Converting between fractions, decimals, and percentsUse the definition of the word percent to write each percent as a fraction and then as a decimal.

The distance between the parallel lines measured in the y direction is 3 units.

given data

y = - 3x + 4

y = - 3x + 1

let line 1 be y = - 3x + 4 and line two be y = -3x + 1

Analyzing the two lines show that the slope is equal hence parallel

slope = -3

The y intercept of the line or just the intercept is what varied

The difference between these two pints represents the distance between them measured in the y direction.

The difference is solved as

4 - 1 = 3 units

The distance is 3 units

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Given:

The dimensions of the room are,

The dimensions of the carpet are,

To find:

The number of rolls of carpet.

Explanation:

The number of rolls of carpet is calculated by,

Therefore, the number of rolls of carpet is 8.

Final answer:

The number of rolls of carpet is 8.

No, becuase not all the posible values of x make the inequality true.

For example, if x = 0

7(0) - 5 > 2

0 - 5 > 2

- 5 > 2 This is not true.

Tommie will make $12.65 per hour after his raise.

We will perform addition of value equal to mentioned percentage. So, representing this as equation -

Amount of money earned after raise = 11.5 + 10%×11.5

Converting percentage to whole number

Amount of money earned after raise = 11.5 + (10/100×11.5)

Performing multiplication and division on Right Hand Side of the equation

Amount of money earned after raise = 11.5 + 1.15

Performing addition on Right Hand Side of the equation

Amount of money earned after his raise = $12.65

Therefore, after increase in 10% raise, Tommie will earn total $12.65.

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The ratio of time spent studying math to studying English is 7:2.

According to the question,

We have the following information:

One spends 1 hour a week to study English and 3.5 hours to study math.

Now, we know that the ratio can be simply understood as the division.

So, we will divide the number of hours devoted to math by the number of hours devoted to English.

Ratio of time spent studying math to studying English = 3.5/1

Ratio of time spent studying math to studying English = 35/10

(Now, we will convert this fraction into the simplest form by dividing both the numerator and denominator of the fraction by 5.)

Ratio of time spent studying math to studying English = 7/2

Ratio of time spent studying math to studying English = 7:2

Hence, the ratio of time spent studying math to studying English is 7:2.

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Answer:

45 times

Step-by-step explanation:

it is 45 times because it can land on blue or green 5 out of 8 times so u do 72 divided by 8 and u get 9 so I do 9 times 5 and u get 45

We need to graph the following inequality:

First, let's apply the same operations on both sides of the inequality to isolate the variable y on the left side of the inequality. We obtain:

Now, notice that:

represents a line containing all points with coordinates (x,y) such that y=-4x.

The solution to the inequality includes those points, and also the points for which y is greater than -4x.

Thus, the solution to this inequality consists of all the points on that line (solid line) and the whole region above that line:

Notice that, to graph the solid line, we can choose two points on the line, and then join them. We can use the points:

Since (2,1) is the turning point, let's write the function in its vertex form:

Let's use one of the points:

Therefore:

1. The value of f(2) = 0 and g(2) = 0

2. The value of k is 9

A function can simply be described as a law, rule, theorem or expression that explains the relationship between two terms.

These terms are known as;

Given the functions;

To prove that f(2) = g(2)

Substitute the value of x as 2 in the functions, we have;

f(2) = 2^2 - 2(2)

expand the bracket

f(2) = 4 - 4

f(2) = 0

Then for g(2), we have;

g(2) = 2 - 2

g(2) = 0

Then, f(2) = g(2) = 0

If g(k) = 7

Then, we have;

k - 2 = 7

collect like terms to determine the value of k

k = 7 + 2

k = 9

Hence, the value is 9

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Solution:

If a profit of $1.45 was earned on each bag of oranges sold, then the profit, if all 13 bags were sold, would be:

13 x $1.45 = $18.85

so that, the correct answer is:

$18.85

Given:

There are 11 letters in the word 'MISSISSIPPI'

The number of P's are 2.

The probability that the randomly chosen slip of paper have the letter P written on it is,

The probability that the randomly chosen slip of paperdoes not have the letter P written on it is,

The odd against event is calculated as,

Answer: The odds against the paper having the letter P written on it is 9/2 (9:2)

The probability that at most 3 of light bulbs will be defective will be 0.998.

Probability may be defined as an expression which may be used to determine the possibility of occurring of any event. The probability of happening an event surely is 1 and probability of not happening an event is zero. Since, 5 percent of bulbs are defective then

5% = 0.05 Now,

Non defective bulbs = 1 - 0.05 = 0.95

n = number of light bulbs = 7

We can calculate this using binomial distribution.

p(x) = ⁿCₓ × (pˣ)(1-p) ^n-x

Our question says at most 3 is defective, so it will be

(⁷C₀ × 0.05⁰ × 0.95⁷) + (⁷C₁ × 0.05¹ × 0.95⁶) + (⁷C₂ × 0.05² × 0.95⁵) + (⁷C₃ × 0.05³ × 0.95⁴)

= 0.698 + 0.257 + 0.040 + 0.003

= 0.998 which is the required probability.

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Length has 5 cubes

width has 3 cubes

height has 7 cubes

Volume = length x width x height

5/2 * 3/2 * 7/2 = 105/8 = 13.125 ft^2

Answer:

-72

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x-6 = 90 because opposite angles are equal if intercepted in parallel lines

12x=96

x= 8

Answer: 74.43%

Let us first list down the probabilities of the machine working.

First is the probability that none of the components will fail. We can write this probability as:

Next, the probability that one of the components will fail. This will give us:

Then, the probability that 2 of the components will fail.

Adding all of these probabilities and we will have:

Therefore, the probability that the machine will be working would be 74.43%.

10. |x - 4| - 4 = 1/2x

⇒ Multiplying by 2,

2 |x - 4| - 8 = x

So, x - 4 = (x + 8)/2

             = -(x + 8)/2

When,

x - 4 = (x + 8)/2

2x - 8 = x + 8 (Multiplying by 2)

2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)

x = 16

When,

x - 4 = - (x + 8)/2

2x - 8 = -x - 8 (Multiplying by 2)

2x + x = -8 + 8 (Adding 8 and x to both sides)

3x = 0

x = 0

Hence, the solution is x = 16 and x = 0.

13. (3/4)x = 2x - 10

⇒ Subtract 2x from both sides.

-5x/4 = -10

Multiply both sides by 4/(-5).

(-5x/4)×4/(-5) = -10 × 4/(-5).

x = 8 is the solution of the equation.

15. x² - 7x - 8 > 0

⇒ Solve the quadratic equation by splitting the middle term,

x² - 8x + x - 8 > 0

x(x - 8) + 1(x -8) > 0

(x + 1)(x- 8) > 0

-1 and 8 are the critical points of the inequality.

x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.

16. x - 5 > - 2x + 4

⇒ Adding 2x to both sides.

3x - 5 > 4

Adding 5 to both sides.

3x > 9

Divide both sides by 3.

x > 3 is the required solution represented by blue shade region in the graph.

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The imaginary number 'i" can be written in another form below:

Whenever we have the root of a negative number, we use the imaginary number 'i' to write it in an easier form.

For example:

Therefore:

Answer: C(x) > a(x) , meaning c(X) has the greatest average rate of change over the given interval.

Explanations :

• The greatest average rate of change = slope

• given by formula :

• The average rate of change over the given interval = 7-1 = 6

and

• We can see that b(x) has constant average rate of change at 2 , therefore this will not be considered for this purpose of the exercise.

and

• The average rate of change over the given interval =, 8 -1 = 7

in conclusion , C(x) = 7 , whereas a(x) = 6 ,

Therfore C(x) > a(x)

Answer:

[tex] \frac{1}{3} [/tex]

Step-by-step explanation:

[tex] \frac{3}{94} = 0.31 \\ \\ \frac{1}{3} = 0.33[/tex]

Rajan must climb down 25 ft to return to the bottom of the climbing wall

Height climbed from the bottom of the wall = 15ft

Height: The measurement of an object's height from the base to the top is known as height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Additional height climbed = 10ft

Total height climbed = 25ft

He should climb down the distance, as climbing up will further move him away from the bottom of the wall

Distance to climb down to the bottom of the wall = 25ft

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A premise or premiss is a true or false statement that helps form the body of an argument, By law of syllogism the statement is true. Your cat will chase mice.

A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion.

If the following two statements are true: (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .

If you have a cat, then it will chase mice.

is the given statement.

Let p is you have a cat

q is chase mice.

r is cat will chase mice.

iby the law of syllogism Your cat will chase mice. because  (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .

Hence by law of syllogism the statement "if you have a cat, then it will chase mice" is true.

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Step-by-step explanation:

if I understand you correctly, then you got

sin(60°) = sqrt(3/2)

and now we have to find cos(60°) based on that.

but : sin(60°) = sqrt(3/4) = sqrt(3)/2

I will continue with that.

one major observation with the trigonometric functions in a norm circle (radius = 1) is that sine and cosine are the legs of a right-angled triangle.

the radius at the angle is the Hypotenuse.

and so, Pythagoras applies

c² = a² + b²

c is the Hypotenuse, a and b are the legs.

so,

radius² = sin²(x) + cos²(x)

and because radius = 1

1² = 1 = sin²(x) + cos²(x)

in our case

1 = sin²(60) + cos²(60)

1 = (sqrt(3)/2)² + cos²(60) = 3/4 + cos²(60)

cos²(60) = 1 - 3/4 = 1/4

cos(60) = sqrt(1/4) = 1/2

The mixed fraction 11 [tex]\frac{7}{16}[/tex] - 4[tex]\frac{7}{12}[/tex]  is equivalent to the fraction to 6 41/48

An equation shows the relationship between two or more numbers and variables.The mixed fraction 11 7/16 is equivalent to the fraction (11 * 16 + 7)/16 = 183/16

The mixed fraction 4 7/12 is equivalent to the fraction (4 * 12 + 7)/12 = 55/12

Substituting:= 18 [tex]\frac{3}{16}[/tex] - 5 [tex]\frac{5}{12}[/tex]

Simplifying:= 329/48

= 6 41/48

11 [tex]\frac{7}{16}[/tex] - 4 [tex]\frac{7}{12}[/tex] is equal to 6 [tex]\frac{41}{48}[/tex]

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Let t be the time in hours it takes a block of ice to melt at T degrees.

Since both variables have an inverse relation, we can say that:

Where alpha is a constant value.

Since we know that a block of ice melts in 2.5 hours when the temperature is 54 degrees, we can plug in such data and find alpha as following:

Therefore, our expression would be:

For T = 45,

We can conclude that it would take 3 hours for the block of ice to melt.

We are given a rectangle ABCD

Recall that a rectangle is a quadrilateral in which all angles are right angles (90°)

Each pair of interior angles are supplementary. The two right angles add to a straight angle which means that the opposite sides of a rectangle are parallel.

In quadrilateral ABCD, if m∠A = m∠B = m∠C = m∠D = 90° then AB || DC and AD || BC

Hence, a rectangle is also a parallelogram.

Option B is the correct answer.

To make red brass alloy ratio of copper : zinc is 16 :3 ,then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.

As given,

Ratio given to make red brass alloy using copper and zinc is:

Copper :Zinc=16 :3

Given quantity of copper to make red brass alloy=40 kg

Let y kg be the quantity required to make red brass alloy using 40 kg copper

Using ratio and proportion we get,

40 :y=16 :3

⇒y ×16=40×3

⇒y=120/16

⇒y=7.5 kg

Therefore, to make red brass alloy ratio of copper : zinc is 16 :3 , then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.

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4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)

5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)

6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)

7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)

8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)

9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)

10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)