|x - 3|= 2x - 15

8 - 2|6 - x|= 20

If the miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, the number of hours it would take Jack to travel 665 miles is 9.5 hours.

Let x represent the number of hours it would take Jack to travel

Formulate an equation

175 / 2. 5 = 665 / x

The denominator cannot equal 0 because the fraction is defined

so,

x ≠ 0

Hence,

1750 × 25x / 25 = 665 × 25x /x

Reduce the fraction

1750x = 665 × 25

1750x = 16,625

Divide both side by 1750x

x = 16,625 / 1750

x = 9.5

Therefore it will take Jack 9.5 hours.

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In 9.5 hours Jack can travel for 665 miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Suppose 2 pens cost 10 dollars, therefore 1 pen costs (10/2) = 5 dollars.

From this unitary value, we can determine the cost of any no. of pens.

Given, Jack drove 175 miles in 2.5 hours.

∴ In one hour Jack can drive (175/2.5) miles.

= 70 miles.

So, to travel 665 miles Jack needs (665/70) hours.

= 9.5 hours or 9 hours and 30 minutes.

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In the given angle, the value of x is 9°.

As we can see that the two triangles are congruent as 2 pairs of sides are similar to each other.

So, with this the equation will be:

Therefore, in the given angle, the value of x is 9°.

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Since we used x and x+2 as consecutive odd integers. "x" to represent Henry's age, Henry's age is 27. Since we used the expression "x+2" to represent Cameron's age, Cameron's age is "27+2" which is just 29.

So the consecutive odd integers, just means they're separated by a value of 2. This can be generally expressed as "a and a+2" where the these two values would be consecutive odd integers assuming "a" is an integer.

So let's express the Henry's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive odd integer, Cameron's can be expressed as "x+2"

So the equation we need to set up is 2(Cameron's age) + (Henry's age) = 85

So we can substitute variables we defined to express Cameron and Henry's age:

2(x+2)+x= 85

Distribute the 2:

2x+4+x

Add like terms:

3x+4=85

Subtract 4 from both sides:

[tex]3x= 81[/tex]

Divide both sides by 3:

x=27

Since we used "x" to represent Henry's age, Henry's age is 27. Since we used "x+2" to represent the Cameron's age, Cameron's age is "27+2" which is just 29.

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The single complex number corresponding to each expression:

1. √(-9) = 3i

2. √(-16) = 4i

3. √(-6)√(-24) = 12

4. √(-3)√(-75) = 15

5. (2+√(-12))/2 = 1 + 3i

6. (4 + √(-20))/2 = 2 + 5i

We represent √(-1) as i which is an imaginary number. Complex numbers are numbers of the kind a + ib, where a and b are real numbers.

Hence all real numbers are also complex numbers (i.e., when b = 0).

Also we use some formula for square roots:

√(ab) = (√a )(√b)

Now, to find the single complex number corresponding to each expression:

1. √(-9) = √(9) x √(-1) = 3i

2.  √(-16) = √(16) x √(-1) = 4i

3. √(-6)√(-24) = √(-6 x -24) = √(144) = 12

4. √(-3)√(-75) = √(-3 x -75) = √(225) = 15

5.  (2+√(-12))/2 =  (2+√4√3√(-1))/2 =  (2+2 x (√3)i)/2  = 1+(√3)i

6. (4 + √(-20))/2 = (4 + √4√5√(-1))/2 = (4 + 2 x (√5)i )/2 = 2 + (√5)i

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P ( All three are not caused by firmware ) = 8423 %

The probability that the entire batch will be accepted = 0.8423

We are told that out of the 6225 cases of heart pacemaker malfunctions, 346 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 6225 - 346 = 5879

So, the probability of the first case not being affected by the firmware is;

P( first case not caused by firmware ) = 5879/6225

Also,

The probability of the second case not being affected by the firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 5878/6224

Similarly,

The probability of the third case not being affected by the firmware is given as;

P(third case not caused by firmware | first and second not caused by firmware) = 5877/6223

Now that we have the three probabilities, it is clear that the occurrences are not independent because the likelihood of one event depends on the likelihood of the others.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P( All three not caused by firmware ) = P(first case not caused by firmware ) × P( second case not caused by firmware | first case not affected by firmware) × P( third case not caused by firmware | first and second not caused by firmware)

Substituting the values,

P(All three not caused by firmware) = ( 5879/6225 ) × ( 5878/6224 ) × ( 5877/6223 )

P(All three are not caused by firmware) = 0.84232558432 = 84.23 %

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We can determine the area of the enlarged picture as follows:

*First, we determine the new dimensions, that is:

*Secondly, we find the area using the formula of area for a rectangle, that is:

From this, we have that the area of the picture after being enlarged equals 250 in^2.

Answer: What do you need help with?

Step-by-step explanation:

1: Comment what u need help with

2: We will help you

3: You have been helped :)

Answer:

After doing the math I got 74.44

The equation which represent the prize money given to each person is $1500/w.

For the given condition in question;

Let 'w' be the number of coworkers.

The total money given to buy raffle tickets and won $1500.

This cam be written as;

w worker -------> $1500.

For 1 worker, use unitary method.

Divide both side by w.

1 worker -------> $1500/w.

Thus, the prize money given to each worker is $1500/w.

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

Explanation:

We can use a counter-example.

Pick any positive real number you want to replace x.

I'll pick x = 7

Use the change of base formula to get the following

[tex]\log_{3}(\text{x}) = \frac{\log(\text{x})}{\log(3)}\\\\\log_{3}(7) = \frac{\log(7)}{\log(3)}\\\\\log_{3}(7) \approx \frac{0.8451}{0.4771}\\\\\log_{3}(7) \approx 1.7713\\\\[/tex]

and

[tex]\log_{2}(\text{x}) = \frac{\log(\text{x})}{\log(2)}\\\\\log_{2}(7) = \frac{\log(7)}{\log(2)}\\\\\log_{2}(7) \approx \frac{0.8451}{0.3010}\\\\\log_{2}(7) \approx 2.8076\\\\[/tex]

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

So if x = 7, then we have,

[tex]\log_{3}(\text{x}) > \log_{2}(\text{x})\\\\\log_{3}(7) > \log_{2}(7)\\\\1.7713 > 2.8076\\\\[/tex]

The last statement is false, so the first statement is false when x = 7.

It turns out that you could pick any positive real number for x and will always get a false statement when saying [tex]\log_{3}(\text{x}) > \log_{2}(\text{x})[/tex]

If  She then flew to New York where the temperature was 67 degrees. The change in temperature from when Tina left Atlanta and arrived in New York is : D:15°.

Given :

Beginning temperature = 72 degrees

Increase in temperature = 21 degrees

Decrease in temperature = 11 degrees

Temperature outside Atlanta = 67 degrees

First step is to calculate the temperature in Atlanta using this formula

Temperature = (Beginning temperature + Increase in temperature - Decrease in temperature )

Let plug in the formula

Temperature =  72 + 21 -11

Temperature = 82 degrees

Second step is to calculate the change in temperature

Change in temperature = Temperature in Atlanta - Temperature in New York

Change in temperature = 82 degrees - 67 degrees

Change in temperature = 15 degrees

Therefore the correct option is D.

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Here, we want to select the inequality that best represents the situation

Let the number of weeks be x

Total value saved in x weeks at $35 per week will be 35 * x = 35x

Adding this to what she had initially, the total expression becomes 35x + 45

This sum must be the same or greater than what she plans to save

The inequality is thus;

The complementary angle to 38° is 52°.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius.

Let the angle be x°

Then the compliment of the angle = (90-x)°

and supplement of the angle = (180-x)°

According to question, (180-x) + 14 = 3(90-x)

or, 180-x+14 = 270-3x

or, -x+3x = 270-194

or, 2x = 76

or, x = 76/2 = 38°

Hence, the complementary angle to 38° is = 90-38 = 52°

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From the figure, we observe that,

Non-rigid motions are used to map figure 1 onto figure 2.

Here, resizing (stretching horizontally, vertically, or both ways) is a non-rigid transformation.

So, the answer is,

The figures are congruent because non-rigid motions are used to map figure 1 onto figure 2.

The point corresponding to point C is H.

Answer:

Should the essay be 3-5 paragraphs? Also I can't write the essay here or otherwise your school will find out you plagiarized it.

Step-by-step explanation:

I can send it to you privately.

Answer:

C. If I did not go walking, then it is cold.

Step-by-step Explanation:

A conditional statement is a hypothesis followed by a conclusion. The hypothesis in this example being “If it is cold” and then followed by a conclusion “I will not go walking”.

A converse statement swaps the hypothesis and the conclusion of a conditional statement.

Answer:

I believe the answer is $17.75

Step-by-step explanation:

As if you have a base fee of 13.75 then 0.10 for each additional mile. Then 40 miles x 0.10 is 4. Hope this helps.

The product of the numbers are-

For the given number;

Part a: 107 × 11

   1 0 7

 ×   1  1

 ---------

    1 0 7

+ 1 0 7 x

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

1  1  7  7

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

Thus, 107×11 = 1177

Part b: 72×13

   7  2

 × 1  3

 ---------

  2 1  6

+ 7  2   x

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

  9  3   6

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

Thus, 72×13 = 936

Part c: 466×27

 4  6  6

 × 2  7

 ---------

 3 2 6 2

+9 3 2  x

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

1 2 5 8 2

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

Thus, 466×27 = 12582

Therefore, product of the number are found.

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Answer:

The absolute value is the distance between a number and zero on a number line. There are always two numbers on the number line that are the same distance from zero. For instance, the numbers 4 and -4 are each a distance of 4 units away from zero. represents the distance from 4 to zero, which equals 4.

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P(A) given that A and B are independent is; 35%

P(A|B) is defined as a conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B"

Now, the formula to find P(A|B) is;

P(A|B) = P(A∩B) / P(B)

Where;

P(A∩B) = P(A) *  P(B)

Thus;

P(A|B) = (P(A) *  P(B))/(P(B)

Plugging in the relevant values gives;

0.35 = P(A)

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In this simple economy where the market basket for CPI contains two items, the CPI for year 2 is 102.22%.

The CPI means the Consumer Price Index.

The CPI economically indicates the inflationary trend, using a basket of selected consumer goods and services, and computes their total costs for each period.

The base year's total costs set to 100% are used to compare with the current year's.

Price       1 Bottle of     1 Bar of   2 Bars      Total Cost

              Shampoo       Soap     of Soap    Mkt Basket

                    (a)               (b)             (c)          (a) + (c)

Year 1        $6.50           $1.25     $2.50          $9.00

Year 2      $6.60            $1.30     $2.60         $9.20

CPI for Year 1 (base year) = 100% ($9/$9 x 100)

CPI for Year 2 = 102.22% ($9.20/$9 x 100)

Thus, year 2's Consumer Price Index is 102.22%, compared to year 1's.

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Answer:

102.22

Step-by-step explanation:

Edmentum.

Titanium is used in aerospace (jet engines, missiles, and spacecraft), military, industrial processes (chemicals and petrochemicals, desalination plants, pulp, and paper), automotive, agriculture (farming), medical prostheses, orthopedic implants, dental and endodontic instruments and files, dental implants, sporting goods, jewelry, cell phones, and other applications, titanium can be alloyed with iron, aluminum, vanadium, and molybdenum, among other elements. And it's half life as per question is [tex]A(t)=A(500)*0.5^{\frac{t}{6} }[/tex]

The chemical element titanium has atomic number 22 and the symbol Ti. A transition metal with a silver hue, low density, and high strength that is resistant to corrosion in sea water, aqua regia, and chlorine can be created by reducing the only form it is found in the nature—an oxide.

William Gregor found the titanium in Cornwall, Great Britain, in 1791. Martin Heinrich Klaproth gave the metal the Titans' name from Greek mythology. The element is found in practically all living organisms, as well as bodies of water, rocks, and soils. It is mostly found in the minerals rutile and ilmenite, which are widely distributed in the Earth's crust and lithosphere. The Kroll and Hunter procedures are used to separate the metal from its main mineral ores. Titanium dioxide, the most prevalent substance, is a well-liked photocatalyst and is utilized in the production of white pigments. In addition, there are other substances such titanium tetrachloride (TiCl4), which is used in smoke screens and catalysts, and titanium trichloride (TiCl3), which is a catalyst in the creation of polypropylene.

This equation can be used to calculate the quantity of unstable nuclei left after time t:

[tex]N(t)=N(0)*0.5^{\frac{t}{T} }[/tex]

where,

N(t) = remaining quantity of substance after time t has elapsed

N(0)=  initial quantity of this substance

T= half life

So, as per question,

[tex]A(t)=A(500)*0.5^{\frac{t}{6} }[/tex]

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Answer:

A = 500 (1-0.5)^t/6 =500 (0.5)^t/6

Step-by-step explanation:

Took the test, this is the correct answer

A(t)=P (1-decay rate)^t

P=initial amount

Decay rate = 1/2=0.5

t=time

Make sure use t in minutes for the next calculation

For this type of question the first step is to calculate the slope of the line given by th equation x+2y=7, for this we recall the slope intercept form ( y=mx+b) and put the equation in that form

Then, m=-1/2. Now, since the equation of the line we are looking for is parallel to the previous line the slope must be the same, now we recall the point slope equation

Substituting m=-1/2, and recalling that the line is passing through (-3,4) we get that the point slope equation the line is :

Finally to put it in the slope intercept form, we solve the equation for y:

For part b) we recall that the standard form of the equation of a line is:

Now, we solve for the constant of the equation:

The last equation is the standard form of the equation of the line.

Answer:

m= 0

Step-by-step explanation:

Since the two points have the same y-coordinates, the line passing through them is a horizontal line. Horizontal lines have a slope of zero.

Prove:

[tex]\boxed{slope = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]

Slope between (6, 5) and (-9, 5)

[tex] = \frac{5 - 5}{ - 9 - 6} [/tex]

[tex] = \frac{0}{ - 15} [/tex]

= 0

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The standard error mean if σ = 64 and n = 64 is 8.

The standard error mean is given by the formula σ/√N. In the question provided, we need to note that the standard error mean is designated by σM.

Now applying the formula, we will have this:

σM = 64 ÷√64

The root of 64 = 8.

Therefore, the standard error mean is equal to 64 divided by 8 which is 8.

So, we can arrive at the conclusion that given the standard error mean of σ = 64 and n = 64, the standard error mean will be 8.

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The value of x of the Quadratic Equation, (x - 7)² = 36 when the right-hand side is positive is 13 and for the negative right-hand side, it is 1. So the value of x could be 13 and 1 both.

Split into two equations:

(x - 7)² = 36

(x- 7) = √36 or (x- 7) = -√36

For equation (x- 7) = √36 value of x:

x - 7 = √(6)²

x - 7 = 6

x = 13

For equation (x- 7) = -√36 value of x:

x - 7 = -√(6)²

x - 7 = - 6

x = 1

∴ value of x could be 13 and 1 both.

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Answer:

A. would be a quotient of 34 and a remainder of 14

B. would be a quotient of 22 and a remainder of 10

C. would be a quotient of 20 and a remainder of 34