Sketch the graph of y= (x-3)2 - 25, then select the graph that corresponds
to your sketch.

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

Learn more about simple interest here:

brainly.com/question/30964674

#SPJ11

Answer:

719.24 is the correct answer

Seismic hazard analysis is a method of probability assessment that would most likely be used to assess the probability that a major earthquake will occur in California in the next three years.

Seismic hazard analysis is a method used to assess the probability of earthquakes occurring in a specific location, and it involves analyzing the historical records of earthquakes, geological data, and the tectonic plate movements in the area. This method is used to predict the likelihood of future earthquakes and their potential magnitude and intensity.

In the case of California, a seismic hazard analysis would likely be used to assess the probability of a major earthquake occurring in the next three years. The data collected from this analysis would help the government and the public prepare for potential earthquakes and minimize the damage caused by such events.

Read more on Probability:

https://brainly.com/question/251701

#SPJ4

Answer:

B,C,E (last one)

Step-by-step explanation:

To factor x² + 4x + 9 over the set of complex numbers, follow the steps below:

Step 1: Find the discriminant of the quadratic equation. The discriminant (D) is the part under the square root sign in the quadratic formula. D = b² - 4ac, where a, b, and c are the coefficients of x², x, and the constant term respectively. In this case, a = 1, b = 4, and c = 9. So, D = 4² - 4(1)(9) = 16 - 36 = -20. Since the discriminant is negative, the quadratic expression has two complex roots.

Step 2: Use the quadratic formula to find the roots. The quadratic formula is given by: x = (-b ± \(\sqrt{D}\))/2a Plugging in the values of a, b, c, and D in the formula, we get: x = (-4 ± \(\sqrt{-20}\))/2(1) = (-4 ± 2i*\(\sqrt{5}\))/2 = -2 ± i*\(\sqrt{5}\). So, the two roots of the quadratic equation are -2 + i * \(\sqrt{5}\) and -2 - i * \(\sqrt{5}\).

Step 3: Write the quadratic equation in factored form using the roots. x² + 4x + 9 = (x - (-2 + i * \(\sqrt{5}\)))(x - (-2 - i * \(\sqrt{5}\)))= (x + 2 - i * \(\sqrt{5}\))(x + 2 + i * \(\sqrt{5}\)). Therefore, the quadratic expression x² + 4x + 9 can be factored over the set of complex numbers as (x + 2 - i * \(\sqrt{5}\))(x + 2 + i * \(\sqrt{5}\)).

For more questions on: factor

https://brainly.com/question/25829061

#SPJ8

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

Learn more about  balance from

https://brainly.com/question/28767731

#SPJ11

The quadratic function that best fit the given data is y = 2x² - 5/2x - 8.

In algebra, quadratic function is defined as a function in the second degree or power. It can be expressed as y = f(x) = ax² + b x + c, where a, b, and c are constants.

Using only three points from the given data, we can determine the quadratic equation that fits the data.

Let P1 = (-2 , 5)

P2 = (0 , -8)

P3 = (2 , -5)

Substitute the points in the expression f(x) = y = ax² + b x + c.

5 = a(-2)² + b(-2) + c     ⇒     5 = 4a - 2b + c     (equation 1)

-8 = a(0)² + b(0) + c     ⇒     -8 = c     (equation 2)

-5 = a(2)² + b(2) + c     ⇒     -5 = 4a + 2b + c     (equation 3)

Substitute equation 2 in equation 1 and 3.

5 = 4a - 2b + -8     ⇒     13 = 4a - 2b     (equation 4)

-5 = 4a + 2b + -8     ⇒     3 = 4a + 2b     (equation 5)

13 = 4a - 2b     (equation 4)

-(3 = 4a + 2b)    (equation 5)

10 =       -4b

b = -5/2

Substitute the value of b in equation 4.

13 = 4a - 2(-5/2)

4a = 13 - 5

a = 2

If a = 2, b = -5/2 and c = -8, then the quadratic equation should be y = 2x² - 5/2x - 8.

Learn more about quadratic function here: https://brainly.com/question/1497716

#SPJ4

Hey there!

The correct answer is 2x²3y³

Hope it helps and have an amazing day!

The final expression of 2 x X x X x 3 x y x y x y is 2x²y³.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The expression: 2 x X x X x 3 x y x y x y

There are two X and three y.

Now,

X x X = X²

y x y x y = y³

Now,

2 x X x X x 3 x y x y x y

= 2x²y³

Thus,

The expression is 2x²y³.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

Step-by-step explanation:

You cannot subtract JUST a denominator. The subtraction sign is lower down because of the odd printing just like the equal signs.

1. The first thing you have to do is change this from a mixed fraction into an improper fraction in order to subtract. This becomes:

2. This one requires you to multiply your denominator so that it is the same for both fractions. The least common denominator (LCD) for these fractions is 12

3. This is fairly straight-forward the denominators already match so just subtract the numerators

4. Because we have a full number we must make it into a fraction in order to subtract it and also turn the mixed fraction into an improper fraction

5. This problem requires multiple steps the first would be to make improper fractions then get a LCD and then of course subtract.

6. For this we will use another LCD.

The vertex of this quadratic function x² - x - 12 = 0 is (0.5, -12.25).

The axis of symmetry of this quadratic function x² - x - 12 = 0 is 0.5.

In this exercise, you are required to determine the vertex and axis of symmetry of the given quadratic function that is written in standard form.

In Mathematics, the vertex form of a quadratic equation is represented by the following mathematical equation:

y = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can logically deduce the following mathematical equation and parameters from its graph:

x² - x - 12 = 0

Vertex = (0.5, -12.25).

Axis of symmetry = 0.5

Read more on vertex here: brainly.com/question/14946018

#SPJ1

Answer:

3 meters

Step-by-step explanation:

Number of shelves = 4

Length of each shelf = 0.55 meter long

Total length of 4 shelves = 4 × 0.55 meters

= 2.2 meters

Since he can only buy the shelving in whole meter lengths.

Pedro will need to buy 3 meters of shelving

He couldn't buy 2 meters because of the remaining .2 meters from 2.2 meters, therefore, the nearest whole meter length to 2 meters is 3 meters

The length c in the triangle using law of sine is 6.3

From the question, we have the following parameters that can be used in our computation:

The triangle

The length C in the triangle can be calculated using the following law of sine equation

a/sin(A) = b/sin(B)

In this case, we have

a = 15

A = 125

b = c

B = 20

Substitute the known values in the above equation, so, we have the following representation

c/sin(20) = 15/sin(125)

Evaluate

c = sin(20) * 15/sin(125)

So, we have

c = 6.3

Hence, the value of c is 6.3

Read more abiut law of cosine at

https://brainly.com/question/4372174

#SPJ1

The speed that Morris is travelling is 0.3 ft/s

Speed is the ratio of distance covered with respect to time.

Given the following parameters

Speed of Annesha = 50mi/hr

Speed of Moris = 3ft/s less than Aneesha

Convert 50mi/hr to ft/hr

50mi/hr = 73.3ft/s

Speed of Morris = 73.3 - 3

Speed of Morris =70.3 ft/s

Hence the speed that Morris is travelling is 0.3 ft/s

Learn more on speed here; https://brainly.com/question/14101278

#SPJ1

Answer: c. OSRN

Step-by-step explanation:

Sides of similar shapes are proportional.

For Rectangle LOSP,

Length = LO = 4+6+8 = 18 units

Width = OS= 12 units

Here, \(\dfrac{18}{12}=\dfrac{3}{2}\)  [proportionality constant]

a. For Rectangle LMQP,

Length = MQ = 12 units

Width = LM = 4 units

Here, \(\dfrac{12}{4}=3\neq\dfrac32\)

LMQP is not similar to LOSP.

b. Similarly, for LNRP,

Width = LN= 4+6 = 10

length = NR = 12

\(\dfrac{12}{10}\neq\dfrac32\)

LNRP is not similar to LOSP.

c. For OSRN,

Length = OS = 12

Width = ON = 8

\(\dfrac{12}{8}=\dfrac32\)

OSRN is similar to LOSP.

d. For MNRQ,

Length= NR = 12

Width = MN = 6

\(\dfrac{12}{6}=2\neq\dfrac32\)

MNRQ  is not similar to LOSP.

Hence, the shape similar to rectangle LOSP is OSRN.

A nonzero complex number has exactly n distinct nth roots.

The number 81 has four fourth roots, which are:

3

-3i

-3

3i

These roots lie on a circle of radius √3 in the complex plane.

To understand the first part of the question, we need to know what an nth root of a complex number is. An nth root of a complex number z is a complex number w that, when raised to the nth power, equals z. In other words, if we write z in polar form as z = r(cosθ + i sinθ), then its nth roots are given by:

w_k = r^(1/n)(cos((θ+2kπ)/n) + i sin((θ+2kπ)/n)), where k = 0, 1, 2, ..., n-1.

Note that there are exactly n distinct nth roots of a nonzero complex number.

For the second part of the question, we want to find the fourth roots of 81. To do this, we need to write 81 in polar form. We have:

81 = 81(cos0 + i sin0) = 81(1 + 0i).

So, the magnitude of 81 is 81 and its argument is 0. Thus, the fourth roots of 81 are given by:

w_0 = 81^(1/4)(cos(0/4) + i sin(0/4)) = 3

w_1 = 81^(1/4)(cos(2π/4) + i sin(2π/4)) = -3i

w_2 = 81^(1/4)(cos(4π/4) + i sin(4π/4)) = -3

w_3 = 81^(1/4)(cos(6π/4) + i sin(6π/4)) = 3i

So, there are four fourth roots of 81: 3, -3i, -3, and 3i. Note that these are distinct complex numbers.

Finally, we want to know on what circle in the complex plane these fourth roots lie. We can represent each fourth root as w = r(cosθ + i sinθ) and solve for r. For example, if we take w = 3, we have:

3 = r(cosθ + i sinθ).

Squaring both sides and using the fact that cos^2θ + sin^2θ = 1, we get:

r^2 = 3^2 = 9.

So, r = √9 = 3. This means that all the fourth roots of 81 lie on a circle of radius 3 in the complex plane. In fact, these roots are equally spaced around the circle, since their arguments differ by 2π/4 = π/2.

To learn more about nonzero complex number visit:https://brainly.com/question/27215569

#SPJ11

1. Markway can borrow $667,500 if each bond is sold at a premium of $30.

2. Markway can borrow $621,000 if each bond is sold at a discount of $10.

3. Markway can borrow $656,250 if each bond is sold at 92% of par.

4. Markway can borrow $773,250 if each bond is sold at 103% of par.

1. When each bond is sold at a premium of $30, the total premium amount is $30 x 750 = $22,500. The face amount of each bond is $900, so the borrowing amount would be $900 x 750 + $22,500 = $667,500.

2. When each bond is sold at a discount of $10, the total discount amount is $10 x 750 = $7,500. The face amount of each bond is $900, so the borrowing amount would be $900 x 750 - $7,500 = $621,000.

3. When each bond is sold at 92% of par, the selling price per bond is 92% x $900 = $828. The borrowing amount would be $828 x 750 = $656,250.

4. When each bond is sold at 103% of par, the selling price per bond is 103% x $900 = $927. The borrowing amount would be $927 x 750 = $773,250.

In each scenario, the borrowing amount is determined by multiplying the selling price per bond by the number of bonds. The presence of a premium or discount affects the borrowing amount accordingly.

Learn more about selling price here:

https://brainly.com/question/13797424

#SPJ11

Answer:

Step-by-step explanation:

The angles 107° and x are supplementary angles, therefore sum to 180°:

Answer:

A. No

B. Yes

C. No

D. Yes

E. Yes

Step-by-step explanation:

3(x + 2) = 3x + 6

A. 3x + 2 is not 3x + 6

B. 3(2 + x) = 6 + 3x is equal to 3x + 6

C. 3x + 2x is not the same as 3x + 6

D. x + 2x + 2 + 4 = 3x + 6 is equal to 3x + 6

E. x + x + x + 1 + 1 + 1 + 1 + 1 + 1 = 3x + 6 is the same as 3x + 6

Answer:

(5, 20)

Step-by-step explanation:

(5, 20) is the only ordered pair which falls on the line

Answer:

Step-by-step explanation:

Total no. of children = 366

let the number of boys be x

and the no. of girls be x + 28

According to the question,

x + x + 28 = 366

2x + 28 = 366

2x = 366 - 28

2x = 338

x = 338 / 2

x = 169

So the no. of boys = x = 169

and the no. of girls = x + 28 = 169 + 28 = 197

( you can also recheck it by adding the no. of boys and the no. of girls

that is, 169 + 197 = 366 which equal to the total no. of children )

Hope this helps

plz mark as brainliest!!!!!!

Answer:

The answer is $312.00.

Step-by-step explanation:

First you need to find the amount for the groceries and utilities.

The groceries would be $780.00 and the utilities would be $468.00.

Next you have to add them together which would be $1248.00.

Then you have to find the amount for savings.

The Savings would be $936.00.

Lastly you have to subtract $936.00 from $1248.00.

Your final answer will be $312.00.

The given differential equation, y'' - 2y' + y = x^2e^(-x), is a second-order linear homogeneous differential equation with variable coefficients.

In the differential equation, the term y'' represents the second derivative of y with respect to x, y' represents the first derivative of y with respect to x, y represents the function y(x), and x^2e^(-x) is a non-homogeneous term on the right-hand side of the equation.

To classify the differential equation, we can examine the coefficients of the derivatives. Since the coefficient of y'' is 1 (non-zero), and the coefficients of y' and y are -2 and 1 (non-zero), respectively, the equation is a non-constant coefficient homogeneous differential equation.

In summary, the given differential equation, y'' - 2y' + y = x^2e^(-x), is a second-order linear non-constant coefficient homogeneous differential equation with a non-homogeneous term on the right-hand side.


To learn more about differential equation click here: brainly.com/question/32538700

#SPJ11

Answer:

2)  $40 per shirt

3)  80/9 m = 8.9 m (nearest tenth)

Step-by-step explanation:

The first question has been answered here: https://brainly.com/question/27846862

------------------------------------------------------------------------------------------------------

Question 2

Given information:

Let \(x\) = number of $1 increases

Let \(y\) = total revenue (in dollars)

From the given information:

Therefore, we can create a quadratic equation with the given information:

\(\implies y = (20+x)(300-5x)\)

As we need to find the maximum amount of revenue, we need to find the vertex of \(y\).  As the equation is already factored, the quickest way to do this is to the find the mid-point of the zeros (since a quadratic curve is symmetrical).

\(\begin{aligned}y & =0\\\implies (20+x)(300-5x) & =0\\\implies (20+x) & =0 \implies x=-20\\\implies (300-5x) & = 0 \implies x=60\end{aligned}\)

\(\textsf{Midpoint}=\dfrac{-20+60}{2}=20\)

Therefore, Sammy should have 20 $1 increases to maximize the revenue, so the new price will be:

\(\implies \$20 + 20 \times \$1 = \$40\: \sf per\:shirt\)

------------------------------------------------------------------------------------------------------

Question 3

Given information:

As the bridge is modeled as a parabola, and we have been given the width and height, we can create a quadratic equation using the vertex form.

Vertex form:  \(y=a(x-h)^2+k\)

where:

Middle of the bridge = 30 m ÷ 2 = 15 m

Max height of the bridge = 10 m

Therefore, the vertex of the parabola is (15, 10)

\(\implies y=a(x-15)^2+10\)

We know that when \(x = 0, y = 0\).  Therefore, substitute these values into the equation and solve for a:

\(\implies 0=a(0-15)^2+10\)

\(\implies 0=225a+10\)

\(\implies 225a=-10\)

\(\implies a=-\dfrac{10}{225}\)

\(\implies a=-\dfrac{2}{45}\)

Therefore, the equation of the parabola is:

\(\implies y=-\dfrac{2}{45}(x-15)^2+10 \quad \quad \textsf{for }0\leq x\leq 30\)

The horizontal distance at 5 m right of the middle is:

\(\implies \dfrac{30}{2}+5=20\:\sf m\)

Therefore, to find the height at this point, input \(x=20\) into the equation and solve for y:

\(\implies -\dfrac{2}{45}(20-15)^2+10=\dfrac{80}{9}\:\sf m\)

Therefore, the height of the bridge at 5 m to the right of the middle is:

\(\dfrac{80}{9}\:=8.9\: \sf m\:(nearest\:tenth)\)

Answer:

It's answer is....abkt

Step-by-step explanation:

It's simple add all and there will be your answer

The probability that the mixture will test positive is approximately 0.4744 or 47.44%

In this blood testing procedure, the mixture will test positive if at least one of the individual samples tests positive. To determine the probability of the mixture testing positive, we can first find the probability that all individual samples test negative and then subtract that from 1.

The probability that an individual sample tests negative is 1 - 0.12 = 0.88, since there is a 0.12 chance that it tests positive. As there are 5 samples, and we assume they are independent, we can multiply the probabilities together to find the probability that all samples test negative: 0.88^5 ≈ 0.5256.

Now, to find the probability that the mixture tests positive (meaning at least one individual sample is positive), we can subtract the probability of all samples being negative from 1: 1 - 0.5256 ≈ 0.4744.

To learn more about probability click here

brainly.com/question/30034780

#SPJ11

When a trapezoid is rotated 180° on the coordinate plane, the angles of the trapezoid remain the same, but their orientation is reversed. The correct answer is A. 20.

When a shape is rotated 180° on the coordinate plane, the angles of the shape remain the same, but their orientation is reversed.

In this case, angle B is 20° in the original trapezoid. After a 180° rotation, angle B' will be the same as angle B, but in the opposite direction. Therefore, angle B' will also be 20°.

Hence, the correct answer is A. 20°.

Learn more about ”trapezoid ” here:

brainly.com/question/31380175

#SPJ11

Answer:

6:12

Step-by-step explanation:

Add 1+2=3

18/3=6

6x1=6

6x2=12

Out it back in the ratio

6:12

The median high temperature for the last seven days in Stockton, CA is 94°F.

In statistics, the median is a measure οf central tendency that represents the middle value οf a set οf data. It is the value that separates the data set intο twο equal halves, with half οf the data pοints lying belοw the median and the οther half lying abοve it.

Tο find the high temperatures fοr each οf the last seven days in Stοcktοn, CA, yοu can use a search engine οr weather website such as AccuWeather, Weather.cοm, οr The Weather Channel. Here are the high temperatures fοr the last seven days in Stοcktοn, CA as οf my knοwledge cutοff οf September 2021:

Day 1: 92°F

Day 2: 94°F

Day 3: 97°F

Day 4: 96°F

Day 5: 93°F

Day 6: 90°F

Day 7: 87°F

To find the median high temperature, you can first arrange the temperatures in order from lowest to highest:

87°F, 90°F, 92°F, 93°F, 94°F, 96°F, 97°F

Since there are an odd number of temperatures, the median is simply the middle temperature, which is 94°F.

Therefore, the median high temperature for the last seven days in Stockton, CA is 94°F.

To learn more about Median from given link.

https://brainly.com/question/28060453

#SPJ1

Answer:

Step-by-step explanation:

Let's solve your inequality step-by-step.

8x−7≤−6−(1−8x)

Step 1: Simplify both sides of the inequality.

8x−7≤8x−7

Step 2: Subtract 8x from both sides.

8x−7−8x≤8x−7−8x

−7≤−7

Step 3: Add 7 to both sides.

−7+7≤−7+7

0≤0

Answer:

All real numbers are solutions.

Answer:

All real numbers are answers

Step-by-step explanation:

PLZ mark brainliest!