Calculate the problem A sum of money was shared between Mario, Giana and Allan in the 2:3:7. If Allan received $640 more than Giana, find the total sum of money shared

Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.

The vertex of the given graph is (5, 0)

A vertex is a point on a polygon where two rays or line segments meet, and the sides or edges of the object come together. Vertex is the plural form of vertices.

A straight line that can be extended endlessly is known as a ray. An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle.

Thus, we can state that a vertex is formed when two line segments or rays intersect.

Here we have a graph  

The equation of the graph is y = |x - 5| + 1  

As we can see that two lines are intersected at a point (5, 0)

Therefore,

The vertex of the given graph is (5, 0)

Learn more about Graphs at

https://brainly.com/question/29119716

#SPJ1

Equation of line DC is y = -1/2 x - 8

Equation of line AD is y = 2x + 2

Equation of line BC is y = 2x - 8

The equation of the line 2y + x = 4 is arranged in slope intercept form to have

y = -x/2 + 2

The slope is -1/2

with a slope of -/2 and points (0, -8) line DC is written as

y - -8 = -1/2 (x - 0)

y + 8 = -1/2 x

y = -1/2 x - 8

Equation of line AD

line AD is a perpendicular line  to line DC hence the slope is negative reciprocal of the slope of line DC

slope = 2

point A(0, 2) line AD is written as

y - 2 = 2 (x - 0)

y - 2 = 2x

y = 2x + 2

Equation of line BC

line BC is a parallel to line AD hence the slopes are equal

slope = 2

point C (0, -8) line AD is written as

y - - 8 = 2 (x - 0)

y + 8 = 2x

y = 2x - 8

Learn more about linear function at:

https://brainly.com/question/15602982

#SPJ1

The length of major arc CBD is given as follows:

C = 40.39 m.

The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:

C = 6.28r.

For this problem, the parameters are given as follows:

Hence the arc length is given as follows:

C = 5/7 x 6.28 x 9

C = 40.39 m.

More can be learned about the radius of a circle at brainly.com/question/24375372

#SPJ1

The compound interest rate charged is given as follows:

13% per year.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 12000, A(t) = 22109.22, n = 1, t = 5.

Hence the interest rate is obtained as follows:

22109.22 = 12000(1 + r)^5

(1 + r)^5 = 22109.22/12000

1 + r = (22109.22/12000)^(1/5)

1 + r = 1.13

r = 1.13 - 1

r = 0.13.

More can be learned about compound interest at https://brainly.com/question/2455673

#SPJ1

The values that van be put in the table based on the information will be:

Buying price (dollars) 100.

Mark-up 80.

Selling price 180

Commission 20

Profit 60

Buying price (dollars) 10

Mark-up 8

Selling price 18

Commission 2

Profit 6

Buying price (dollars) 55

Mark-up 44

Selling price 99

Commission 11

Profit 33

Buying price (dollars) 125

Mark-up 100

Selling price 225

Commission 25

Profit 75

It should be noted that the markup is 80% of the buying price. For example, when the buying price is $10, the markup will be:

= 80% × $10

= $8

The selling price is that addition of buying price and markup. This will be:

= $10 + $8

= $18

The commission is 25% of markup. This will be:

= 25% × 8

= $2

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Answer:

D.) QIII

Step-by-step explanation:

Because 1.2 radians is in between 7π/6 and 5π/4

If Pat can knit 2cm in 35 minutes, then would take Pat approximately 2800 minutes to knit a scarf that is 160cm long.

If Pat can knit 2cm in 35 minutes time

then she can knit 1cm in (35/2) minutes, or 17.5 minutes.

To determine the total time to knit a 160cm scarf

Pat would need to work a total of

160cm x 17.5 minutes/cm = 2800 minutes.

Hence,

It would take Pat approximately 2800 minutes to knit a scarf that is 160cm long. This is equivalent to about 46.7 hours or 1.94 days of work

Learn more about Time and Work here brainly.com/question/3854047

#SPJ4

Pat is knitting a scarf . On average she can knit 2cm in 35mins. How long will take her to knit a scarf that is 160cm long?​

Answer:

x[tex]\leq[/tex]52

Step-by-step explanation:

x[tex]\leq[/tex]52

now, we're assuming the deposits of $5000 are made at the beginning of the year.

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 5000\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]A=5000\left[ \cfrac{\left( 1+\frac{0.032}{1} \right)^{1 \cdot 25}-1}{\frac{0.032}{1}} \right]\left(1+\frac{0.032}{1}\right) \\\\\\ A=5000\left[ \cfrac{\left( 1.032 \right)^{ 25}-1}{0.032} \right]\left(1.032\right) \implies A \approx 193148.73[/tex]

Answer:

the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer

Step-by-step explanation:

To factor the equation 2 - 8 + 33 = 0, we start by collecting all the terms on one side of the equation:

2 - 8 + 33 = 0

becomes

33 - 8 + 2 = 0

Next, we can rewrite this as:

33 - 6 = 0

Finally, we factor the left-hand side of the equation to get:

33 - 6 = (33 - 3) - 3 = 30 - 3 = 27 - 0

So the factored form of the equation 2 - 8 + 33 = 0 is 27 = 0.

Verification: We can verify that the factored form of the equation is correct by substituting 0 for 27 and checking that the equation holds. So, if we replace 0 for 27 in equation 27 = 0, we get:

27 = 0, which is true.

Therefore, the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer.

The double-angle identity for cosine is cos(2x) = cos²(x) - sin²(x).

To derive the reduction identities, we can use this double-angle identity and manipulate it to express cosine or sine of x in terms of cosine or sine of a smaller angle. Here are the steps for deriving the reduction identity for cosine: Start with the double-angle identity: cos(2x) = cos²(x) - sin²(x).

Divide both sides by cos²(x): cos(2x) / cos²(x) = (cos²(x) - sin²(x)) / cos²(x).

Use the identity sin²(x) + cos²(x) = 1 to replace cos²(x) in the denominator: cos(2x) / cos²(x) = (1 - sin²(x)) / cos²(x).

Rearrange the right-hand side: cos(2x) / cos²(x) = 1/cos²(x) - sin²(x) / cos²(x).

Recognize that 1/cos²(x) is equal to sec²(x), and use the identity tan²(x) + 1 = sec²(x) to replace it: cos(2x) / cos²(x) = sec²(x) - tan²(x).

Simplify using the identity cos(x)/sin(x) = cot(x): cos(2x) / cos²(x) = cosec²(x) - cot²(x).

Simplify the left-hand side using the identity cos(2x) = 2cos²(x) - 1: (2cos²(x) - 1) / cos²(x) = cosec²(x) - cot²(x).

Rearrange and simplify: 2 - (1/cos²(x)) = cosec²(x) - cot²(x).

Recognize that 1/cos²(x) is equal to sec²(x) and cosec(x) is equal to 1/sin(x): 2 - sec²(x) = 1/sin²(x) - cot²(x).

Simplify the left-hand side using the identity 1 - sin²(x) = cos²(x): cos²(x) - sec²(x) = 1/sin²(x) - cot²(x).

Recognize that sec(x) is equal to 1/cos(x) and cot(x) is equal to cos(x)/sin(x): cos²(x) - 1/cos²(x) = sin²(x)/cos²²(x) - cos²x)/sin²(x).

Simplify: cos⁴(x) - 1 = sin²(x) - cos⁴(x).

Rearrange: 2cos⁴(x) = sin²(x) + 1.

Finally, recognize that sin²(x) + cos²(x) = 1, and use it to replace sin²(x): 2cos⁴(x) = cos²(x). This is the reduction identity for cosine: cos²(x/2) = (1 + cos(x))/2.

To derive the reduction identity for sine, we can use the same double-angle identity for cosine and manipulate it to express sine of x in terms of sine or cosine of a smaller angle. The steps are similar but may require using different.

To learn more about double-angle identity click here

brainly.com/question/17080744

#SPJ4

The measure of <E= 60, <F= 95 and <G= 25 degree.

In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.

Given:

The two triangles are similar.

In triangle JKL using Angle Sum Property

<J + <K + <L = 180

95 + 60 + <K = 180

155 + <K = 180

<K = 180- 155

<K = 25 degree

Thus, the measure <E= 60

and, the measure <F= 95

and, the measure of <G= 25.

Learn more about Similarity here:

https://brainly.com/question/26451866

#SPJ1

Answer:

118

Step-by-step explanation:

Let the original number be x.

After subtracting 3, the result is x - 3.

When this result is multiplied by 5, we get (x - 3) * 5 = 575.

Expanding and solving for x, we have:

5x - 15 = 575

5x = 590

x = 118

So the original number was 118.

The area of the given figure is 12 square meters

The given figure is a parallelogram

Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four

The height of the parallelogram = 2 meters

The base length of the parallelogram = 6 meters

The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram

Substitute the values in the equation

The area of the parallelogram = 2 × 6

Multiply the numbers

= 12 square meters

Therefore, the area is 12 square meters

Learn more about parallelogram here

brainly.com/question/29147156

#SPJ4

I have solved the question in general , as the given question is incomplete

The complete question is :

What is the area of the figure ?

If the weight of the bucket is 70 lb , then the work required to lift the bucket from bottom is 135240 foot-pounds  .

We use the formula : Work = Force × Distance to calculate the work done

where "Force" is weight of bucket filled with water and "Distance" is  height it is lifted.

The weight of bucket filled with water is =  70 pounds.

We convert this to a force in pounds force, by using g = 32.2 feet per second squared ;

So , Force = Weight × Gravity

⇒ 70 lb × 32.2 ft/s² = 2254 lb-ft/s²

The distance that the bucket is lifted is = 60 feet ;

So , work required to lift bucket from bottom of well to top is :

⇒  Work = Force × Distance = 2254 lb-ft/s² × 60 ft

⇒ 135240 foot-pounds

Therefore , it will require 135240 foot-pounds of work to lift the bucket filled with water from the bottom of the well to the top.

Learn more about Work here

https://brainly.com/question/29032079

#SPJ4

The given question is incomplete , the complete question is

A bucket that weights 70lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep.  

Compute the work required to lift the bucket from the bottom of the well to the top .

The y-intercept of the graph of a function is the point at which the graph intersects the y-axis. In other words, it's the value of the function when x=0.

So to find the y-intercept of f(x) = 57(3.2)x, we can substitute x=0 into the function:

f(0) = 57(3.2)(0)

f(0) = 0

So the y-intercept of this function is (0,0).

The  probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability

The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one

Here, the product will operate properly within an expected time frame is the dimension of quality

Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability

Therefore, the given statement is know as the reliability

Learn more about reliability here

brainly.com/question/14841972

#SPJ4

From the given choices, we get:

No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.

The correct option is D.

A computer experiment in which you can select a random sample from the given probability distributions is called a simulation.

Given:

A student wants to simulate 28 birthdays,

but she does not have a calculator or software program available,

so she makes up 28 numbers between 1 and 365.

By comparing with the definition:

From the given choices, we get,

D. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.

Hence, D is the correct option.

To learn more about the simulation;

https://brainly.com/question/16359096

#SPJ1

When eight more than the quotient of a number 'b' and 25 is greater than 6 then the inequality representing the value of b is b > -50.

The expression used to represents :

Quotient of a number b and 25 is equal to b / 25

Next step is :

8 more than the b / 25 is equal to ( b / 25 ) + 8

Then ,

( b / 25 ) + 8  is greater than 6 is given by

⇒ ( b / 25 ) + 8 > 6

Simplify the above inequality for 'b' we get,

⇒ ( b / 25 )  > 6 - 8

⇒ ( b / 25 )  > -2

Multiply both the side by 25 we get,

⇒ b > - 2 × 25

⇒ b > -50

Therefore, the inequality representing the value of 'b' for the condition of quotient and a number is equal to b > -50.

The above question is incomplete , the complete question is:

8 more than the quotient of a number b and 25 is greater than 6 , then the value of b is ?

Learn more about quotient here

brainly.com/question/16134410

#SPJ4

Explanation:

The left-most digits are more significant than digits on the right.

For example, in the very large number 1,234,567 the "1" and "2" are more important than the "6" and "7". We focus on the more important digits when rounding. This would mean 1,234,567 rounds to 1,200,000 = 1.2 million = 1.2*10^6

Going back to 3.162, we have "3" and "1" as the left-most digits. We'll bump 3.1 up to 3.2 because of the digit 6 fits the criteria of "5 or larger".

Put another way: 3.162 is closer to 3.2 than it is to 3.1

This is why 3.2 is the final answer.

m∠1 = m∠5, because alternate exterior angles are congruent.

Angles formed by intersecting two parallel lines with a transversal are known as angles in parallel lines.

Given:

lines a and b intersect a transversal, c.

The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.

m∠1 = m∠5 (Alternate exterior angles are congruent)

m∠1 = m∠5, because alternate exterior angles are congruent.

learn more about alternate exterior angles here:

brainly.com/question/2279752.

#SPJ9

The Complete Question is attached below.

The solution of the equations y = 3x + 2 and - 4x + 2y = 8 by elimination method will be (2, 8).

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The equations are given below.

y = 3x + 2

2y = 6x + 4

6x - 2y = - 4         ...1

- 4x + 2y = 8        ...2

Add both equations, then we have

6x - 4x = - 4 + 8

2x = 4

x = 2

Then the value of 'y' is given as,

y = 3(2) + 2

y = 6 + 2

y = 8

The solution of the equations y = 3x + 2 and - 4x + 2y = 8 by elimination method will be (2, 8).

More about the solution of the equation link is given below.

https://brainly.com/question/29797035

#SPJ1

The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.

When a coin is flipped the probability of getting a heads and a tail is 50%.

Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

The given value 4.1 x 10^-4 can be written in standard form as 0.00041

The standard form can be done by following the format of multiplying a *10^b where b is the power and a is the digit.

A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.

Hence 4.1 x 10^-4 = 0.00041

Learn more about standard form at:

https://brainly.com/question/19169731

#SPJ1

Circle A is larger.

Circle A's radius is 58 cm and circle B's radius is 57 cm.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

We have,

Area of a circle = πr²

Circumference of a circle = 2πr

Circle A:

Area of a circle = 10562.96

πr² = 10562.96

r² = 3364

r = 58 cm ____(1)

Circle B:

Circumference = 357.96

2πr = 357.96

r = 357.96/6.28

r = 57 cm ______(2)

From (1) and (2)

58 > 57

So,

Circle A is larger.

Thus,

Circle A is larger.

Learn more about circle here:

https://brainly.com/question/11833983

#SPJ1

Answer:

Step-by-step explanation:

There are 256 people in a room. If they are divided into groups of 4, how many groups are there?

Answer: 64

The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

Learn more about circle click here:

https://brainly.com/question/29275331

#SPJ4

False. The probability of the union of two events occurring can be greater than the probability of the intersection of two events occurring.

The probability of the union of two events A and B, written as P(A union B), is the sum of the individual probabilities of the two events minus the probability of their intersection.

P(A union B) = P(A) + P(B) - P(A intersection B)

If the two events are not mutually exclusive, meaning that they have a non-empty intersection, then P(A union B) will be greater than P(A intersection B).

In other words, the union of two events gives you the combined probability of both events happening, while the intersection gives you the probability of both events happening simultaneously, which is always smaller or equal to the probability of either event happening.

To learn more about intersection please click on below link.

https://brainly.com/question/26496929

#SPJ4

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring? TRUE/ FALSE.