Probability: is the answer: 0.53125

Step 1: Calculate the length of the diagonal. To calculate the length of the diagonal, use the Pythagorean Theorem: a2 + b2 = c2, where a is the length of one side and b is the length of the other side. In this case, a is 25 cm and b is 32 cm, so we have 252 + 322 = c2, which gives us c2 = 900 + 1024 = 1924. Taking the square root of this gives us c = 43.8 cm.

Step 2: Calculate the distance between the shorter sides. To calculate the distance between the shorter sides, subtract the length of the diagonal (43.8 cm) from the length of the longer side (32 cm), which gives us a total of 8.2 cm.

Therefore, the distance between the shorter sides is 8.2 cm.

Algebraic word problems involve converting sentences into equations and then resolving those equations. and only one variable. The variable typically represents an unknowable quantity in a real-world situation.

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To use the linear combination method to solve the system of equations:

2x – 3y = 13

3x + y = -8

We can multiply the second equation by 3 to get:

9x + 3y = -24

Now we can add this equation to the first equation to eliminate the y term:

2x – 3y + 9x + 3y = 13 - 24

Simplifying the left-hand side and the right-hand side of the equation:

11x = -11

Finally, we can solve for x:

x = -1

Substitute x = -1 in either of the original equations:

2x – 3y = 13

2(-1) - 3y = 13

-2 - 3y = 13

-3y = 15

y = -5

Therefore, the solution to the system of equations is x = -1 and y = -5.

Explanation: We used the linear combination method to eliminate one of the variables by adding the two equations together. Then, we solved for the remaining variable and substituted the value back into one of the original equations to solve for the other variable.

Answer:

t ≈ 2.61

Step-by-step explanation:

13.7t - 4.7 = 9.9 + 8.1t ( subtract 8.1t from both sides )

5.6t - 4.7 = 9.9 ( add 4.7 to both sides )

5.6t = 14.6 ( divide both sides by 5.6 )

t ≈ 2.61 ( to the nearest hundredth )

Step-by-step explanation:

It may be your last point

[tex]y = 2x + 6[/tex]

[tex]y = 2(2) + 6 = 10 \: not \: 8[/tex]

You have the point (2,8) when it should be (1,8)

Keep me updated

The solution is Option A.

The inequality equation is x ≥ 1.4 ( 50 )

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

The number of tablets XYZ Tech sold last week = 50 tablets

The number of tablets XYZ Tech needs to sell this week = 40 % more

So , number of tablets XYZ Tech needs to sell this week = 50 +( 40/100 )50

On simplifying the equation , we get

The number of tablets XYZ Tech needs to sell this week = 50 ( 1 + 0.4 )

The number of tablets XYZ Tech needs to sell this week = 1.4 ( 50 )

Now , they have to sell at least 40 % more

So , the inequality equation is x ≥ 1.4 ( 50 )

Hence , the inequality equation is x ≥ 1.4 ( 50 )

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The function g(x) = 8x is increasing over the interval from x=3 to x=5.

The graph of the function g(x) = 8x is shown below.

We can observe that the graph of g(x) is a staright line passing through origin (0, 0)

This means that the function g(x) is a linear function.

For x = 3, the value of function would be,

g(3) = 8 × (3)

g(3) = 24

And for input value x = 5, the value of function would be,

g(5) = 8 × (5)

g(5) = 40

This means that the value of function g(x) increases from x = 3 to x = 5

Also, from the graph the function g(x) is increasing over the interval [3, 5]

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Money will the group have at the end of 10 years are $82,719.58.

Money is a kind of trade that is utilized in business dealings and other types of economic activity. All economic agents within a particular nation or geopolitical region accept it as a form of asset that is used to store purchasing power and is accepted as payment. It functions as a store of value, a unit of account, and a medium of exchange. Because it allows people to buy and sell goods and services, is crucial.

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] is the formula for computing the amount after compound interest.

Where P is the principal amount, which is $50,000, A is the amount due after 10 years, r is the interest rate, which is 6%, n is the number of times the interest is compounded each year, which is 12, and t is the number of years, which is 10.

Putting the values in the formula,

[tex]A=50,000(1+\frac{0.06}{12})^{(12\times 10)}[/tex]

[tex]A=50,000(1.005)^{120}[/tex]

A=50,000(1.71958)

A=82,719.58

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Using the equation given, the four ordered pair solutions are:

x     |   y  

0       5

-2      -5

6       35

-8     -35

To find the ordered pair solutions to the given equation as shown in the table, plug in the known value into y = 5x + 5 to find the other coordinate pair.

Therefore:

When x = 0:

y = 5(0) + 5

y = 5

When y = -5:

-5 = 5x + 5

-5 - 5 = 5x

-10 = 5x

-10/5 = x

-2 = x

x = -2

When x = 6:

y = 5(6) + 5

y = 35

When y = -35:

-35 = 5x + 5

-35 - 5 = 5x

-40 = 5x

-40/5 = x

-8 = x

x = -8

The four ordered pair solutions are:

x     |   y  

0       5

-2      -5

6       35

-8     -35

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Answer:9

Step-by-step explanation:

add

Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon.

To make up for the higher sale price,

it will take him more than 66 years.

And hybrid cars save money in the long term.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

Deselectric costs $11900 more than the Deswagon.

Unit cost:

Deselectric: $0.11 per mile.

Deswagon: $0.12 per mile.

Kweku drives about 18,000 miles a year.

That means

the cost for each car;

Deselectric: 18000 x 0.11 = $1980

Deswagon: 18000 x 0.12 = $2160

The more cost is,

= $2160 - $1980

= $180 of savings in a year.

Now, the make-up for the higher sale price,

= 11900/180

= 66.11 in years.

And hybrid cars save money in the long term.

Therefore, it will take him more than 66 years.

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The system of equations has no solution

From the question, we have the following parameters that can be used in our computation:

y = x - 7

y = x + 7

By substituting the first equation in the second equation

So, we have the following representation

x + 7 = x - 7

Evaluate the like terms

7 = -7

The above equation is false

Hence, the system has no solution

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Answer:

y = 2

Step-by-step explanation:

2x + y = 8 → (1)

x - 3y = - 3 → (2)

multiplying (1) by 3 and adding will eliminate y

6x + 3y = 24 → (3)

add (2) and (3) term by term to eliminate y

7x + 0 = 21

7x = 21 ( divide both sides by 7 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

2(3) + y = 8

6 + y = 8 ( subtract 6 from both sides )

y = 2

Answer:

y = 2

Step-by-step explanation:

The question has given us two equations with two unknown variables and told us to solve the system of equations.

To do this, there are multiple methods. The method used in this solution will involve taking any one of the variables and making it the subject of both equations and then equating the resulting equations.

Let's take the first equation:

[tex]2x + y = 8[/tex] ,

and rearrange it to make x the subject:

[tex]2x + y = 8[/tex]

⇒ [tex]2x = 8 - y[/tex]         [Subtracting y from both sides]

⇒ [tex]x = \frac{8 - y}{2}[/tex]  ------(i)         [Dividing both sides by 2]

Now let's take the second equation and rearrange it to also make x its subject:

[tex]x - 3y = -3[/tex]

⇒ [tex]x = -3+3y[/tex]  ------(ii)        [Adding 3y to both sides]

As both equations (i) and (ii) are equal to [tex]x[/tex], we can say:

(i) = (ii)

⇒ [tex]\frac{8-y}{2} = -3+3y[/tex]

⇒ [tex]8 - y = 2(-3+3y)[/tex]        [Multipying both sides by 2]

⇒ [tex]8-y = -6 +6y[/tex]

⇒ [tex]8 - y - 6y=-6[/tex]            [Subtracting 6y from both sides]    

⇒ [tex]8-7y=-6[/tex]

⇒ [tex]-7y = -6-8[/tex]                [Subtracting 8 from both sides]

⇒ [tex]-7y = -14[/tex]

⇒ [tex]y = \frac{-14}{-7}[/tex]                          [Dividing both dies by -7]

⇒ [tex]y = \bf 2[/tex]

Therefore, the answer to the question is 2.

We can now easily calculate the value of x by substituting y = 2 into either equation (i) or (ii).

Substituting into (i):

[tex]2x + 2= 8[/tex]

⇒ [tex]2x = 6[/tex]

⇒ [tex]x = \bf 3[/tex]

Answer: To find the least common denominator (LCD) of fractions with variables, you need to determine the smallest number that all the denominators will divide into evenly.

One method to find the LCD is to multiply all the denominators together and simplify the expression. For example, if the denominators are x and y, the LCD would be xy. Another method is to find the greatest common factor (GCF) of all the denominators, and then divide each denominator by the GCF to obtain the LCD.

In either case, it may be necessary to factor the denominators to determine the GCF and simplify the expression for the LCD.

Step-by-step explanation:

Answer:

The vertex form of 8-2x=3(y+1)^2 is: y= -1/6x^2 + 4x - 8.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

204000$ is the new selling price

I think

Answer:

2040000

Step-by-step explanation:

15%of 240 000 is 36 000

240 000 - 36 000 = 204000

Constant: Mug price = $8.95, Refill price = $1.50, Rate: Refill rate = $1.50, Equation: 8.95 + 1.50x = 26.95, Solve: x = 15 refills​. Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.

To calculate the number of refills Jalissa purchased last month, we must first define the constants of the equation. The cost of the mug is $8.95 and the cost of the refill is $1.50. After establishing these constants, we can create an equation using the rate of refills ($1.50) and the total amount that Jalissa spent ($26.95). The equation is 8.95 + 1.50x = 26.95. This equation can then be solved to find the value of x, which is the number of refills Jalissa purchased. To solve the equation, subtract 8.95 from both sides to get 1.50x = 18. This equation can then be divided by 1.50 to find the value of x, which is 15. This means that Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.

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The commission he earned last month was amount of $360.

The commission is determined by the product of the commission rate and the total sales.

A salesman receives a 6% commission on all merchandise sold.

He sold $6000 in merchandise last month.

Salesman earns 6% = 6/100 = 0.06

Now, we have to evaluate 6% of $6000

= 0.06 x 6000

Apply the multiplication operation, and we get

= 360$

Thus, the commission he earned last month was the amount of $360.

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The question seems incomplete, the complete question would be as:

A salesman earns 6% commission on all the merchandise that he sells. Last month he sold $6000 worth of merchandise. How much commission (in dollars) did he earn last month?

The transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

The vertices of the triangle are L (-7, 4), M(-3, 0) and N(-8, 1).

a. Translation: (x,y) → (x + 5, y-6) is as follows:

L' = (-7 + 5, 4 - 6) = (-2, -2)

M' = (-3 + 5, 0 - 6) = (2, -6)

N' = (-8 + 5, 1 - 6) = (-3, -5)

b. Reflection in line y = -x is as follows:

Here, the value of y coordinate is negative x coordinate and x coordinate is negative y coordinate.

L' = (-7, 4) = (-4, 7)

M' = (-3, 0) = (0, 3)

N' = (-8, 1) = (-1, 8)

Hence, the transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).

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The a1 of the sequence is  28715.

The sum of a geometric series can be found using the formula:

S = a / (1 - r)

where:

S is the sum of the series

a is the first term of the series

r is the common ratio, which is the ratio of any term to its preceding term

For a1;

Sn= a1 - anr/ r - 1

Where;

Sn = 21825

n = 125

r = 15

Thus;

2185 = a1 - (125 * 15)/15 -1

2185 * 14 = a1 - 1875

-30590 = a1 - 1875

a1 = 30590 + 1875

a1 = 28715 as we cans see

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The center of the ellipse will be (3, 0). And the lengths of the major and minor axes will be 4.4721 and 2, respectively.

Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.

The equation of the ellipse is given below.

5x² + y² − 30x + 40 = 0

Convert the ellipse into standard form. Then we have

5x² + y² − 30x + 40 = 0

5[x² − 6x] + y² + 40 = 0

5[x² − 6x + 9] − 45 + y² + 40 = 0

5(x − 3)² + y² = 5

(x − 3)² + y² / 5 = 1

The equation center of the ellipse is (3, 0). Then the major axis is given as,

Major axis = 2 √5

Major axis = 4.4721

Then the minor axis is given as,

Minor axis = 2 x 1

Minor axis = 2

The center of the ellipse will be (3, 0). And the lengths of the major and minor axes will be 4.4721 and 2, respectively.

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The correct equation is given below.

5x² + y² − 30x + 40 = 0.

Answer:

The interest amount Karen needs to pay each month is $1000 * .0025 = $2.5.

So, she needs to pay $1100 - $1000 = $100 in interest.

Therefore, Karen will have to pay for 100 / 2.5 = 40 months.

Rounding to the nearest month, Karen will have to pay for 40 months.

Answer:

Perpendicular: = -3/4

Parallel= 4/3

Hope this helps

a) So x = 5 is the critical point, and the vertex is at (5, -3).

b) the y-intercept is (0, -3).

c) y = 2/3 * (x - 5) - 3 for x >= 5

y = -2/3 * (x - 5) - 3 for x < 5

d) The slopes of the two pieces are 2/3 and -2/3 respectively.

(a) To find the vertex, set the derivative of the equation to 0 and solve for x:

dy/dx = 2/3 * d/dx |x-5| = 2/3 * sign(x-5) = 0, where sign(x-5) = 1 if x > 5, sign(x-5) = -1 if x < 5, sign(x-5) = 0 if x = 5.

So x = 5 is the critical point, and the vertex is at (5, -3).

(b) The axis intercepts are the points where the graph crosses the x-axis and y-axis.

The x-intercepts occur when y = 0:

2/3 * |x-5| - 3 = 0

2/3 * |x-5| = 3

|x-5| = 9/2

x = 5 +/- 9/2 = 5 + 9/2 = 7 or x = 5 - 9/2 = 2.5

So the x-intercepts are (7, 0) and (2.5, 0).

The y-intercept occurs when x = 0:

y = 2/3 * |0-5| - 3 = -3.

So the y-intercept is (0, -3).

(c) The graph is a piecewise linear function with two pieces:

y = 2/3 * (x - 5) - 3 for x >= 5

y = -2/3 * (x - 5) - 3 for x < 5

(d) The slopes of the two pieces are 2/3 and -2/3 respectively. These slopes are related because the graph is symmetrical about the vertical line x = 5, with the two pieces being reflections of each other across the line.

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Answer: The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line. Plugging in the given points, we get:

slope = (-1 - 3) / (2 - (-4)) = -4 / 6 = -2/3

So the ratio expressing the slope of line k is -2/3.

Step-by-step explanation:

Hello!

Answer:

The slope of the line that runs through the two points (-3,1) and (-17,2) is

[tex]m= - \frac{1}{14}[/tex]

Step-by-step explanation:

Use the formula of slope to find [tex]m[/tex]

Hope this helps!

Answer:

11

Step-by-step explanation:

lets suppose the number is x

twice the number would be 2x and 15 more than that will be

2x + 15

and this is equal to 37

2x + 15 = 37

2x = 37 - 15

2x = 22

x = 22/2

x = 11

Answer:

6 days

Step-by-step explanation:

This is an easy problem if you think about it. Let’s start by identifying unnecessary information. I’ll go ahead and point this out: we don’t need to know how long it takes Johnny to watch the episodes. The question already says he’s only watching 12 episodes per day, so the time information is useless. If you rewrite the problem with only message information, you get something like this:

“The show Johnny wants to binge watch is 61 episodes long. If Johnny were to watch 12 episodes a day, how many days would it take him to finish the show?”

That makes it seem so much easier! Let’s start by dividing the show into sets of 12 episodes. 61 divided by 12 is 5 R1. Since he needs another day to finish the show, even if he only watches one episode, the answer is 6 days.

The volume of the prism is 360cm³

A prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases.

The volume of a prism is expressed as base area x height

The height = 10cm

base area = ½b×h

= ½ × 6× 12

= 36cm²

therefore;

volume = 36 × 10 = 360cm³

therefore the volume of the shape is 360cm³

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Answer: 3/10

Step-by-step explanation: Convert given fractions into like terms. In this case 1/5 becomes 2/10 and 1/2 becomes 5/10. Add them up and you get 7/10. Subtract from the total of 10/10 and the result is 3/10. Since the final fraction can't be simplified, this is the final answer.