-by-step explanation:

Given that the total ratio(units) of the carpet is 9(2+3+4). So first, you have to find the length of carpet in 1 unit :

\(9 \: units = 360 \: cm\)

\(1 \: unit = 360cm \div 9\)

\(1 \: unit = 40 \: cm\)

Next, you have to find the length of carpet in 4 ratio as the question wants the longest length :

\(4 \: units = 40 \: cm \times 4\)

\(4 \: units = 160 \: cm\)

Answer:

160cm

Step-by-step explanation:

2+3+4= 9

4/9 x 360= 160cm

The smallest value that the expression can have is -1.

We must determine the smallest difference between any two numbers chosen at random from the first 1 through 25 of the first 25 full numbers.

When we select the lowest and second-smallest numbers from the set, the difference is at its smallest. As a result, a = 1 and b = 2.

The expression is given by a - b:

1 - 2 = -1

Therefore, the smallest value that the expression can have is -1.

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Answer: 24 & 25

Step-by-step explanation:

It says 1-25 so 1 will be B and 25 will be A. Next You subtract 25/25-1 which will equal to 24 and  25/25*1=25

So now You have 24 and 25 and 25 is A because when it says to subtract A & B, A is gonna be Bigger that B  so now u have your answer and You can copy below. :)

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Answer:

ST=13

Step-by-step explanation:

3x + 7 +4x - 3= 5x + 12

7x+4=5x+12

2x+4=12

2x=8

x=4

plug 4 into x for ST

Answer:

It will take 15 hours to read a book with 180 pages

Step-by-step explanation:

First, let's set up a ratio to find how many pages she reads per hour:

36:3 = 12:1

Now we can set up fractions to solve:

\(\frac{12}{1} =\frac{180}{x}\)

Cross multiply:

\(12x=180\)

Divide each side by 12:

\(x=15\)

Answer:

Point A:

(3, -5)

Point B:

(6, -2)

Point C:

(5, -7)

Step-by-step explanation:

Background:

Moving to the right means adding to the x.

Moving to the left means subtracting from the x.

Moving up means adding to the y.

Moving down means subtracting from the y.

So take each point and add 3 to the x, and subtract 4 from they y.

Point B:

(3, 2) → (6, -2)

Point A:

(0, -1) → (3, -5)

Point C:

(2, -3) → (5, -7)

Answer:

Now x is equals to 11

-2(11) + 1 = - 22 + 1 = - 21

The answer is - 21

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1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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Answer:

1.  x = 4

2. x = -1

3. x = 0

Answer:

Step-by-step explanation:

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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Answer:10

Step-by-step explanation:

14−(3+5)+2

2

=

Add 3 and 5 to get 8.

14−8+2

2

Subtract 8 from 14 to get 6.

6+2

2

Calculate 2 to the power of 2 and get 4.

6+4

Add 6 and 4 to get 10.

10