Victoria depoited $15,000 into a aving account that earn an annual imple interet rate of 0. 2%. To the nearet tenth of a year, how long will it take for the account to reach $15,500?

Answer:

OP/PQ

Step-by-step explanation:

You need corresponding sides in triangle OPQ.

The ratio equivalent to the given ratio is OP/PQ

Two shapes are said to be similar if their corresponding sides are in the same proportion and the corresponding angles are congruent.

Given are two triangles having two pairs of the corresponding angles equal,

So, according to the definition of the similar figures, we can say that the triangles are similar,

Also,

Their corresponding sides will be in the same proportion.

Therefore,

RS / OP = ST / QP = RT / QO

Hence, the ratio equivalent to the given ratio is OP/PQ

Learn more about similar figures, click;

https://brainly.com/question/20368229

#SPJ2

Answer: read below and learn how to do it so you won’t struggle the rest of highschool college and the real world!

Step-by-step explanation:

you just plug in 2 for p and -1 for q and solve.

(4x2+3x-1)^2

4x2 =8 3x-1 =-3

(8+-3)^2

(5)^2

5x5=25

••therefore your answer is 25

it’s basic algebra. it’s not calculus:)

100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Let P, R and S are three persons with ages 26 years, 27 years and 28 years

We need to find the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

x(11/10)ⁿ=y(11/10)ⁿ⁻¹=3(11/10)ⁿ⁻²

x.121/100=y.11/10=3

x/100=y/110=3/121

Hence,  100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

The new pay amount Helena will earn per month after the pay increase is equal to £3575.25

What is Percentage Increase?

In the question, it is given that Helena earns a monthly pay of £3150.

Now, we have to calculate the monthly pay earned by Helena when she receives a pay increase of 13.5%.

For calculating the new monthly pay amount, first, find 13.5% of the original pay.

[tex]\implies \frac{13.5}{100} \times 3150=425.25[/tex]  -------(1)

Next, adding the original monthly pay with the increased pay calculated in (1), we get the new monthly pay.

[tex]\implies 3150+425.25=3575.25[/tex]

Therefore, the new pay amount Helena will earn after the pay increase is equal to £3575.25

To learn more about the percentage increase from the given link

https://brainly.com/question/11712455

#SPJ1

Answer:

G.

8+4 / 4 = x+9 / x

8x = 36

x=4.5

BC=x+9 =13.5

Answer:

g(x) will be the line y=x, reflected across the y-axis and shifted down 2 units.

Step-by-step explanation:

The -x negates every x-value, which has the effect of reflecting the graph across the y-axis. The -2 moves the graph down 2 units.

In the triangle WYC, the length of the side YC is 4.76 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to a side of a triangle divides the other two sides in the same ratio.

Given, In a ΔMRC and ΔWYC MR = 14, CR=28, WY = 6, and MW = 17.88.

Now, MR = 14 and MW = 17.88.

Therefore, (MW/MR) = 17.88/14 = 1.28.

So, If WY = 6, then WE = (1.28)(6) = 7.66.

Now, In the ΔWYC, WY = 6 and WE = 7.66.

Therefore from the Pythagoras's theorem,

WE² - WY² = YC².

YC² = (7.66)² - 6².

YC² = 22.68.

YC = 4.76.

learn more about triangles here :

https://brainly.com/question/2773823

#SPJ1

if we have a class of 15 students and we want to choose a committee of 5 students, their order and position don't matter, 3003 many different ways are there of creating a 5-person committee among the 15 students.

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

Since order and position doesn't matter in this problem, use the combination formula.

The combination formula is: n! / (n-r)! r!

where n is the total number of items (15 in this case) and r is the number of items being selected at once (5 in this case)

Plugging our numbers into the formula:

= 15! / (15-5)! 5!

= 3003 ways.

So, there are 3003 ways of picking 5 people from a group of 15.

To know more about combination formula refer to:

https://brainly.com/question/28065038

#SPJ4

Answer: To write a linear equation to model the relationship between the height h of the candle and time t, we need to find the slope and y-intercept of the line that represents this relationship.

The slope of the line is given by the rise over the run, or the change in the y-value (the height of the candle) over the change in the x-value (the time). We can calculate the slope by taking the difference in the height of the candle after 5 hours and 3 hours, and dividing it by the difference in the time:

slope = (16.5 - 18) / (5 - 3) = (-1.5) / (2) = -0.75

The y-intercept of the line is the point at which the line crosses the y-axis. This is the height of the candle when the time is 0. We can use the height of the candle after 3 hours as the y-intercept, since this is the height when the time is 3:

y-intercept = 18

We can use these values to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Plugging in the values we found, we get:

h(t) = -0.75t + 18

This is the linear equation that models the relationship between the height h of the candle and time t.

To predict how tall the candle will be after burning for 8 hours, we can plug in t = 8 into the equation:

h(8) = -0.75(8) + 18 = -6 + 18 = 12 inches

This means that the candle will be 12 inches tall after burning for 8 hours.

Therefore, the correct answer is (d) h(t) = 0.75t + 20.25; 14.25 inches.

To write a linear equation to model the relationship between the height of the candle and time, we can use the information given. We know that after 3 hours, the candle is 18 inches tall, and after 5 hours, it is 16.5 inches tall.

We can set up a system of linear equations to represent this information. Let's call the height of the candle h and the time t. Then we can set up the following system:

h = 18 - 3t

h = 16.5 - 5t

To solve this system, we can set the two equations equal to each other and solve for t:

18 - 3t = 16.5 - 5t

1.5 = 2t

t = 0.75

This tells us that the height of the candle decreases by 0.75 inches per hour.

Now we can use this information to predict how tall the candle will be after 8 hours. We can plug in 8 for t in the equation h = 18 - 3t to find the height of the candle:

h = 18 - 3(8)

h = 18 - 24

h = -6 inches

So the candle will be about 6 inches shorter after burning for 8 hours. This means it will be about 10.5 inches tall.

The correct option is c, h(t) = -0.75t + 15.75; 9.75 inches.

This is because we found that the height of the candle decreases by 0.75 inches per hour, which is represented by the coefficient of t in the equation. The y-intercept, 15.75, represents the initial height of the candle, which we found to be 16.5 inches.

Happy to help!

Answer: 17

Step-by-step explanation:

11x - 39 = 10x - 22

11x = 10x + 17

x = 17

Answer:

x=13/3

Step-by-step explanation:

Answer:

5 minutes

Step-by-step explanation:

Given:
It takes five machines five minutes to make five widgets

Let's first determine how much time it takes one machine to make one widget

1 machine will take 5 times as long to make 5 widgets

Therefore for 1 machine to make 1 widget it will take 1/5th of the time

To make 100 widgets, 1 machine will take 5 x 100 minutes or 500 minutes

If we use 100 machines this time will be reduced by 100

Answer: The answer is 97

Step-by-step explanation:

Since Adam is above sea level, the number 73 is positive. The number 24 would be negative since it's below sea level.

73 - ( -24) = 97

To check to make sure it's right we can do this:

-24 + 97 = 73

73 - 97 = -24

[tex]-\dfrac{3}{8} x\leq 24[/tex]

Multiply both sides by [tex]-\dfrac{8}{3}[/tex]:

[tex](-\dfrac{8}{3} )\times(-\dfrac{3}{8} x)\leq (-\dfrac{8}{3} )\times24[/tex]

When multiplying or dividing by negative numbers, the sign will flip.

[tex]\fbox{x}\geq \fbox{-64}[/tex]

Answer:

The equation that represents the line of Paul's grade downfall is:

y = (-20)x + 130

This equation states that for every decrease of 1 in the value of x (representing the number of weeks), the value of y (representing Paul's math average) decreases by 20.

Step-by-step explanation:

To find the equation that represents the line of Paul's grade downfall, we can use the two given points to plot the line on a coordinate plane. The point (2, 90) represents the value that after 2 weeks, Paul's math average is 90, and the point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to 50. We can plot these two points on the coordinate plane as follows:

(2, 90)

(4, 50)

To find the equation of the line that passes through these two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the two points, we get:

m = (50 - 90) / (4 - 2)

= -40 / 2

= -20

To find the y-intercept of the line, we can substitute the coordinates of one of the points and the slope into the slope-intercept form of the equation:

y = mx + b

Substituting the coordinates of the point (2, 90) and the slope of -20, we get:

90 = (-20)(2) + b

= -40 + b

= b - 40

Solving for b, we get:

b = 90 + 40

= 130

The probability that the student answers exactly 1 question correctly is

                            [tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]

What is the binomial coefficient?

In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set.

There are a total of [tex]$3^5=243$[/tex] possible ways that the student can answer the quiz. To count the number of ways that the student can answer exactly 1 question correctly, we can use the binomial coefficient formula:

      [tex]\binom{5}{1}=5[/tex]

This counts the number of ways that the student can choose which 1 question to answer correctly.

For each of these 5 ways, there are 3 ways to choose the incorrect answer for each of the other 4 questions, so the total number of ways that the student can answer exactly 1 question correctly is

[tex]$5\cdot 3^4=135$[/tex].

Therefore, the probability that the student answers exactly 1 question correctly is

              [tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]

To learn more about binomial coefficients, visit:

https://brainly.com/question/14216809

#SPJ1

The Total number of registered doctors will be 246753.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Let the total number of doctors be x.

Since 23.1% of all registered doctors were female. If there were 55,700 female registered doctors that year. This will be:

23.1% × x = 55700

0.231x = 55700

Divide

x = 57000 / 0.231

x =246753

The doctors are =246753.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

The line which is parallel to the given line y=-4/3x+1 is y = -4/3x + 2

What is the equation of the line?

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.

Given that the equation of the line is:

y = -4/3x + 1                                                           ..........(1)

To find the equation of the line is parallel to the given line equation.

We know that the given equation is in the slope-intercept form

y = mx+c, where m is the slope and c, is the intercept.

Compare with given equation(1) we get

m = -4/3  and c=1

Now change the y-intercept c=1 to an intercept of c= 2

Therefore (1) becomes

y = -4/3x + 2

Hence, The equation of line y = -4/3x + 2 is the parallel line to the given equation of the line.

To learn more about the equation of line visit,

https://brainly.com/question/13763238

#SPJ1

Answer: (x+5)(2x+10)

Step-by-step explanation: I see your comment, so try to help you fast, I am in a rush, so can't type all the work on paper yet, sorry!

The Perimeter of the paper 11 feet and the missing data in the table is: 8, 10, 18.6, 28, 2l + 6

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is given that the length of the paper is 2.5 feet, and the breadth of the paper is 3 feet.

Using the perimeter of the rectangle:

Perimeter of the paper = 2(l+w) = 2(5.5) = 11=2(l+w)=2(5.5)=11 feet.

The missing data in the table is: 8, 10, 18.6, 28, 2l + 6

Thus, the Perimeter of the paper 11 feet and the missing data in the table is: 8, 10, 18.6, 28, 2l + 6

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ1

Answer:

y+6=(1)/(3) (x+2)

Step-by-step explanation:

substitute (-2,-6) until equality is found

y+6=(1)/(3) (x+2)

(-6)+6=(1)/(3) ((-2)+2)

0 = 1/3 (-2+2)

0 = 0

confirm it with a graph

Answer: S

Step-by-step explanation:

Answer:

16 years old

Step-by-step explanation:

2x+3=35

  -3.  -3

2x=32

/2. /2

x=16

Leon is 16 years old

Hopes this helps please mark brainliest

Answer:

28

Step-by-step explanation:

Determine which integer in the solution set will make the equation true. t − 42 = −14 {−56, −28, 3, 28}

replace 28 for t:

t − 42 = −14

28 − 42 = −14

−14 = −14

Answer:

  28

Step-by-step explanation:

You want the value of t that satisfies t − 42 = −14.

The solution to this 1-step linear equation is to add the opposite of the unwanted constant (-42).

Adding 42 to both sides of the equation gives ...

  t -42 +42 = -14 +42

  t = 28

The integer that makes the equation true is 28.

We shall therefore obtain a square as a result. Since each square is a rectangle, the same perimeter and smaller area will be produced by using length and breadth of 90 yards.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Here,

original length=110 yards

original width=70 yards

perimeter=2(110+70)

=2*180

=360 yards

x+y=180

y=180-x

area=xy

A=x(180-x)

A=180x-x²

A'=180-2x

A'=0

2x=180

x=90 yards

y=90 yards

We shall so receive a square as a result. Given that each square is a rectangle, a length and width of 90 yards will result in a smaller area and the same perimeter.

To know more about area,

https://brainly.com/question/15489889

#SPJ1

The length of RB of the given triangle is; RB = 54 cm

We are given that in △QRS;

Point A is between points Q and R

Point B is between points R and S

AB∥QS

QA = 23 cm

QR = 41 cm

RS = 123 cm

Let us first find the ratio between RS and QR.

Ratio = RS ÷ QR

Ratio = 123 ÷ 41 = 3

QA × 3

23 × 3 = 69

Thus;

BS = 69

Thus;

RB = RS - BS

RB = 123 - 69

RB= 54 cm

Read more about missing triangle length at; https://brainly.com/question/9348063

#SPJ1

The values of x and y are obtained as 12.99 and 7.5 respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

For the given triangle, the trigonometric ratios are used as follows,

Cos(30°) = x/15

=> √3/2 = x/15

=> x = 15√3/2

=> x = 15 × 0.866

       = 12.99

And,

Sin(30°) = y/15

=> 1/2 = y/15

=> y = 15/2

       = 7.5

Hence, for the given triangle the values of x and y are given as 12.99 and 7.5 respectively.

To know more about trigonometric ratio click on,

https://brainly.com/question/25122825

#SPJ1

Yes the given C and D lines are parallel

How to know two lines are parallel lines?

Any two parallel lines that are crossed by a transversal can be recognized by the following characteristics.

The fundamental characteristics listed below make it simple to recognize parallel lines.

as the sum of the given angle c and d i.e. 48+132 is 180 it clearly shows that it is the Pairs of interior angles on the same side of the transversal which proves that the given lines C and D are parallel  

Learn more about parallel lines from the link below

https://brainly.com/question/16701300

#SPJ1

Answer:

I was going to answer but there is no attachment.

Step-by-step explanation: