set of integers x such that x - 5 ​

Using the z-distribution, the p-value for the test is of 0.0040.

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which:

For this problem, the parameters are given as follows:

\(\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40\)

Hence the value of the test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

z = (33.8 - 32)/(4.3/sqrt(40))

z = 2.65.

Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.

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Answer:

Step-by-step explanation:

Remark

The two black suites are

Clubs

Spades

Each of them has 13 cards so the total number of black cards is 2*13 = 26

Add to that the hearts which also has 13 cards

The total number of possible good cards is 13 + 26 = 39

Answer

P(hearts or Black) = 39/52

P(hearts or Black) = 3/4

P(hearts or Black) = 0.75

Answer: 4 ways because 4 times four is 18

Step-by-step explanation:

Answer: 7315 (i think this is right)

The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer:

Lizzie practiced for 7 + 4 + 14 + 20 = 45 minutes on Thursday and Friday altogether.

Step-by-step explanation:

Answer:

plug in -3 and 2 into the equations you should get two different numbers

Step-by-step explanation:

3(-3)+2(-3)=24

3(2)+2(2)=24

Answer:

Step-by-step explanation:

Example:

see attached for prefixes

Answer:

decimal point

Step-by-step explanation:

To convert a metric unit, you are going to either multiply or divide.

Some examples include:

Best of Luck!

The value following are

vertex: (6, -9)

y-intercept: (0, 27)

X = 3, 9

Finding Vertex (Part A)

Consider the formula -b/2a. This formula gives you the x-coordinate of the vertex.

\(y = 1x^2 - 12x + 27\)

a = 1

b= -12

c =27

-b/2a = - (-12)/2(1) = 12/2 = 6 (x-coordinate of vertex)

When solving for the y-coordinate of the vertex you will need to substitute your 'x" back into the equation.

\(y = 1(6)^2 - 12(6) + 27\)

y = 36 - 72 + 27 = -9 (y-coordinate of vertex)

--------------------------------------------------------------------------

Y- Intercept (Part B)

When looking for the y-intercept your "x" must always be 0.

Substitute 0 in every "x" in the equation.

y =\(1(0)^2 - 12(0) + 27\)

y = 27

y-intercept: (0, 27)

-----------------------------------------------------------------------------

X- Intercepts (Part C)

To find the values of the "x" factor.

\(y = 1x^2\) - 12x + 27

\(0 = 1x^2\) - 12x + 27

0 = (x  - 3     )(x   -  9 )

(x-3) = 0             (x-9) = 0

x = 3                    x = 9

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Answer:

21 cards left to be signed

Step-by-step explanation:

1/3 of 72 is 24

So Harrison signed 24

3/8 of 72 is 27

Sp Alwine signed 27

24+27=51

So 72-51=21

21 cards left to be signed

Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, 21 cards are left when Harrison signs 1/3 of the cards and Alwine signs 3/8.

The distance of the fire from each tower is:

i. From Pine Knob: 41 kilometers

ii. From Colt Station: 15 kilometers

Bearing as a topic in mathematics can be used to determine the exact position or location of an object considering its angle of position and distance to a reference point.

Considering the given question; let the distance of the fire (F) from Pine knob (PK) be represented by x, and that from Colt Station (CS) be represented by y.

Angle at PK = 80 - 65

                    = 15^o

Angle at CS = 65 + 70

                    = 135^o

Angle at F can be determined as;

15 + 135 + F = 180   (sum of angle in a triangle)

150 + F = 180

F = 30^o

So that applying the Sine rule to determine the distances of the fire from PK and CS, we have;

a/Sin A = b/Sin B = c/Sin C

29/Sin 30 = y/Sin 15 = x/ Sin 135

29/Sin 30 = y/Sin 15

y = (29*Sin 15)/ Sin 30

  = 7.5052/ 0.5

  = 15.0104

y = 15 kilometers

29/Sin 30 = x/Sin 135

x = (29*Sin 135)/ Sin 30

  = 20.5059/ 0.5

  = 41.0118

x = 41 kilometers

Therefore, the distance from Pine Knob to the fire is 41 kilometers. While the distance from Colt Station to the fire is 15 kilometers.

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The quotient when 480 is divided by -60 is 8.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

The numbers given are 480 and -60.

Both are in opposite signs, that is one negative and other positive.

So the quotient will be negative.

Now divide 480 by 60.

Since both of the numbers contain 0 at the end, cancel it.

Then it becomes 48 divided by 6.

48 / 6 = 8

Hence the quotient is 8.

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Answer:

B.

Step-by-step explanation:

The answer is B.  If you go down from the y intercept 2 times, and then to the right 3 times, you get to the x intercept.

Answer: y = -2/3x + 2

Step-by-step explanation:

The graph shows a constant negative slope and also has a y-intercept.

The y-intercept is the point that intersects the y axis. We see that the point (0,2) intersects the y- axis, and we can use the positive value 2 at the end of equation of a line:  y = mx + b

# = number

The slope is rise/run, or the # of y/# of x -> 2/3

since the slope is going downward, the slope would be negative -> -2/3

So the equation of the line is : y = -2/3x + 2

Answer:

-6x - 2y = 12

Step-by-step explanation:

Answer:

225 cm 2

Step-by-step explanation:

Answer:

Surface Area = 6* (5 inches) 2 = 6* (25 square inches)

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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Answer:45 * t = 2.5 * (1-t)...the equation will have one solution.

Step-by-step explanation:

For this case, the first thing you should know is:

d: v * t

Where,

d: distance

v: speed

t: time

To go to school by bus we have:

d = 45 * t

To return from school we have:

d = 2.5 * (1-t)

how the distance is the same:45 * t = 2.5 * (1-t)

9514 1404 393

Answer:

  3 ft

Step-by-step explanation:

The post is 4/24 = 1/6 as tall as the streetlight, so we expect its shadow to be 1/6 as long as that of the streetlight:

  (1/6)(18 ft) = 3 ft

The parking meter post shadow is 3 feet long.

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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Answer:

yoo :)

Step-by-step explanation:

Answer:

3.292

Step-by-step explanation:

The interest Raymond will pay this month is $54.98

What does APR mean?

APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate

monthly interest=21.99%/12

What is the monthly interest amount in dollars?

The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month

monthly interest=$3,000*21.99%/12

monthly interest=$54.98

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Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

\(\dfrac{1213}{9999}\)

Step-by-step explanation:

We are required to express \(0.\overline{1}+0.\overline{01}+0.\overline{0001}\) as a common fraction.

The bar on top of the decimal part indicates the decimal number is a repeating decimal.

Therefore:

\(0.\overline{1}=\dfrac{1}{10-1}= \dfrac{1}{9}\\\\0.\overline{01}=\dfrac{1}{100-1}= \dfrac{1}{99}\\\\0.\overline{0001}=\dfrac{1}{10000-1}= \dfrac{1}{9999}\\\\\\$Therefore$:\\0.\overline{1}+0.\overline{01}+0.\overline{0001} \\=\dfrac{1}{9}+\dfrac{1}{99}+\dfrac{1}{9999}\\\\=\dfrac{1213}{9999}\)

Answer:

No

Step-by-step explanation:

here's a little trick, add a zero to make both numbers the same.

it's doesn't change the value.

so .27 and .3 become .27 and .30

and .30 is greater

We must identify the angle ∠DCA, to identify it we must see the points, the angle will that we search will be the angle that the segments do, for example:

The angle ∠ABE is the angle formed by the segment AE and the segment AB.

Then, let's look at the picture and identify the segments and their angles.

We can see in green the segments, and in red the angle ∠DCA

Answer:

46 boxes

Step-by-step explanation:

1012 / 22 = 46

Step-by-step explanation:

If this were to make a triangle, then 30.1 and 0.8 would be the shorter sides and 31 would be the longest side.

The sum of the lengths of the shorter sides is 30.1+0

8=30.9.

Since this is less than the length of the segment that would be the longest side, by the triangle inequality theorem, these side lengths would not make a triangle.