5. Graph the system of inequalities. Then, identify a coordinate point in the solution set.2x -y > -3 4x + y < 5

Confidence interval is written in the form,

(point estimate +/- margin of error)

The given scenario involves population proportion

The formula for the point estimate is

p' = x/n

where

p' = estimated proportion of success. p' is a point estimate for p which is the true proportion

x represents the number of success

n represents the number of samples

From the information given,

n = 74

x = 22

p' = 22/74 = 0.297

The formula for finding margin of error is expressed as

A) The point estimate is 0.297

B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031

Thus,

the lower limit would be 0.297 - 0.031 = 0.266

Expressing in percentage, it is 0.266 x 100 = 26.6%

the upper limit would be 0.297 + 0.031 = 0.328

Expressing in percentage, it is 0.328 x 100 = 32.8%

Thus, the confidence interval is between 26.6% and 32.8%

in order to shift the 4 to the ones place, divide the given number 584,900 by 100. After dividing the the number 584,900 by 100, the new number is 584.900. It is clear that 4 is at ones olace.

Step 1: Write out the equation.

Step 2: Divide both sides of the equation by 5Q, we have

this implies that

The total net operating income (NOI) of both divisions is $1,03,500.

So, the total net operating income:

Now, substitute the values and get the NOI as follows:

Therefore, the total net operating income (NOI) of both divisions is $1,03,500.

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The sequence is arithmetic because the common difference is 4.

Answer:

the sequence is arithmetic. the cd is 4

Step-by-step explanation:

1 + 4 = 5

5 + 4 = 9

9 + 4 = 13

Solution

For this case we can verify the answer using the point x= 0 if we replace we got:

y=8 cos (pi/40* 0) = 8 cos (0) = 8

y= -8 sin (pi/40 *0)= -8 sin(0) = 0

y= -8cos(pi/40*0)= -8 cos (0)= -8

y= 8 sin (pi/40 *0)= 8 sin(0) = 0

Then the correct option would be:

y= -8cos(pi/40*0)

In option A, if expression is simplify with out using associative property then addition of 4/9 and -2/9 is easy, as compare to addition 6 and 4/9. So no need to apply associateive property to option A.

In option B, 60 and 40 can be easily add as compare to 40 and -27 so this expression do not need to apply associative property.

In option C, the expression is easier to simplify if 5/2 and -1/2 is added, which is possible if associative is apply to the expression.

Thus option C use associative property to make the simplification easier.

Answer: Option C.

Answer:

y = (-1/8)x + (29/4)

Step-by-step explanation:

(10, 6), (2, 7)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁         7 - 6             1             -1

m = ------------ = ----------- = ----------- = ---------

       x₂ - x₁          2 - 10         -8              8

y - y₁ = m(x - x₁)

y - 6 = (-1/8)(x - 10)

y - 6 = (-1/8)x + (5/4)

   +6                 +6

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

y = (-1/8)x + (29/4)

I hope this helps!

We are not concerned with the tiles needed for the kitchen.

From the given information, there are two bathroom floors with the same measurement in terms of area. The area of each floor is 30.5 square feet

Area of both bathroom floors = 30.5*2 = 61 square feet

Area of the third bathroom = 42.5 square feet

Area of the three bathroom floors = 61 + 42.5 = 103.5 square feet

Given that the tile costs 2.39 per sqare foot, the least amount of money that the company would spend for all three tiles is

103.5 * 2.39 = 247.365

Rounding up to the nearest cent means rounding up to the nearest hundredth or 2 decimal places

Rounding up to the nearest cent, it becomes 247.37

448 books in each box

Number of books: 4032

Number of boxes: 9

Since each box had the same number of books, divide the number of books by the number of boxes.

4032/9 = 448

The expression which represents the written form of the basic form expression; 2√3 as a single form is; √12.

It follows from the task content that the basic form expression be written as it's equivalent single form expression.

Since the given radical expression is; 2√3; it follows that the expression can be written as a single form expression as follows;

First, the square of 2, 2² is equal to 4;

Hence, by the converse;

2 = √4.

The given expression can therefore be written as; √4 • √3.

The expression above can therefore be written in its single form as; √(4 × 3) = √12.

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Solution

- The first integral is bounded by the x-values of [6, 22]

- The second integral is bounded by the x-values of [6, 14]

- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.

- The extra values are from 14 to 22.

- Thus, we have:

Final Answer

The two unit vectors orthogonal to both j-k and i+j  are [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]

Let a bar = j- k  = < 0,1,-1>

b bar = i+j = <1,1,0>

the cross product a x b bar is orthogonal to both a and b bar

= i ( 0-(-1) ) -j ( 0-(-1) ) + r (0-1)

= i-j-k

A unit vector is a vector whose length is 1 unit

There the unit vector is :

[tex]\frac{i-j-k}{\sqrt{1^2+(-1)^2+(-1)^2} } = \frac{i-j-k}{\sqrt{3} }[/tex]

= [tex]\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]

The second unit vector orthogonal to both a and b bar would be negative of the previous vector.

= [tex]-\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]

Hence the two unit vectors orthogonal to both j-k and i+j are  [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]

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Explanation:

5x - 4y + 2z = 21 ...equation 1

-x - 5y + 6z = -24 ....equation 2

-x - 4y + 5z = -21 ...equation 3

Using elimination method:

multiply equation 2 by 5:

-5x - 25y + 30z = -120 ....equation 2a

add equation 2a from 1:

5x - 5x -4y -25y + 2z + 30z = 21 - 120

0 - 29y + 32z = -99

-29y + 32z = - 99 ....equation 4

multiply equation 3 by 5:

-5x - 20y + 25z = -105 ...equation 3a

add equation 1 and 3a

5x - 5x - 4y - 20y + 2z +25z = 21 - 105

0 - 24y + 27z = -84

-24y + 27z = -84 ...equation 5

-29y + 32z = - 99 ....equation 4 (×-24)

-24y + 27z = -84 ...equation 5 (×-29)

696y - 768x = 2376 ...(4a)

696y -783x = 2436 ...(5a)

subtract 5a from 4a

696y - 696y -768x -(-783x) = 2376 - 2436

0 - 768x + 783x = -60

15x = -60

x = -60/15

x = -4

substitute for x in equation 4a:

696y - 768(-4) = 2376

696y + 3072 = 2376

696y = 2376 -3072

696y = -696

y = -696/696

y = -1

substitute for y in equation 4:

-29(-1) + 32z = -99

29 + 32z = -99

32z = -99 - 29

32z = -128

z = -128/32

z = -4

So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:

Then we get:

Then the speeds of the planes are 275mph and 315mph.

x = 7

9(11 - x) = 3(3x -9)

Expanding the expression:

9(11) - (9x) = 3(3x) -3(9)

99 - 9x = 9x - 27

collect like terms:

99 + 27 = 9x + 9x

126 = 18x

Divide both sides by 18:

126/18 = 18x/18

x = 7

The equation s = 45t, where s is the distance in miles and it is the time in hours, can be used to simulate the distance driven by a car over a period of time then the car will travel 135 hours in 3 hours.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

Given: The distance traveled by car at a constant rate is proportional to the time spent driving.

In the equation d = 45 t, d denotes the distance (in miles) and t denotes the time (in hours).

d / t = 45 miles per hour

The constant of proportionality = 45 miles per hour.

Also, the distance traveled by car in 1 hour = 45 miles

The distance traveled by car in 3 hours = 3 × 45 = 135 miles

Therefore, a car will travel 135 hours in 3 hours.

The complete question is:

The distance traveled by car at a constant rate is proportional to the time spent driving. In equation d = 45t, d represents the distance (in miles) and t represents the time (in hours).

A. What is the constant of proportionality? _____ miles per hour

B. How far will the car travel in 3 hours? _______ miles

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Let's convert the given relationships into an equation.

Let's name the two number x and y.

The sum of the two numbers is 51: x + y = 51

One number is 15 more than the other: x = y + 15

Using the equations that we generated from the given relationships, let's determine the value of the two numbers by substitution.

Let's substitute x = y + 15 to x + y = 51.

Since we now get the value of y, y = 18, let's determine the value of x.

Therefore, the value of the two numbers is 18 and 33.

The length of the trail is equal to 3mi and the selling price of the item is equal to $120.

In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.

In this question, we have to use the ratio given to determine the length of the trail.

Given that the ratio is 5in : 2mi, we have to convert the values to uniform units.

[tex]1mi = 63360in\\2mi = x\\x = 126720[/tex]

The ratio is now 5in : 126720in

Given that on the map, the length is 7.5in

[tex]5 = 126720\\7.5 = x\\x = 190080in[/tex]

Let's convert this into mi.

[tex]190080in = 3mi[/tex]

The actual length of the trail is 3in.

b)

To find the selling price of the item, let's use the percentage given to do that.

We can find 40% of 200 and then subtract the value from 200.

[tex]40\% of 200 = 0.4 * 200 = 80[/tex]

The discount price is $80 and we can find the selling price here.

[tex]selling price = actual price - discount price\\selling price = 200 - 80\\selling price = 120[/tex]

The selling price of the item is $120

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If s is between r and t, then:

RS + ST = RT

Where RS = 2z + 6

ST = 4z - 3

RT = 5z + 12

So, we get:

(2z + 6) + (4z - 3) = 5z + 12

Solving for z, we get:

2z + 6 + 4z - 3 = 5z + 12

6z + 3 = 5z + 12

6z + 3 - 5z = 12

z + 3 = 12

z = 12 - 3

z = 9

Answer: z = 9

The length of the lines GH and CH are 16 units and 12 units.

So, the measure of lines GH and CH:

We know that AC ⊥ GH hence cuts GH in two equal lines.

But,

We can observe that △GCH is an isosceles triangle.

Therefore, the length of the lines GH and CH is 16 units and 12 units.

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We have the following parameters

the general equation of a circle with center (0,0) is the following,

Let's use the following tigonometric identity,

solving for cos and sin in the equations we are given,

replace,

Since we have two different numbers in the denominator, this is not a circle equation but an elipse, of the form,

where,

a is the vertex and,

b is the covertex

thus, in the x axis, the vertex is 7 and the y-axis the covertex is 5

Now, let's determine the direction by replacing

when Θ = 0 , then x = 7*cos0 = 7*1 = 7 , and y = 5*sin0 = 5*0 = 0

when Θ = 90° or π/2 , then x = 7*cos90° = 7*0 = 0 , and y = 5sin90° = 5*1 = 5

If we draw this, we can see that the direction is counterclockwise as in the bottom right image.

Let w represent the cost of each wallet.

Let b represent the cost of each belt.

Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This means that

56w + 63b = 3920

This month, they sold 94 wallets and 22 belts, for a total of $3,230. This means that

94w + 22b = 3230

We would solve the equations by applying the method of elimination. To eliminate w, we would multiply the first equation by 94 and the second equation by 56. The new equations would be

5264w + 5922b = 368480

5264w + 1232b = 180880

Subtracting the second equation from the first, we have

5264w - 5264w + 5922b - 1232b = 368480 - 180880

4690b = 187600

b = 187600/4690

b = 40

Substituting b = 40 into 56w + 63b = 3920, we have

56w + 63(40) = 3920

56w + 2520 = 3920

56w = 3920 - 2520 = 1400

w = 1400/56

w = 25

Thus, the boutique charges $25 for each wallet and $40 for each belt

Answer

Percent of students who did not pass the test = 77.8%

Explanation

The percent of an event is given as

For this question,

Percent of the event = Percent who did not pass the test = ?

Number of elements in the event

= Number of students who did not pass the test

= (Total number of students) - (Number of students who passed the test)

= 18 - 4

= 14

Total number of elements = Total number of students in the class = 18

Percent of students who did not pass the test

= (14/18) × 100%

= 0.778 × 100%

= 77.8%

Hope this Helps!!!

Sam would ride 18.125 miles when hw would ride at the rate of 14.5 miles/hour.

According to the question,

We have the following information:

Speed of Sam = 14.5 miles/hour

Distance to be covered = ?

Time taken to cover the distance = 1 hour and 15 minutes

Now, we will convert the time given in minutes into hour.

We have 15 minutes.

We know that 1 hour is equal to 60 minutes.

So, we will convert 15 minutes into hour:

15/60 hour

0.25 hour

So, the total time taken = (1 + 0.25) hour

Time taken = 1.25 hour

We know that the following formula is used to find the speed:

speed = distance/time

Distance = speed*time

Distance = 14.5*1.25

Distance = 18.125 miles

Hence, the distance covered by Sam in 1 hour and 15 minutes is 18.125 miles.

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To answer this question, we can proceed as follows:

1. Subtract 3.5 to both sides of the equation:

2. Multiply by 2 to both sides of the equation:

We can check this result as follows:

This result is TRUE. Then, the value for h = 7.2.

The equation of a line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" from the equation given in the exercise in order to write it in Slope-Intercept form:

You can notice that the equation has this form:

Where "b" is the y-intercept.

Then, it's a horizontal line, which means that its slope is:

Since it is a horizontal line, the lines perpendicular to that line is a vertical line, whose slope is undefined and whose equation is:

Where "k" is the x-intercept.

Knowing that the x-coordinate of any point on a vertical line is always the same, and knowing that this line passes through this point:

You can determine that the equation of the line is:

Answer:

======================

We can represent the quadratic equation in vertex or standard forms.

Vertex form:

Standard form:

Use the vertex form with given coordinates of the vertex:

Use the other point to find the value of a:

The equation is:

Convert it to standard form:

Answer:

[tex]y=-6x^2-12x+2[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:  

[tex]y=a(x-h)^2+k[/tex]

where (h, k) is the vertex.

Given:

Substitute the given values into the vertex formula and solve for a:

[tex]\implies 2=a(0-(-1))^2+8[/tex]

[tex]\implies 2=a(1)^2+8[/tex]

[tex]\implies 2=a+8[/tex]

[tex]\implies a=-6[/tex]

Substitute the vertex and the found value of a into the vertex formula, then expand to standard form:

[tex]\implies y=-6(x-(-1))^2+8[/tex]

[tex]\implies y=-6(x+1)^2+8[/tex]

[tex]\implies y=-6(x^2+2x+1)+8[/tex]

[tex]\implies y=-6x^2-12x-6+8[/tex]

[tex]\implies y=-6x^2-12x+2[/tex]

Therefore, the quadratic function in standard form whose graph has the given characteristics is:

[tex]y=\boxed{-6x^2-12x+2}[/tex]

The formula to calculate the slope is

A is right

also, the slope can be calculated with rise and run

the correct formula is D.

and also apply E

the answer will be A,D and E