A savings account of $5, compounded at an annual interest rate of 7% for 5 years will have how much total in the account?

A sequence of transformations that would map PQ onto RS include the following: A. a 90° clockwise rotation about the origin, then a reflection in the x-axis.

In Mathematics and Geometry, a reflection over the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

For a 90° clockwise rotation about the origin, the new coordinates of P is given by:

(x, y)            →      (y, -x)

P (-6, 10)      →      (10, -(6)) = P' (10, -6)

Next, we would apply a reflection over or across the x-axis;

(x, y)                →      (x, -y)

P' (10, -6)       →      (10, -(-6)) = S (10, 6)

Read more on rotation here: brainly.com/question/28854313

#SPJ1

The missing side in the similar figure below is 42.

We are given a diagrammatic expression of two triangles and we are asked to find the missing side in a similar triangle. To be able to solve this question, we need to understand what are triangles and the possible types of triangles.

A triangle is a plane figure that has three sides and three angles. The major types of triangles include:

The example of the triangle given is a right-angle triangle and can be solved by using the Pythagoras theorem.

The Pythagoras theorem states that the hypotenuse squared is equal to the sum of the opposite squared and the adjacent squared.

hyp² = opp² + adj²

48² = x² + 24²

2304 = x² + 576

x² = 2304 - 576

x² = 1728

x = √1728

x = 41.57

x ≅ 42

Learn  more about triangles here:

https://brainly.com/question/12852445

Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

Read more about angles here:

https://brainly.com/question/25716982

#SPJ1

The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

Answer:

2 hours?

Step-by-step explanation:

I put it in a calc

Answer:

The square of a prime number is prime

Hi!

So, first, let's just form the equation:

We know that all the side lengths equal 12 cm.

So the equation will be:

5 + 3 + x = 12

The answer you put in the box is:

5 + 3 + x

To find the value of x, we just solve this equation:

5 + 3 + x = 12

Combine like terms:

8 + x = 12

Same to both sides:

x = 12 - 8

x = 4

I hope this helped, let me know if you have any questions.

Answer:

13

Step-by-step explanation

I noticed that 9 and 12 were skipped to 15 so I subtracted 15 to 6 and got 9 so I did 4 plus 9 and got 13 so yup hope this helped!!!

Answer:

10

Step-by-step explanation:

You will do cross multiplication 4×15 over 6= 10

The required GCF for the expression is 5y

Since we are not given the expression to get the GCF. Using the function

5x²y + 25y²

From both terms, find the common factor

From both factors, we can see that 5 and y are common to both

GCF = 5 × y

GCF = 5y

Hence the required GCF for the expression is 5y

NB: Same process is application to any other expressions

Learn more here: https://brainly.com/question/219464

Answer:

A) The interval(s) where the function is increasing are: $[-3,-1]$ and $[1,3]$.

B) The interval(s) where the function is decreasing is: $[-1,1]$.

C) The interval(s) where the function is constant is: $[-4,-3]$ and $[3,4]$.

D) The domain of the function is $[-4,4]$.

E) The range of the function is $[-1,3]$.

Step-by-step explanation:

Sure, here is a step-by-step explanation:

The given graph is a piecewise function consisting of three line segments, so we need to analyze the behavior of the function on each segment.

A) To find the interval(s) where the function is increasing, we look for the parts of the graph where the slope of the line is positive. We see that the function is increasing on the intervals $[-3,-1]$ and $[1,3]$. To write this in interval notation with a union, we can write: $[-3,-1] \cup [1,3]$.

B) To find the interval(s) where the function is decreasing, we look for the parts of the graph where the slope of the line is negative. We see that the function is decreasing on the interval $[-1,1]$. So, the interval where the function is decreasing is $[-1,1]$.

C) To find the interval(s) where the function is constant, we look for the parts of the graph where the slope of the line is zero. We see that the function is constant on the intervals $[-4,-3]$ and $[3,4]$. So, the interval where the function is constant is $[-4,-3] \cup [3,4]$.

D) To find the domain of the function, we need to consider all the values of $x$ for which the function is defined. From the graph, we see that the function is defined for all $x$ in the interval $[-4,4]$. So, the domain of the function is $[-4,4]$.

E) To find the range of the function, we need to consider all the values of $y$ that the function can take. From the graph, we see that the smallest value of $y$ is $-1$ and the largest value is $3$. So, the range of the function is $[-1,3]$.

Answer: i don’t know

Step-by-step explanation:

Answer:34

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. A boat is marked up 20% on the original price. The original price was $50. What is the sale price of the boat before sales tax?

$50(1+0.20) = $60

2. Fred buys a video game disk for $4. There was a discount of 20%. What is the sales price?

$4(1-0.2) = $3.20

3. A painting is on sale at 50% off. The sale price is $320. What was the original price?

X*(1-0.5) = $320

X = $320/0.5

X = $640

Answer:

B

Step-by-step explanation:

got it

Answer:

B is correct

Step-by-step explanation:

A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. Which statement is true of the box plot of this data set?

The box will go from 10 to 12.

A line dividing the box will be at 12.

The left whisker will go from 4 to 15.

The right whisker will go from 12 to 20.

Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.

Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.

In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.

The number of pages Li Wei can read in a week = 90

The number of pages Collen can read in a week = 126

Li Wei's reading rate per hour = 30 pages

Collen's reading rate per hour = 24 pages

Let the hours that Li Wei and Colleen can be on the same page= x

The total number of pages Li Wei can read = 90 + 30x

The total number of pages Colleen can read = 126 + 24x

For Li Wei and Colleen to be on the same, the two expressions are equated.

90 + 30x = 126 + 24x

6x =  36

x = 6

Learn more about equivalent expressions at https://brainly.com/question/2972832.

#SPJ1

Answer:

C≈17.91

Step-by-step explanation:

Answer:

17.91

Step-by-step explanation:

Answer:  x = -5

Step-by-step explanation:

x = -5

For a vertical line in a coordinate plane, all points on the line have the same x-coordinate, so we can define the line just by giving the x-coordinate of any point on that line.

I hope this helps.

Answer:

7.616

Step-by-step explanation:

=7.6

The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

Learn more about trigonometric ratios on https://brainly.com/question/23130410

#SPJ1

The difference quotient for the function f(x)=-3x²+6x-6 is -3h+6.

Now, let's move on to finding the difference quotient for the function f(x)=-3x²+6x-6. The difference quotient is a formula used to find the average rate of change of a function between two points.

The formula for the difference quotient is:

f(x+h) - f(x)

So, to find the difference quotient for the function f(x)=-3x²+6x-6, we first need to find f(x+h) and f(x):

f(x+h) = -3(x+h)² + 6(x+h) - 6

= -3(x² + 2xh + h²) + 6x + 6h - 6

= -3x² - 6xh - 3h² + 6x + 6h - 6

f(x) = -3x² + 6x - 6

Now we can plug these values into the difference quotient formula:

f(x+h) - f(x)

= [-3x² - 6xh - 3h² + 6x + 6h - 6] - [-3x² + 6x - 6]

= [-3x² - 6xh - 3h² + 6x + 6h - 6 + 3x² - 6x + 6] / h

= [-3h² + 6h] / h

= -3h + 6

This tells us the average rate of change of the function between x and x+h is -3h+6.

To know more about function here

https://brainly.com/question/28193995

#SPJ1

Answer:

60°

Step-by-step explanation:

In similar triangles, the corresponding angles are congruent.

          ∠O = R

          O = 70°

In ΔOMN,

      ∠O + ∠M + ∠N = 180     {Angle sum property of triangle}

       70 + 50 + Ф    = 180

               120 + Ф  = 180

Subtract 120 from both sides,

                        Ф  = 180 - 120

                         Ф = 60°  

The true statement is if k = - 1 there are solutions, but if k = - 3 there are no solutions

Given: |x+3|-2=k

Below are rules for solving absolute value equations:

1. If p is positive and |y| = p, then

x = p   OR    y = -p

(two equations are set up)

2. If p is negative and |y| = p, then

No solution

3. If p is zero  and |y| = p, then

One solution

Using the rules:

|x+3|-2=k

when k = -1

|x+3|-2= -1    

|x+3| = 1

Rule 1 is applicable here. Thus, there are solutions  

when k = -3

|x+3|-2 = -3

|x+3| = -1

Rule 3 is applicable here. Thus, no solution

Therefore, if k = - 1 there are solutions, but if k = - 3 there are no solutions.     The 2nd option is the true statement

Learn more about absolute value equation on:

brainly.com/question/28728226

#SPJ1

If the sample size 86 is drawn from population having mean 90 and S.D. as 24 , then the probability that mean will be more than 89 is 0.6517  .

In the question ,

it is given that ,

the sample size of the population (n) is = 86 ;

the mean (μ) = 90 , the standard deviation(σ) is = 24 ;

The probability that the mean will be more than 89 is represented as :

P(x > 89) = P((x-μ)/σ√n > (89 - 90)/24√86 )

= P(z > -0.39) ⇒ 1 - P(z ≤ -0.39)

from z table , we write the simplified equation as ;

= 1 - 0.3483

= 0.6517 .

Therefore , the required probability is 0.6517  .

The given question is incomplete , the complete question is

A sample of size 86 will be drawn from a population with mean 90 and standard deviation 24 . Find the probability that mean will be more than 89. Round the answer to at least four decimal places.

Learn more about Probability here

https://brainly.com/question/17285542

#SPJ4

The value of square root of x + y squared + z squared is 30

x = 2, y = 3 and z = -5

\(( \sqrt{x + y} )^{2} + z ^{2} \)

substitute the value of x, y and z

\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)

simplify the square root and square

\( = (2 + 3) + 25\)

\( = 5 + 25\)

\( = 30\)

Ultimately, x + y squared + z squared is 30

Read more on algebra:

https://brainly.com/question/4344214

#SPJ1

The Probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

To find the probability that the randomly chosen coin is gold, given that it is small, we need to determine the number of small gold coins and the total number of small coins.

From the given information, Marco has 12 small gold coins and 3 small silver coins, making a total of 12 + 3 = 15 small coins.

The probability that the coin is gold, given that it is small, can be calculated as the ratio of the number of small gold coins to the total number of small coins:

P(Gold|Small) = Number of Small Gold Coins / Total Number of Small Coins

P(Gold|Small) = 12 / 15

Simplifying the fraction, we have:

P(Gold|Small) = 4 / 5

Therefore, the probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

For more questions on Probability .

https://brainly.com/question/25839839

#SPJ8

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

For similar questions on water bill

https://brainly.com/question/31119915

#SPJ11

Answer:

c = 45 and e = 30

Step-by-step explanation:

Since we know that A = 45, B = 90, we can calculate C knowing that the total angle of a triangle is 180, so you do 180-45-90 = 45

Finding the angle C helps us find F by subtracting 45 from 180, since a straight line is 180 degrees, which is 135.

We know that E = 15, and what was said earlier about how the toal angle is 180 in a triangle, we can subtract 15 and 135 from 180, which is 30.

Hope that answers your question

Answer: D

Step-by-step explanation: y=2 so 2+2=4+1=5

Complete Question

The complete question is shown on the first uploaded image  

Answer:

a

\(P(X < 65) =  0.003467\)

b

\(P(86 <  X <  110 )= 0.63928 \)

c

\(P(X > 120 ) =0.062024\)

Step-by-step explanation:

From the question we are told that

 The  mean is  \(\mu  =  \$ 100\)

 The  standard deviation is  \(\sigma  =  \$ 13\)

 Generally the probability that the  monthly utility bills is less than  $65  is  mathematically represented as

     \(P(X < 65) =  P(\frac{X  -  \mu }{\sigma }  < \frac{65  -  100 }{13 }   )\)

Generally

  \(\frac{X  -  \mu }{\sigma } =  Z (The\ standardized \ value \ of\  X )\)

So

 \(P(X < 65) =  P(Z < -2.70  )\)

From the z-table

    \(P(Z < -2.70  ) =  0.003467\)

So  

   \(P(X < 65) =  0.003467\)

Generally the  probability that a randomly selected utility bill is between $86​ and $​110 is mathematically represented as

 \(P(86 <  X<  110 )=  P( \frac{86 -100}{ 13} <  \frac{X - \mu}{\sigma } < \frac{86 -100}{ 13}    )\)

=>  \(P(86 <  X <  110 )=  P( \frac{86 -100}{ 13} < Z < \frac{110 -100}{ 13} )\)      

=>    \(P(86 <  X <  110 )=  P(-1.08 < Z < 0.77 )\)      

=>    \(P(86 <  X <  110 )= P(Z < 0.77 ) -  P(Z < -1.08 ) \)    

From the z-table

    \(P(Z < 0.77 ) = 0.77935\)

and  

   \(P(Z < -1.08 ) =  0.14007\)

So

     \(P(86 <  X <  110 )= 0.77935  -  0.14007 \)    

=>   \(P(86 <  X <  110 )= 0.63928 \)    

 Generally the probability that the  monthly utility bills is  more than $120  is mathematically represented as

         \(P(X >120 ) =  P(\frac{X  -  \mu }{\sigma }  > \frac{120  -  100 }{13 })\)

=>   \(P(X > 120 ) =  P(Z > 1.538   )\)

From the z-table

    \(P(Z > 1.54  ) =  0.062024\)

So  

   \(P(X > 120 ) =0.062024\)