Peter and Patty are very competitive and they both are saving money in their piggy banks. Peter has $90 and
Patty has $120. Patty's mom gives her a bonus of 20% of what she already has and Patty adds it to her piggy
bank. Peter's dad tells him that he will give him a bonus so that Peter has the same total as Patty. What percent of
Peter's money must the bonus from his dad be?

Answer:

[tex]\frac{x}{x+2}[/tex]

Step-by-step explanation:

[tex]\frac{x^2+5x}{x^2+7x+10}[/tex] ← factorise numerator and denominator

= [tex]\frac{x(x+5)}{(x+5)(x+2)}[/tex] ← cancel (x + 5) on numerator / denominator

= [tex]\frac{x}{x+2}[/tex]

The diameter of a circle is defined as being twice the length of its radius.

If SU = 16.2 centimeters then the value of RT = 8.1 cm.

The diameter of a circle is defined as being twice the length of its radius. The radius of a circle is measured from the center to one of the circle's endpoints, whereas the diameter is measured from one end of the circle to another end of the circle, passing through the center.

In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.

The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.

Here, SU is the diameter and RT is the radius.

Radius of the circle = 1/2 d

Where d = 16.2 then

substitute the value of d in the above equation, and we get

Radius of the circle  = 1/2 (16.2)

Radius of the circle = 8.1

Therefore, the value of RT = 8.1 cm.

The complete question is:

If SU = 16.2 centimeters, what is RT?

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The expression that is equal to [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex] is [tex]\frac{x^{2}+22x }{(x+2)(x+3)(x-3)}[/tex].

In the given question

[tex]=\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex].....(i)

First solving the denominator of both the terms ,

=x²-9

=x²-(3)²  

=(x+3)(x-3)    ...using identity a²-b²=(a+b)(a-b)   .....(ii)

=x²+5x+6

=x²+3x+2x+6       ...by splitting the middle term

=x(x+3)+2(x+3)

=(x+2)(x+3)       ....(iii)

Substituting the value of (ii) and (iii) in   (i)

we get,

[tex]=\frac{5x}{(x+3)(x-3)} -\frac{4x}{(x+2)(x+3) }[/tex]

taking LCM as (x+2)(x+3)(x-3) we get ,

[tex]=\frac{5x(x+2)-4x(x-3)}{(x+2)(x+3)(x-3)} \\ \\ =\frac{5x^{2} +10x-4x^{2} +12x}{(x+2)(x+3)(x-3)}[/tex]

Simplifying the like terms in the numerator we get

[tex]=\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex]

Therefore , the expression that equals [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex]  is [tex]\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex].

The correct option is (c).

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The range of the average width of the index finger which is between 1.6 centimeters and 2 centimeters gives;

1. The symbols to use for the inequality are ≤ and ≥

2. The average width expressed as an inequality is; 1.6 ≤ w ≤ 2

3. The inequality for the average width in inches is 0.624 ≤ w ≤ 0.78

1. With regards to working with number ranges or intervals, the term inclusive means that the endpoints of the (closed) interval are included in the range.

The inequality symbol to be used in an inclusive interval are ≤ and ≥ (the symbols < and > are used for an exclusive measurements)

2. The minimum width = 1.6 centimeters

Maximum width = 2 centimeters

The average width in centimeters, w, written as an inequality is therefore;

3. The given conversion factor is 1 cm. = 0.39 inches.

Therefore;

1.6 cm = 1.6 × 0.39 in. = 0.624 in.

2 cm = 2 × 0.39 in. = 0.78 in.

The inequality for the average width in inches is therefore;

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The equation of line is ax + by + c = 0.

A line's equation has the conventional form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.

With the aid of the line's slope and a point on the line, the equation of a line may be created. For a better understanding of how a line's equation is created, let's learn more about the line's slope and the necessary point on the line. The slope of a line is the angle that the line makes with the positive x-axis and can be stated as a numerical integer, fraction, or as the tangent of that angle. The term "point" refers to a coordinate system point with the x and y coordinates.

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Answer:

-11

Step-by-step explanation:

step 1

Move the variable to the left-hand side and change its sign

8x-10x=22

step 2

collect like terms

-2x=22

step 3

Divide both sides of the equation by -2

x=-11

Based on the investment portfolio given, the weighted average ROR of the investments would be 2.1%

First, find the total portfolio value:

= 2,600 + 3,700 + 575 + 1,225

= $8,100

The weighted average Rate of Return (ROR) on the investments is:

= (2,600 / 8,100 x 1.7%) + (3,700 / 8,100 x 3.2%) + (575 / 8,100 x 12.9%) + (1,225 / 8,100 x -5.6%)

= 2.076

= 2.1%

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Answer:

2.1%

Step-by-step explanation:

I got it right.

The ​decreases SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.

It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.

It is given that:

Sample Data

M1 = 10 M2 = 15

SS1 = 90 SS2 = 70​

As we know,

The F ratio:

F = S²(x)/S²(y)

From the data given we can say:

Reduce SSwithin and boost the F-magnitude. ratio's

Thus, the ​decrease SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.

The question is incomplete.

The complete question is attached in the picture.

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$34.52 is the function for the given number of minutes.

What is a formula for linear equations?

The function is

long- distance cell phone calling fee = Monthly service fee + Rate*Minutes used

long- distance cell phone calling fee = $4.52 + $0.12*250 = $34.52

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The right triangle B and c altitude length are same that is 6.

Given that,

In the given picture there are 2 right triangles.

They are B and C.

2 sides of the triangle B is 3 and [tex]3\sqrt{3}[/tex].

2 sides of the triangle C is 6 and [tex]6\sqrt{2}[/tex].

The angle for both the right triangle B and C is 90°.

We have to find the length of the altitude of right triangles B and C.

By using the Pythagorean theorem we can find the length of the altitude of the right triangle B and C.

The simplest way is to use the Pythagorean theorem if you are aware of two additional right triangle sides:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Where the sides of the right triangle are a, b, and c.

First, We will find for the right triangle B.

Here, a=[tex]3\sqrt{3}[/tex] and b=3

Now, substitute in the formulae

[tex](3\sqrt{3})^{2} +3^{2}=c^{2}[/tex]

[tex]27+9=c^{2}[/tex]

[tex]36=c^{2} \\[/tex]

[tex]c^{2} =36\\[/tex]

Taking square root on both sides

[tex]\sqrt{c^{2} } =\sqrt{36}[/tex]

[tex]c=6[/tex]

Therefore, the length of the altitude of right triangle B is 6.

Now, We will find for the right triangle C.

Here, b=6 and c=[tex]6\sqrt{2}[/tex]

Now, substitute in the formulae

[tex]a^{2} +6^{2}=(6\sqrt{2}) ^{2}[/tex]

[tex]a^{2} +36=72[/tex]

[tex]a^{2}=72-36 \\[/tex]

[tex]a^{2} =36\\[/tex]

Taking square root on both sides

[tex]\sqrt{a^{2} } =\sqrt{36}[/tex]

[tex]a=6[/tex]

Therefore, the length of the altitude of right triangle B is 6.

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Answer: the circle is not a function

the square is a function

Step-by-step explanation:

Independent events are the ones whose occurrence is unrelated to any other event.

Dependent events include those that are dependent on previous events.

If the probability of an event A occurring is not impacted by the occurring of some other event B, then A & B are referred to as independent events.

Consider the example of a die roll. If A is the event 'the number appearing is odd' and B is the event 'the number showing up is a multiple of 3,'

P(A) = 3/6 = 1/2

P(B) = 2/6 = 1/3

A and B are also the events 'the number showing up is odd & a multiple of 3', implying that;

P(A ∩ B) = 1/6

P(A│B) = P(A ∩ B)/ P(B) = 1/2

Then P(A) = P(AB) = 1/2, implying that the happening of event B has had no effect on the probability of occurring of event A.

Dependent events include those that are dependent on previous events. The outcomes of previous events have an impact on these events. Dependent events are two or maybe more events that are dependent on one another.

When two events, A and B, are interdependent, the probability of their occurrence is:

P(A and B) = P(A) · P(B|A)

Assume we desire to have a queen.

The chances of obtaining a queen on the first draw are 4 from out 52 cards. If we receive a queen in the first draw, we have a 3 out of 51 chance of obtaining a queen in the second draw.

As a result, these are referred to as dependent events because the probability of a second event is determined by the results of the first draw.

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Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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Answer:

See below

Step-by-step explanation:

Rotating CLOCK wise would result in -4,3 becoming  3,4 in the first quadrant

The measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ =  6.7 and the triangle XYZ must be an acute triangle

In this questions we have been given the the coordinates of the triangle XYZ.

X(-5, 9), Y(2, 1), Z(-8, 3)

We need to find  the measures of the sides of ΔXYZ .

We find the the measures of the sides using distance formula.

XY = √[(1 - 9)² + (2 + 5)²]

XY = √[-8² + 7²]

XY = √(64 + 49)

XY = √(113)

XY = 10.6

Now side YZ

YZ = √[(3 - 1)² + (-8 - 2)²]

YZ = √[(2)² + (-10)²]

YZ = √4 + 100

YZ = √104

YZ = 11.2

And the length of side XZ would be,

XZ = √[(3 - 9)² + (-8 + 5)²]

XZ = √(-6² + -3²)

XZ = √(36 + 9)

XZ = √45

XZ = 6.7

We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.

the sum of the squares of the two smaller sides is,

= 6.7² + 10.6²

= 44.89 + 115.54

= 160.43

= 12.67²

And 11.2² = 125.44

Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.

Therefore, the measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ =  6.7 and the triangle XYZ must be an acute triangle

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Answer:

Step-by-step explanation:

first you need to make the 3/8 and 6/7 into 21/56 and 48/56 then you take the -4 and 8 then add then together you get 4 then you still have the 21/56 and 48/56 which you need to add so 48 + 21 = 69/56 or 1 and 13/56 you then add the 1 to the 4 which gives you 5 then add the 13/56 to it which gives you your answer of 5 and 13/56

Answer:120 plus 80 plus 17 equals 217

Step-by-step explanation:

Answer:

Step-by-step explanation:

217

Answer:

what is the value of x? Ans. varies

Step-by-step explanation:

The maximum possible length of ribbon left on the roll is 24.5 m.

Find bounds, Roll

30 → nearest half metre.

0.5 ÷ 2 = 0.25

LB = 30 – 0.25 = 29.75

GB = 30 + 0.25  = 30.25

Piece

5.8 →  nearest 10cm or 0.1m

(10÷100=0.1)

0.1÷2 = 0.05

LB = 5.8 – 0.05 = 5.75

GB = 5.8 + 0.05 = 5.85

Max length left = GB roll – LB piece

=30.25 – 5.75

=24.5m

The metric system's default unit of measurement for length. 100 centimeters equal to 1 metre. A meter is a common metric unit that is around 3 feet, 3 inches long. It measures 100 times more than a Centimetre, or 0.01 meters, in size. 1000 meters make up one kilometre.

Hence, the maximum possible length of ribbon left on the roll is 24.5 m.

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The pieces of cake that Jeff will eat in 1 hour is 3

The pieces of cake that Gene will eat in 1 hour is 4

The pieces of cake that Mike will eat in 1 hour is 5

It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake

In order to determine the pieces of cake that Jeff can eat in 1 hour, divide 6 by 2.

6/2 = 3 pieces of cake

In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 2 pieces of cake by 2.

2 x 2 = 4 pieces of cake

In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 4 pieces of cake by 60 minutes and divide the result by 48 minutes.

(4 x 60) / 48 = 5 pieces of cake

It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake, because they all eat less than 8 slices of cake in one hour.

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The number of green and yellow balls is 24 and 36 respectively.

Given that,
Masha bought red, green, and yellow balloons for a party.
red balloons =  40 .
The number of green balloons Masha purchased = 3/5 of the red balloons.
The number of green balloons is again = 2/3 of yellow balloons.

Fraction is described as the number of compositions that comprise the Whole.

Here,
according to the question
Number of red ballons = 40
The number of green balloons Masha bought is 3/5 of the number of red balloons = 40 * 3/5
               = 8* 3
               = 24
The number of green balloons is also 2/3 of the number of yellow balloons.
= 3/2 * 24
= 36

Thus, the number of green and yellow balls is 24 and 36 respectively.

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16 = -4(-3) + 4 is an equation in slope-intercept form for the line passing through points (-4,16) and (3,-5)

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope.

We have been asked to write an equation in slope-intercept form for the line passing through (-4,16) and (3,-5)

First we will find the slope(m)

We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (-4,16) and (3,-5)

⇒ m = [tex]\frac{-5- 16}{3 - (-4)}[/tex]

⇒ m = [tex]\frac{-21}{7}[/tex]

⇒ m = -3

We know that the equation for slope(m) and y - intercept(b) of a line is given by :

y = mx + b

Here lets take equation 16 = -4(-3) + b .Here x and y is substituted with the second two points.

⇒  16 = -4(-3) + b

⇒  16 = 12 + b

⇒  b = 16 - 12

⇒  b = 4

The equation in the slope intercept is as follows:-

16 = -4(-3) + 4

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Answer:

...

Step-by-step explanation:

For every x ∈ R and each δ > 0 the interval (x−δ, x δ) carries both rational and irrational numbers. This implies that x can't be an interior factor of Q, and that x is a boundary point of Q. Therefore the indoors of Q is empty and the boundary of Q is R. Thus Q = b(Q) ∪ Q = R ∪ Q = R.

Answer:

4

Step-by-step explanation:

Hello!

Simplify the expression by combining like terms.

The simplified expression is 4.

The simplified form of the given expression is 4.

To solve the expression 10y + 12 - 7y - 8 - 3y,

We need to combine like terms and simplify.

Simplify the expression by combining the like terms (the terms that have the same variable and the same exponent).

We have 10y, -7y, and -3y,

Which can be combined to give us a total of 0y.

This means that the variable y has been eliminated from the expression.

Combine the constant terms (the terms that don't have a variable or that have a variable raised to the power of 0).

We have 12 and -8, which can be combined to give us 4.

So, the simplified expression is 4.

We can express this mathematically as follows:

10y + 12 - 7y - 8 - 3y = (10y - 7y - 3y) + (12 - 8)

                                 = 0y + 4 = .

In other words, the expression simplifies to the constant term 4.

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The solution of the given equation 1080 = 15³ˣ⁻⁴ is (x = 2.19), round to the nearest hundredth.

A logarithmic term represents a number in logarithmic form. A log term is another name for it.

A quantity can also be the sum of two or even more quantities. As a result, a term can consist of the product of two or more quantities, one of which must be in logarithmic form. For such cases, this same terms are known as log terms.

A quantity can also be defined as the quotient of two quantities. But, if a term includes a quotient of quantities, or at least one of the quantities can also be expressed in log form, this same terms are known as log terms.

Now, consider the given equation given in the question;

1080=15³ˣ⁻⁴

Take log on the both sides;

㏒1080 = ㏒15³ˣ⁻⁴

Using the power rule on the second side of the equation;

㏒1080 = (3x - 4)㏒15

Taking log on one side and other variables on other side.

3x - 4 = ㏒1080/㏒15

Use calculator to find the values of both log.

3x - 4 = 2.57

3x = 6.57

x = 2.19

Therefore, the solution of the given function 1080=15³ˣ⁻⁴ is (x = 2.19), rounded up to nearest hundredth.

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In Δ JLP, m ∠ JMP = 3x - 6, JK = 3y - 2, and LK = 5y - 8 then the value of LK = 7.

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution. It is sometimes referred to as "the middle" value in a data set.

The middle number is discovered by sorting all data points and selecting the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).

Since [tex]$\overline{P K}$[/tex] is a median, JK = KL.

3y - 2 = 5y - 8

simplifying the above equation, we get

3y - 5y - 2 = 5y - 5y - 8

-2y - 2 = -8

Adding 2 on both sides of the equation

-2y - 2 + 2 = -8 + 2

-2y = -6

y = 3

Substitute the value of y in LK, then we get

LK = 5y - 8

= 5(3) - 8

= 15 - 8

LK = 7

Therefore, the value of LK = 7.

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a. The formula solved for t when r is the simple interest per year is t = I/Pr

b. Using the new formula, the value of t in the table is 3 years

From the question, we are to solve the given formula for t

The given formula is

I = Prt

To solve for t, we will divide both sides of the equation by Pr

I/Pr = Prt/Pr

I/Pr = t

∴ t = I/Pr

b.

I = $75

P = $500

r = 5% = 0.05

t = 75/(500×0.05)

t = 75/25

t = 3 years

Hence, the value of t in the table is 3 years

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