Solve for k and graph the solution. 0≥ k+14 3 > – 2

Answer:

The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.

In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of 2(7) (3.6) + 2(7) (2.4) + 2(3.6) (2.4), which simplifies to 50.4 + 33.6 + 17.28, or 101.28 square centimeters.

So, the surface area of this rectangular prism is 101.28 square centimeters.

Received message. The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is `2lw + 2lh + 2wh`, where `l` is the length, `w` is the width and `h` is the height. In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of `2(7)(3.6) + 2(7)(2.4) + 2(3.6)(2.4)`, which simplifies to `50.4 + 33.6 + 17.28`, or **101.28 square centimeters**. So, the surface area of this rectangular prism is **101.28 square centimeters**.

Step-by-step explanation:

The two equivalent expressions are 6(x − y) and 6x − 6y.

These expressions look different but their simplified forms are same expressions are called equivalent expressions.

The 1st expression shows subtracting the number of packages of cherry snacks from the number of packages of strawberry snacks in each box.

When we multiplying the difference by the number of boxes then, it will be: 6(x-y)

Now, total number of cherry snacks and subtracting it from the total number of strawberry snacks will be 6x - 6y. So, equivalent expressions means in terms of situation are 6(x − y) and 6x − 6y.

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Answer: 720

Step-by-step explanation: There are 6 choices for the first letter,  5 for the  second,  4 for the third and so on. 6*5*4*3*2=720

Step-by-step explanation:

according to the law of combination

Answer:

B

Step-by-step explanation:

let the mid-point of DE be ( x , y )

x = (8+4)/2 = 6

y = (6+10)/2 = 8

the mid- point of DE is ( 6 , 8 )

The given probabilities are as follows:

The probabilities are determined using the formula below:

Spinner landing on at least one A:

number of at least one A = 7

Spinner landing on at least one A = 7/16

Spinner landing on C and D in any order:

number of landing on C and D in any order = 2

Spinner landing on C and D in any order = 2/16

Spinner landing on C and D in any order = 1/8

Spinner landing on two Bs:

number of  landing on two Bs = 1

Spinner landing on two Bs = 1/16

Spinner landing on C on the second spin:

Number of landing on C on the second spin = 4

Spinner landing on C on the second spin = 1/4

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As we used the distributive property of multiplication to rewrite 7+21 as a product of 7 x (1+3) or 7 x 4.

However, you are asked to express this sum as a product of two factors. A factor is a number that is multiplied by another number to produce a product. Therefore, to express 7+21 as a product of two factors, we need to find two numbers that, when multiplied together, give us the sum of 7+21.

One way to approach this problem is to use the distributive property of multiplication, which states that a(b+c) = ab + ac. We can apply this property by rewriting 7+21 as 7+3*7, since 21 is equal to 3 times 7. Then, we can factor out the common factor of 7 from the expression to get:

7+37 = 7(1+3)

Now, we have expressed 7+21 as a product of two factors: 7 and (1+3), or simply 7 and 4. Therefore, the expression that shows 7+21 written as a product of two factors is:

7 x (1+3) or 7 x 4

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The number of solutions for the given system of linear equations is: Infinitely many solutions.

To determine the number of solutions for the given system of linear equations:

3x - y = 4

6x - 2y = 8

We can use the algebraic method of solving the system of equations by substitution or elimination.

Let's use the algebraic method to determine the number of solutions:

3x - y = 4 (1)

6x - 2y = 8 (2)

We can simplify equation (2) by dividing both sides by 2:

3x - y = 4 (1)

3x - y = 4 (2')

Equations (1) and (2') are equivalent, which means that they represent the same line.

Therefore, the two equations represent the same line, and we have infinitely many solutions.

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Complete question

What’s the numbers that correspond to the corret number of solutions

0 solution, 1 solution, Many solutions

3x - y = 4

6x - 2y = 8

Answer: Sure, here's how to solve the system of equations:

1. Start with the first equation: 3x = y - 2

Solve for y by adding 2 to both sides: y = 3x + 2

2. Substitute the value of y from the first equation into the second equation:

6x = 4 - 2y

6x = 4 - 2(3x + 2) (substitute y = 3x + 2)

6x = 4 - 6x - 4

12x = 0

3. Solve for x by dividing both sides by 12: x = 0

4. Substitute the value of x from step 3 into either equation to solve for y:

y = 3x + 2

y = 3(0) + 2

y = 2

Therefore, the solution to the system of equations is (x, y) = (0, 2).

hope this helpsss :D

Step-by-step explanation:

The force applied to the input piston is  136.25 N.

This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.

Thus, we can equate  the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:

P₁ = P₂

F₁/A₁ = F₂/A₂    (Pressure = Force/Area)

F₂ = 2000 * 9.81 = 19620 N   (F = mg)

A₁ = π * r₁² = π * 5² = 25π cm²

A₂  = π * r₂ ² = π * 60² = 3600π cm²

F₁ = F₂/A₂ * A₁

F₁ = (19620/3600π) * 25π

F₁ = 136.25 N

Therefore, the force applied to the input piston is  136.25 N.

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Question in English

A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?

Answer:

x = -2

Step-by-step explanation:

-4x + 3 = 11

Subtract 3 from both sides:

-4x = 8

Divide both sides by -4:

x = -2

measure of Angle PRT = 90 degrees

A circle with center T exists -- Given

Point R is on the the circle. -- THIS IS AN ASSUMPTION BASED ON THE PICTURE (if you have more information that makes this not true, the rest of this logic fails).

Line segment TR is the radius of the circle. -- Definition of radius

Line PR is tangent to the circle. -- PR touches at exactly one point: R

Angle PRT has a vertex as point R. -- definition of angle PRT

Since PR is tangent to the circle, TR is perpendicular to PR -- consequence of lines perpendicular to circles

Perpendicular lines form right angles. -- Consequence of two congruent angles that form a straight angle pair.

The measure of a right angle is 90 degrees. -- definition of right angle

Therefore, the measure of angle PRT is 90 degrees.

Answer:

14/16 = 0.875

Answer:

B. Y= 5x - 2

Step-by-step explanation:

The Y is negative, you can see the number -5 below the point, if you go to the top, that is, to 0 and count down, the lines are two and the X is positive 5, you can see where the number 5 is and the point is above.

Answer: C

Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1

Answer:

x = 65

Step-by-step explanation:

let the number be 'x'.

If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,

=> 86 + x = 3x - 44

Rearranging,

=> x - 3x = -44 - 86

=> -2x = -130

=> x = 130/2

=> x = 65

Answer:

Therefore, the customer saved $2,448.45.

Step-by-step explanation:

To answer this question, we need to use the percentage discount formula to find the original price and the amount saved.

Let x be the original price of the product. Then, after applying the 12% discount, the price becomes 0.88x. If the total is over $10,000 after this discount, then an additional 3% discount is applied on the remaining balance, which means the final price becomes 0.97 * 0.88x.

We are given that the final price is $13,500, so we can set up an equation and solve for x:

0.97 * 0.88x = 13,500 x = 13,500 / (0.97 * 0.88) x = 15,948.45

Therefore, the original price was $15,948.45.

The amount saved is the difference between the original price and the final price:

15,948.45 - 13,500 = 2,448.45

The p value based on the information will be E. P - value ≥ 0.20

Open Minitab 17. Select 'Stat' -> 'Basic Statistics' -> '2 - Sample t... Select 'Summarized data' from the dropdown menu.

Enter 5 in both Sample size of sample 1 and sample 2, 168 and 172 in Sample mean of Sample 1 and Sample 2. 5.4 and 7.5 in Standard deviation of Sample 1 and Sample 2.

Click on 'Options' and Enter 'Confidence level' 95.0(or the given Cofidence level) , 'Hypothesized difference' 0.0 , 'Alternative hypothesis' 'Difference \\neq Hypothesized difference'. Also the box 'Assume equal variance' can be ticked as requirement.

Click on 'Ok' -> 'Ok'.

Output: -

P - value = 0.361 i.e., P - value ≥ 0.20

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a. The perimeter of the paddock is 120 meters

b. The cost of the wire will be $600

a. To find the missing sides and calculate the perimeter of the paddock, let's analyze the given sketch.

The length of the missing side on the left can be determined by subtracting the known length of 10m from the total height of 20m. Therefore, the left side has a length:

20m - 10m = 10m.

The missing side on the right is equal in length to the known side of 40m.

Now we can calculate the perimeter by adding up all the side lengths:

Perimeter = 10m + 40m + 20m + 10m + 40m

= 120m.

b. To calculate the cost of the wire, we need to multiply the perimeter of the paddock by the cost per meter of fencing wire, which is $5/m.

Wire Cost = Perimeter × Cost per meter

= 120m × $5/m

= $600.

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According to the information, the router cannot cover the kitchen area.

To calculate if the router covers the kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router. So, we have to calculate the square root of 850 ft^2.

From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.

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The equation of the quadratic with a directrix of x = 2 and vertex of (0 , 0)  is: y² =  -8x

The equation of the quadratic with a directrix of y = 4 and vertex of (1, 3)  is: (x - 1)² = -4 (y - 3)

Quadratic equation when the directrix is at x direction is of the form:

(y - k)² =  4P (x - h)

OR

standard vertex form, x = a(y - k)² + h     where a = 1/4p

The vertex

v (h, k) = (0, 0)

P in this problem, is the distance between the vertex and the directrix

P = 0 - 2 = -2

substitution of the values into the equation gives

(y - k)² =  4P (x - h)

(y - 0)² =  4 x -2 (x - 0)

y² =  -8x

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex

v (h, k) = (1, 3)

P in this problem, is the distance between the vertex and the directrix

P = 3 - 4 = -1

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - 1)² =  4 * -1 (y - 3)

(x - 1)² = -4 (y - 3)

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Answer:

  C) x = 5 if and only if x + 5 = 10

Step-by-step explanation:

You want to identify the biconditional statement among those that are given.

A conditional statement is of the form ...

  If P, then Q.

The converse of the above conditional statement is ...

  If Q, then P.

When both the statement and its converse are intended, the statement can be written as the biconditional ...

  If and only if P then Q.

The given example of a biconditional statement is ...

  x = 5 if and only if x +5 = 10.

__

Additional comment

This can be abbreviated ...

  Iff P then Q

meaning "if P then Q, and if Q then P", or "if and only if P, then Q."

Answer:

circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.

Step-by-step explanation:

To find the correct percentages, we need to calculate the percentage of visitors who used each mode of transportation out of the total number of visitors, which is the sum of all the numbers in the table:

Total number of visitors = 120 + 24 + 45 + 30 + 81 = 300

Percentage of visitors who walked = (120 / 300) x 100% = 40%

Percentage of visitors who used a bicycle = (24 / 300) x 100% = 8%

Percentage of visitors who used a car service = (45 / 300) x 100% = 15%

Percentage of visitors who used a bus = (30 / 300) x 100% = 10%

Percentage of visitors who used the subway = (81 / 300) x 100% = 27%

Therefore, the circle graph that correctly represents the data in the table is:

circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.

Answer:

Sure, I can help you with that.

Given:

   * The box is 24 inches long.

   * The width of the box is seven inches less than the height.

   * The volume of the box is 2,880 cubic inches.

To solve:

   * Complete the equation that models the box's volume in terms of its height, x, in inches.

   * Determine if the height of the box can be 15 inches.

Solution:

Let's define the following variables:

* $h$ = the height of the box (in inches)

* $w$ = the width of the box (in inches)

* $l$ = the length of the box (in inches)

We are given that  l=24 and w=h−7. We can use these values to find the volume of the box:

[tex]V = lwh = 24(h - 7)h[/tex]

We can simplify this expression to get the following equation:

[tex]V = 24h^2 - 168h[/tex]

To determine if the height of the box can be 15 inches, we can substitute 15 for $h$ in the equation and see if we get a positive value for the volume.

[tex]V = 24(15)^2 - 168(15) = 2160 - 2490 = -330[/tex]

Since the volume is negative, the height of the box can't be 15 inches.

Therefore, the equation that models the box's volume in terms of its height, x, in inches is [tex]$V = 24x^2 - 168x$[/tex]. Consequently, the size of the box can't be 15 inches.

Answer:

Yes

Step-by-step explanation:

The only answer is height = 15 because the -8 will be rejected

Answer:

Compound Interest Formula: A = P (1 + R/100)^t

A = 1000 (1 + 10/100)^10

A = $2593.74

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The image point of the coordinate X after the rotation is (-1, 5).

When a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.

So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).

Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).

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The shaded area of the portion as shown in the diagram is 78.04 cm².

Area is the region bounded by a plane shape.

To calculate the shaded area of the portion, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Complete question: A 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm. Calculate the area of the shaded portion.

Thus, the probability for the outcome of either purple or orange: P(purple or orange) = 57/97.

a choice that is made at random (entirely by chance, with no predictability). Every person in the population under study need to have an equal probability of getting chosen. Every person who is under investigation has an equal probability of being chosen at random for the sample.

Given bag with balls:

probability = favourable outcome / total outcome

P(purple) = 28/97

P(orange) = 29/97

Thus,

P(purple or orange) = 28/97 + 29/97

P(purple or orange) = 57/97

Thus, the probability  for the outcome of either purple or orange ball : P(purple or orange) = 57/97.

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To enlarge the photo proportionally so that it is as wide as the computer screen, we need to find the scaling factor. The scaling factor is the ratio of the width of the computer screen to the width of the photo:

Scaling factor = 1024 ÷ 640 = 1.6

We can then use this scaling factor to find the new dimensions of the photo:

New width = 640 × 1.6 = 1024 pixels

New height = 300 × 1.6 = 480 pixels

Therefore, the new dimensions of the photo are 1024 × 480 pixels.

2a. We cannot enlarge the photo proportionally so that it is as tall as the computer screen because the aspect ratio of the photo is different from the aspect ratio of the computer screen. The aspect ratio of the photo is 640 ÷ 300 ≈ 2.13, while the aspect ratio of the computer screen is 1024 ÷ 768 ≈ 1.33. This means that if we enlarge the height of the photo to match the height of the computer screen, the width of the photo will be too wide to fit on the screen.

b. We cannot correct the difficulty in (a) by scaling the width of the photo by a factor of 1024 ÷ 640 and the height by a factor of 768 ÷ 300 because this would change the aspect ratio of the photo. The aspect ratio of the photo would become 1024 ÷ (640 × 1024 ÷ 640) ≈ 1.6, which is the same as the aspect ratio of the computer screen. However, the height of the photo would be scaled by a factor of 768 ÷ 300 ≈ 2.56, which would make the photo too tall to fit on the screen.

To enlarge the photo proportionally, we need to scale it up by the same factor in both dimensions. Since we want to scale it so that its width matches the width of the screen, we can find the scaling factor by dividing the screen width by the photo width:

scaling factor = screen width / photo width = 1024 / 640 = 1.6

Now we can use this scaling factor to find the new height of the photo:

new height = photo height x scaling factor = 300 x 1.6 = 480 pixels

Therefore, after the photo is scaled up proportionally, its measurements are 1024 x 480 pixels.

2a. We can't enlarge the photo proportionally so that it is as tall as the computer screen because its aspect ratio (the ratio of its width to its height) is different from the aspect ratio of the screen. The photo's aspect ratio is 640/300 = 2.13, while the screen's aspect ratio is 1024/768 = 1.33. Enlarging the photo so that its height matches the screen's height would require stretching the photo vertically, which would distort the image.

2b. Scaling the width of the photo by a factor of 1024/640 and the height by a factor of 768/300 would not correct the difficulty in part (a) because it would not change the aspect ratio of the photo. The aspect ratio of the photo would still be 2.13, which is different from the aspect ratio of the screen. The photo would still need to be stretched vertically to match the screen's height, which would distort the image.

Multiplying row 1 of the matrix by  1 / 4 would give a resultant matrix of [ 1 / 2    0 | 3 / 4 ]

[ - 1     5   | 4 ].

The question wants to multiply the first row of the matrix alone, with the fraction, 1 / 4.

First step is then to multiply the first row by the fraction of 1 / 4 :

( 1 / 4 ) x 2 = 1 / 2

( 1 / 4 ) x 0 = 0

( 1 / 4 ) x 3 = 3 / 4

The results acquired can then be input into the matrix which would then give a resultant matrix of :

[ 1 / 2   0 | 3 / 4 ]

[ - 1     5   |    4   ]

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Answer:

270

Step-by-step explanation:

I am showing my mental math, hope this helps you:

45 x 6 is the same as 4 x 6 = 10s place value and 5 x 6 = 1s place value:

4 x 6 = 24

5 x 6 = 30

Therefore, the answer is:

2 (4 + 3) 0

270

The value of the expression 45 x 6 is 270.

We have,

To calculate the product of 45 multiplied by 6, you can follow these steps:

- Start by multiplying the units digits of the two numbers: 5 x 6 = 30.

- Write down the units digit of the result, which is 0, and carry over the tens digit, which is 3.

- Multiply the tens digit of the first number by the second number: 4 x 6 = 24.

- Add the carried-over value from step 2 to this result: 24 + 3 = 27.

- Write down the tens digit of the result, which is 7, and carry over the hundreds digit, which is 2.

- Multiply the hundred digit of the first number by the second number: 4 x 6 = 24.

- Add the carried-over value from step 5 to this result: 24 + 2 = 26.

- Write down the hundred digit of the result, which is 6.

- Combine the hundreds, tens, and units digits together: 6, 7, 0.

- The final product of 45 multiplied by 6 is 270.

So, 45 x 6 = 270.

Thus,

The value of the expression 45 x 6 is 270.

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