I need help with this problem

Answer:

The percent discount is 17.3%.

The simplified expression for its perimeter and area are 8x and 4x².

What is the square's perimeter?

What is a square area?

Area of square = a²

= (2x)²

= 4x²

Area of square = 4x²

Perimeter of square = 4*a

= 4 * 2x

= 8x

Perimeter of square = 8x

Hence, the simplified expression for its perimeter and area are 8x and 4x².

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The measurement of ∠RPQ is 20°.

What is the meaning of extended point?

A polygon's extended side or sideline in plane geometry is the line that contains one of the polygon's sides. Several situations call for the extension of a side.

Given that,

In ΔPQR, the side PR is extended to the point S.

The measurement of ∠RPQ is (x+12)°, ∠QRS is (7x+8)°, and ∠PQR is (3x+20)°.

We know that, the exterior angle of triangle is equal to the sum of opposite interior angles.

Therefore,

∠QRS = ∠RPQ + ∠PQR

Putting the value of ∠QRS, ∠RPQ, ∠PQR in the above equation:

(7x+8)° = (x+12)° + (3x+20)°

7x + 8 = 4x + 32

Subtract 4x from both sides:

3x  + 8 = 32

Subtract 8 from both sides:

3x = 24

Divide both sides by 3:

x = 8

Putting x = 8 in ∠RPQ = (x+12)°

∠RPQ = (8+12)° = 20°

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The equation that can be used to determine the pounds of laundry the customer brought in to be washed and folded that month is;

D. 0.53x + 26.00 = 37.66

We are given that;

Monthly service fee for Lundromat = $26

They wash and fold clothes at $0.53 per pound  for those customers with a laundry service.

Now, we are told that a customer paid $37.66 total for the month.

If the number of pounds of clothes is denoted as x, then it means that the equation for this will be;

0.53x + 26.00 = 37.66

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Answer:

-3x^2--20x+(y-8)=0

Answer:10

Step-by-step explanation:

Answer:

$37.50

Step-by-step explanation:

75% of $50:

0.75x50=$37.50

The angle between the ladder and the ground is - 0.075 rad/s.

Pythagoras' theorem is a essential relation in Euclidean geometry among the 3 facets of a proper triangle. It states that the region of the rectangular whose aspect is the hypotenuse (the aspect contrary the proper angle) is identical to the sum of the regions of the squares on the alternative  facets.

cosθ = x/10

On differentiating the above equation,

- sinθdθ/dt = (1/10)dx/dt

dθ/dt = -(1/10)dx/dt/sinθ

sinθ = y/10

= √(100 - 36)/10

= 0.8; dθ/dt

= -(1/10)·0.6 ft/s/0.8

= - 0.075 rad/s

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Answer:

B

Step-by-step explanation:

(x - 1) and 74° are corresponding angles and are congruent , so

x - 1 = 74 ( add 1 to both sides )

x = 75

the top angle of the triangle are alternate angles and are congruent

top angle = 40°

the sum of the 3 angles in a triangle is 180°

sum the 3 angles and equate to 180

y - 2 + 40 + 74 = 180

y + 112 = 180 ( subtract 112 from both sides )

y = 68

The probability that Lamar and Lawrence finish their jobs within 5 minutes of each other on a randomly selected day is 0.2892

Consider the time for the Lamar to finish the job as x and the time for the Lawrence to finish the job as x

Consider the random variable x-y

x-y normal with mean = 105 - 98

= 7

Similarly the variance of the random variable x-y

= 105 + 225

= 325

The standard deviation = [tex]\sqrt{325}[/tex]

= 18.03

Here we have to find the probability that Lamar and Lawrence  finish their jobs within 5 minutes of each other on a randomly selected day

P(|x-y|<5) = P(-5<U<5)

Now we have to convert to standard normal variate Z

Then the it will be

(-5-7)/18.03 = -0.67

(5-7) / (18.03)= 0.11

The probability of the given condition will be

P(-0.67<Z<0.11) = 0.2454 + 0.0438

Add the terms

= 0.2892

Therefore, the probability is 0.2892

The complete question is:

Lamar and Lawrence run a two-person lawn-care service. they have been caring for Mr. Johnson's very large lawn for several years, and they have found that the time it takes Lamar to mow the lawn itself is approximately normally distributed with a mean of 105 minutes and a standard deviation of 10 minutes. meanwhile, the time it takes for Lawrence to use the edger and string trimmer to attend to details is also normally distributed with a mean of 98 minutes and a standard deviation of 15 minutes. they prefer to finish their jobs within 5 minutes of each other. what is the probability that this happens, assuming their finish times are independent?

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These can not be the sides of a Triangle.

What is a triangle and the response?

Triangles are a particular kind of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here.

                       Three-sided polygons include triangles. Three triangle angles added together equal 180 degrees.

Property of triangle

Sum of any two sides > third Side

4 , 5 , 6

4 + 5 > 6 , 4 + 6 > 5 , 5 + 6 > 4

3 , 4 , 5

3 + 4 > 5 , 3 + 5 > 4  , 4 + 5 > 3

2 , 3 , 4

2 + 3 > 4   , 2 + 4 > 3  , 3 + 4>2

1  , 2   , 3

1  + 2  = 3  

Sum of 1 & 2  is not greater than 3

Hence, these can not be the sides of a Triangle.

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We can rewrite the circle equation as:

(x - 1)^2 + y^2 = 9

Then the two true statements are:

"The center of the circle lies on the x-axis"

" The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Remember that a general circle equation with a center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here the equation is:

x^2 + y^2- 2 x - 8 = 0

We can rewrite this as:

(x^2 - 2x) + y^2 = 8

Adding and subtracting 1 in the left side we can complete squares:

(x^2 - 2x + 1) - 1 + y^2 = 8

(x - 1)^2 + y^2 = 9

Tha is our equation, so the center is (1, 0) and the radius is 3 units.

Then the true statements are:

"The center of the circle lies on the x-axis"

" The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

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The lowest temperature in January is -10°C if the lowest temperature in January is less than -6°C.

A scaled way of measuring how hot or how chilly something is a living body's normal level of heat production; see thermometer. a condition of extreme body heat with an average oral temperature of 98.6°F. The ideas of hotness and coolness are expressed numerically as a physical value called temperature.

The calibration of thermometers involves employing a variety of temperature scales with clearly defined reference points and thermometric materials. The Celsius scale (°C), formerly known as centigrade, with the unit symbol °C, is the most commonly used scale, followed by the Fahrenheit scale (°F) and the Kelvin scale (K), which is mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).

Given,

Less than 6° was the lowest temperature recorded in January.

The lowest temperature in January will be=?

It is -10°C.

Therefore, the lowest temperature in January is -10°C.

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Answer:

Acute Scalene Triangle  

Step-by-step explanation:

Look at all three angles of the triangle they are all acute. In addition, all of the angles on the triangle are different making it scalene.

Answer:

50

Step-by-step explanation:

The equations of the lines parallel and perpendicular to the lines f (y = 2), ang g (y = 2·x - 1), with the parallel lines passing through the point P(-2, -1), and the perpendicular line passing through the point Q(3, -2) are;

A. The equation of the line parallel to the line f and passing through the point P is; y = -1

B. Equation of the parallel line to g and passing through P is; y = 2·x + 3

C. Equation of the line perpendicular to f passing through P is; x = 3

D. The equation of the line perpendicular to g and which passes through P is y = -0.5·x - 0.5

Perpendicular lines are lines that intersect forming (right angles) an angle of 90°.

The equation that represents the line f is y = 2

The equation that represents the line y = 2·x - 1

A. The slope of a line parallel to another line are the same, therefore;

The equation of the line parallel to the line y = 2, has a slope which is the coefficient of x of 0.

The line f is parallel to the x-axis

The equation that is parallel to line f and passes through the point P(-2, -1)  therefore has the same y-value as the point P of -1 and an x-value of 0, the equation is therefore;

B. The slope of the line g, y = 2·x - 1 is 2

The slope of the graph of the equation of the line that is parallel to the line g, is also 2

The equation of the line parallel to the line g and passing through the point (-2, -1) is; y - (-1) = 2·(x - (-2)) = 2·x + 4

y + 1 = 2·x + 4

y = 2·x + 4 - 1 = 2·x + 3

The equation of the line parallel to the line g and passing through the point P(-2, -1) is therefore;

C. The line f is parallel to the x-axis, therefore, the line perpendicular to the line f is perpendicular to the x-axis or parallel to the y-axis

The equation of the line perpendicular to the line f and passing through the point Q(3, -2), is therefore;

D. The slope of the line perpendicular to the line g, has a slope that is the negative inverse of the slope of the line g

The slope of the line g is 2, therefore, the slope of the perpendicular line is -1/2

The equation of the perpendicular line to the line of the equation g and passing through the point Q(3, -2) in point-slope form is therefore;

y - (-2) = (-1/2)·(x - 3) = -x/2 + 3/2

y = -x/2 + 3/2 - 2 = -x/2 - 1/2 = -0.5·x - 0.5

y = -0.5·x - 0.5

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Answer:

To find the sum of the two fractions, we first need to express them in a common denominator. Since the denominators of the two fractions are different, we will need to find the least common multiple (LCM) of the two denominators.

The LCM of 4 and 5 is 20, so we can express the two fractions in terms of 20 as follows:

-3 1/4 = -3 5/20

-4 2/5 = -4 8/20

Now that the two fractions have a common denominator, we can add them by adding the numerators and keeping the denominator the same:

(-3 5/20) + (-4 8/20) = (-3 + -4) 13/20 = -7 13/20

Therefore, the sum of the two fractions is -7 13/20.

The sum of −3 1/4 + (−4 2/5) is 7.65

Mixed fractions are type of a fraction which includes a whole number and a fraction.

So, any improper fraction can be written as a mixed fraction. Quotient will be the whole number and in the fractional part, numerator is the remainder and denominator will be the divisor.

[−(3 1/4)] + [−(4 2/5)] = [-(13/4)] + [-(22/5)]

When cross multiplying, we will get

-(13/4 + 22/5) = -(65 + 88)/20 = -153/20 = 7.65

Hence, the sum of −3 1/4 + (−4 2/5) is 7.65.

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The answer to this question would be 5 by 9.

The expanded and simplified form of the given expression is [tex]12a^4b^8-18a^3b^3[/tex]. This expansion represents the distributive property.

In this property, the arithmetic operation is as follows:

x(y+z) = xy+xz

Here the term outside of the brackets is multiplied by each term in the brackets.

The given expression is [tex]6a^2b^3(2a^2b^5-3a)[/tex].

It is expanded by using distributive property,

x(y+z) = xy+xz

Here in the expression, [tex]6a^2b^3(2a^2b^5-3a)[/tex] the term 6a²b³ is multiplied by each term in the brackets. So, we get the expanded term.

I.e.,

6a²b³(2a²b⁵- 3a) = (6)(2)(a²)(a²)(b³)(b⁵) - (6)(3)(a²)(a)(b³)

⇒ 6a²b³(2a²b⁵- 3a) = 12a⁴b⁸ - 18a³b³

Here the like terms when multiplied, their powers should be added.

(∵ [tex]x^m\times x^n = x^{m+n}[/tex])

And there is no further simplification for this expanded form since the variables have different powers.

Therefore, the expanded and the simplified form of the given expression is [tex]12a^4b^8-18a^3b^3[/tex].

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Answer: 18 inches

Step-by-step explanation:

A triangle with three equivalent angles, because of the properties of triangles, would also be an equilateral triangle. This means each side length is 6 inches. 6+6+6=18 inches.

For the given log function, the value of y is 8.

An exponent is a logarithm. In logarithmic form, any exponential expression can be rewritten.

Here given, log function :

Log 5 + Log y = Log 40

Can be also written as,

Log y = Log 40 - Log 5  => (eq1)

Based on log property we know that,

Log m - Log n = Log

That is,

Log 40 - Log 5 = Log

Also be written as,

Log 40 - Log 5 = Log 8   => (eq2)

By solving eq1 and eq2, we get,

Log y = Log 8

∴  y = 8

Therefore, The value of will be y = 8

Hence by solving  Log 5 + Log y = Log 40 , the value of y is 8.

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Value of y is 8.

What is a logarithmic equation?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 10³, its logarithm in base 10 is 3, or log₁₀ (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base a is written as logₐ (x), logₐ x, or even without the explicit base, log x.

Given, the equation is log5 + logy = log40

log 40 can be written as log (5*8)

According to the logarithmic equation of log ab = log a + log b

Thus log 40 = log 5 + log 8

Now, the expression becomes

log5 + logy = log 5 + log 8

⇒ log y = log 8

⇒ y = 8

Thus, value of y is 8.

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The distance between the two lines from the graph is 1 unit.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given equations are as below,

y = x - 1

And,

y = 2x - 4

They can be drawn on a graph as follows,

From the graph the distance between two lines can be calculated as the difference between their x-intercepts as,

2 - 1 = 1 unit.

Hence, the distance between the two lines is given as 1 unit.

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In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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Answer: 60%

Step-by-step explanation:

6/10 = 60/100 = 60%

Answer: 60%

Step-by-step explanation:

6/10=60/100

The Sum of the first six terms of the progression is 14706

What is Geometric Progression?

A geometric progression, also known as a geometric sequence, is a non-zero numerical series in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio.

Solution:

On carefully observing

We can state that, the Common Ratio is -7

Sum(n) = a([tex]r^{n}[/tex] - 1) / r - 1

Sum(6) = -1 (-7^6 - 1) / -7-1

Sum(6) = -1(117648)/-8

Sum(6) = 14706

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Answer:

$97

Step-by-step explanation:

Answer:

$60.00

Step-by-step explanation:

1/4(40) = 10

40 - 10 = 30

30+ 2 = 32

32 - 8 - 8 = 16

16 - 6 = 10

10 + 50 = 60

To determine the length of time it takes for all three moons to return to the same position, you need to find the least common multiple (LCM) of the three time periods.

The LCM of 25 days, 30 days, and 20 days is the smallest number that is a multiple of all three of these numbers. You can find the LCM by listing the multiples of each number and finding the smallest number that is a multiple of all three:

25 days: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, ...

30 days: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, ...

20 days: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ...

The LCM of 25, 30, and 20 is 60 days, so it will take 60 days for the three moons to be in the same position again. Therefore, the correct answer is (c) 300 days.

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Answer:

Step-by-step explanation:

12.1

Answer:

8 [tex]\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{17}{20}[/tex] = [tex]\frac{34}{40}[/tex] Multiplied the numerator and denominator by 2

[tex]\frac{1}{2}[/tex] = [tex]\frac{20}{40}[/tex]  Multiplied the numerator and denominator by 20

[tex]\frac{3}{4}[/tex] = [tex]\frac{30}{40}[/tex]  Multiplied the numerator and denominator by 10

2 + 3 + 1 [tex]\frac{34}{40}[/tex] + [tex]\frac{20}{40}[/tex] + [tex]\frac{30}{40}[/tex]

6 [tex]\frac{84}{40}[/tex]  This can be written

6 + [tex]\frac{40}{40}[/tex] + [tex]\frac{40}{40}[/tex] + [tex]\frac{4}{40}[/tex]  another name for [tex]\frac{40}{40}[/tex] is 1

6 + 1 + 1 +[tex]\frac{4}{40}[/tex]

8[tex]\frac{4}{40}[/tex]  Divide the numerator and denominator by 4 to simplify

8 [tex]\frac{1}{10}[/tex]

the probability that a person picked at random from the group is a male or female is fit to climb Mount Shasta is  0.472 (or in percent near 47.2%).

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

1. Determine the number of male climbers:

200 men - 100%

x men - 12 %

. Of the 60 people in California who are physically capable of climbing Mount Shasta, 24 are men, leaving 36 women.

 The likelihood that a guy will be selected at random from the group is

 The likelihood that a random member of the group is physically capable of climbing Mount Shasta is: 0.472

 0.472 (or, in percentage terms, close to 47.2%).

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