Determine the present value of quarterly payments of $450 for 6 years at 7.5% annual interest, compounded quarterly. PV= R[(1+i)^-n]/i

Answers

Answer 1

Using it's formula, the present value of the amount is: $288.

What is the present value formula?

The present value formula is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

In which the parameters are:

R is the future value.r is the interest rate.n is the number of periods.

Considering quarterly compounding, the parameters for this problem are as follows:

R = 450, r = 0.075/4 = 0.01875, n = 6 x 4 = 24.

Hence the present value is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

[tex]PV = \frac{450}{(1.01875)^{24}}[/tex]

PV = $288

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Related Questions

honestly don’t know this ?

Answers

1 ) 6

2) 6

3) -2

4) 2

5) -2

6) 2

Solve 5x=125 using the one-to-one property of exponents.

A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5


Anyone is here ​

Answers

Answer:

Step-by-step explanation:

hello :

A) X=In(125)

If the length of one leg in this triangle is .find the length of the hypotenuse.

Answers

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

How to find the length of the hypotenuse

In the image attached we have a right triangle with two legs of same length. The hypotenuse of right triangles can be found by Pythagorean theorem, whose form is:

[tex]r = \sqrt{l^{2}+l^{2}}[/tex]

[tex]r = \sqrt{2}\cdot l[/tex], where l is the length of the legs.

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

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Find the hourly rate of pay for each of the following jobs: a) Tamara owns a salon and earns R1050 for 6 hours and 15 minutes of work. ​

Answers

Answer:

  ₹168 per hour

Step-by-step explanation:

The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.

Hours

We know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...

  (15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h

Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.

Hourly rate

The pay per hour is found by dividing pay by hours.

  ₹1050/(6.25 h) = ₹168/h

Tamara's hourly rate of pay is ₹168 per hour.

Can anyone solve question 2 and 10 with step by step explaination??

Answers

Answer:

Question 2: 4 1/2

Question 10: $7.24

Step-by-step explanation:

Question 2:

1 1/2/x = 3/9

x: total pages read3: minutes first spent9: minutes spent total1 1/2: pages read in 3 minutes

to solve for x, we need to use 1 1/2/x and multiply it by x:

1 1/2/x * x

then we need to have 3/9 multiplied by x:

3/9 * x

this is equal to 1 1/2 = 3/9 * x

now you need to multiply both sides by the opposite of 3/9 = 9/3

3/2 * 9/3 = 3/9 * 9/3 * x which equals 9/2 = 4 1/2

final answer: 4 1/2

Question 10:

Jeff bought 3 boxes of cereal $2.99 each which comes up to $8.97,

he bought one gallon of milk for $4.98,

and 4 bananas for $0.50 each which in total is $2.00.

total amount spent: 8.97 + 4.98 + 2.00 = $15.95

We know there is a 20% off discount so what we have to do is take 20% off $15.95!

20%= $3.19

15.95 - 3.19 = 12.76

The total is now $12.76. But, Jeff payed with a $20.00 bill. Because of this, he will get $7.24 back. 12.76 + 7.24 = 20

Final answer: $7.24

If the coordinates of two points are A (-3,5) and B (-9, -6), then find the value of (abscissa of A) + (ordinate of B)​

Answers

Answer:

abscissa of A = -3

ordinate of B = -6

A+B = -3+(-6)= -3-6=

-9

The triangles are similar. Find the value of the variable.

Answers

Answer:

y = 27

Step-by-step explanation:

The given are two similar triangles.

We can use the following equation to find the variables:

[tex]\frac{y-3}{32} = \frac{18}{24}[/tex]

Cross multiply fractions

32*18 = 24(y-3)

576 = 24y - 72

add 72 to both sides

648 = 24y

divide both sides by 24

27 = y

Emily can read 30 pages in 45 minutes. At this rate, how many pages
will she read in 3 hours?

Answers

She can read 120 pages
60x3=180(Number of minutes in 3 hours)
180/45=4
4x30=120

A statistical process control monitoring system samples the inside diameter of ball bearing every hour. Measurements were taken every hour for 25 hours. The target thickness, T, is the average.

Answers

The standard deviation is approximately 0.01307. See the explanation below.

What is standard deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.

How do we calculate the standard deviation?

Step 1: First, lets calculate the variance.

The formula for variance is:

[tex]\sigma^2 = \frac{\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]

To get the variance ( s2 ) we must first get the mean. Our mean is 0.99892.

We subtract each value by the mean and square the difference.

(0.978-0.99892)² = 0.0004376464

(0.982-0.99892)² = 0.0002862864

(0.983-0.99892)² = 0.0002534464

(0.984-0.99892)² = 0.0002226064

(0.987-0.99892)² = 0.0001420864

(0.988-0.99892)² = 0.0001192464

(0.989-0.99892)² = 9.84064e-05

(0.99-0.99892)² = 7.95664e-05

(0.992-0.99892)² = 4.78864e-05

(0.992-0.99892)² = 4.78864e-05

(0.993-0.99892)² = 3.50464e-05

(0.994-0.99892)² = 2.42064e-05

(0.996-0.99892)² = 8.5264e-06

(0.997-0.99892)² = 3.6864e-06

(1-0.99892)² = 1.1664e-06

(1.001-0.99892)² = 4.3264e-06

(1.006-0.99892)² = 5.01264e-05

(1.007-0.99892)² = 6.52864e-05

(1.011-0.99892)² = 0.0001459264

(1.015-0.99892)² = 0.0002585664

(1.015-0.99892)² = 0.0002585664

(1.015-0.99892)² = 0.0002585664

(1.018-0.99892)² = 0.0003640464

(1.02-0.99892)² = 0.0004443664

(1.02-0.99892)² = 0.0004443664.

Step 2: Add all these numbers above

0.0004376464+0.0002862864+0.0002534464+0.0002226064+0.0001420864+0.0001192464+9.84064e-05+7.95664e-05+4.78864e-05+4.78864e-05+3.50464e-05+2.42064e-05+8.5264e-06+3.6864e-06+1.1664e-06+4.3264e-06+5.01264e-05+6.52864e-05+0.0001459264+0.0002585664+0.0002585664+0.0002585664+0.0003640464+0.0004443664+0.0004443664

=0.00410184

Step 3: Now we divide the sum by how many numbers there are. In this case we have 25.

We'll call this number n.

So n=25

For a sample (use 0.00410184 divided by (n-1) ):

So s2 =0.00410184 divided by 24

s2 = 0.00017091

Step 4 - Solve for Standard deviation:

The standard deviation is the square root of the variance. Our variance is 0.00017091.

So we only apply a square root on the variance.

= √ 0.00017091

s = 0.0130732551

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Full Question:

A statistical process control monitoring system samples the inside diameter of ball bearing every hour. Measurements were taken every hour for 25 hours. The target thickness, T, is the average.

0.992 1.015 0.988 0.996 1.015 1.000 0.989 0.994 1.018 0.997 1.020 1.007 1.006 0.982 1.001 0.992 1.020 0.993 0.978 0.984 0.990 1.015 0.983 1.011 0.987

What is the population standard deviation, σ?

Solve the logarithmic equation. write the answer in exact, simplified form. log(-c) + log8= log (7c-75)

Answers

The value of c is 5 when we simplify the  logarithmic equation              log(-c) + log8= log (7c-75). This can be obtained using the properties of the logarithm.

What is the value of c ?

Given that,

log(-c) + log8 = log (7c-75)

log (-8c) = log (7c-75)  (∵ log a + log b = log ab)

- 8c = 7c - 75              

(8+7)c = 75

15c = 75

⇒ c = 5

Hence the value of c is 5 when we simplify the  logarithmic equation              log(-c) + log8= log (7c-75).

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B(x) = 0. 06x^2 - 0. 2x^3, find the dosage at which the resulting blood presure is maximized

Answers

The dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

In the question,

The function is [tex]B(x) = 0. 06x^2 - 0. 2x^3[/tex]

To find the maximum or minimum, take the derivative and set it equal to zero.

⇒ [tex]B'(x) = 2(0. 06)x - 3(0. 2)x^{2}[/tex]

Setting it equal to zero, we get

⇒ [tex]0.12x - 0.6x^{2}=0[/tex]

⇒ 0.6x (0.2-x) = 0

⇒ x = 0 or x = 0.2

Now substitute x = 0.2 in B(x), we get

⇒ [tex]B(0.2) = 0. 06(0.2)^{2} - 0. 2(0.2)^{3}[/tex]

⇒ B(0.2) = 0.0024 - 0.0016

⇒ B(0.2) = 0.0008

To know B(0.2) is maximum, let us find the values for x = 1 and x = 0.01.

For x = 1,

⇒ [tex]B(1) = 0. 06(1)^{2} - 0. 2(1)^{3}[/tex]

⇒ B(1) = 0.06-0.2

⇒ B(1) = -1.04

For x = 0.01,

⇒ [tex]B(0.01) = 0. 06(0.01)^{2} - 0. 2(0.01)^{3}[/tex]

⇒ B(0.01) = 0.000006 - 0.0000002

⇒ B(0.01) = 0.0000058

Thus, x = 0.2 is the maximum.

Hence we can conclude that the dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

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Can someone help me with these problems and show work

Answers

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}f(x)=−1.25⋅ln( x 1 ​ )f, left parenthesis, x, right parenthesis, equals, minus, 1, point, 25, dot, natural log, left parenthesis, start fraction, 1, divided by, x, end fraction, right parenthesis, where xxx is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)g(x)=−1.8⋅ln( x 2.1 ​ )g, left parenthesis, x, right parenthesis, equals, minus, 1, point, 8, dot, natural log, left parenthesis, start fraction, 2, point, 1, divided by, x, end fraction, right parenthesis. Here are the graphs of

Answers

The amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

How to compare both functions?

The functions are given as:

[tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex]

[tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]

Next, we represent both functions on a graph.

From the attached graph, we can see that both functions intersect at (11.34, 3.04)

This means that the amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

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Complete question

A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by [tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex] where x is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is [tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]. Here are the graphs of

Answer:

It gives the initial amount + It gives the solution

Step-by-step explanation:

It gives the initial amount + It gives the solution

We know from the graph given and the data provided that the function can automatically be proven true.

It cannot describe the amount of time as the data says X is how much of the medicine is given, not the time.

It can't be the equal ratio because, for example, 1 milligram of medicine doesn't equal 1h of time in the body.

All you need to do for this is educational guessing, reasoning, and the process of elimination. Hope this helped! have a great day :7)

A teacher chooses two students in a class of 15 girls and 10 boys. The students are randomly chosen. What is the probability that the teacher chooses two girls?

I keep hearing 3/5 and 7/20 but I don’t know which is right, please help.

Answers

Answer: I would go with 3/5, the person who said 7/20 doesn't have any thank you's or ratings besides themselves while 3/5 has thank you's , and confirmation

Step-by-step explanation:

Simplify equation

(answers in the picture)

Answers

Hello !

[tex](x {}^{a} ) {}^{b} = x {}^{a \times b} [/tex]

[tex](b {}^{5} ) {}^{2} = b {}^{ 5\times 2} = b {}^{10} [/tex]

Answer D

Answer:

D

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](b^5)^{2}[/tex] = [tex]b^{5(2)}[/tex] = [tex]b^{10}[/tex]

After being filled, a basketball loses 3.2% of its air every day. Considering that the initial volume of the ball was 840 cubic centimetres when it was inflated, what will be the volume in cubic centimetres after 4 days? (Round your answer to one decimal place).

Answers

Answer:

volume = 840 cubic cm

(3.2/100)×840= 26.88 per day

after 4 days = 26.88×4=107.5

answer is 107.5

The volume (in cubic centimeters) after 4 days, given that the initial volume of the ball was 840 cubic centimeters, is 732.5 cubic centimeters

How to determine the volume after 4 days?

First, we shall determine the volume lost per day. Details below:

Initial volume = 840 cubic centimeters Percentage loss = 3.2%Volume lost per day = ?

Volume lost per day = 3.2% × Initial volume

= 3.2% × 840

= (3.2 / 100) × 840

= 26.88 cubic centimeters

Now, we shall obtain the volume after 4 days. Details below:

Initial volume = 840 cubic centimeters Volume lost per day = 26.88 cubic centimeters Volume lost in 4 days = 4 × 26.88 = 107.52 cubic centimeters Volume after 4 days =?

Volume after 4 days = Initial volume - Volume lost in 4 days

= 840 - 107.52

= 732.5 cubic centimeters

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The graph shows the amount of money that Janice saves each week from her summer job. Which equation best represents the graph?

Answers

The equation which best represents the graph shows the amount of money that Janice saves each week from her summer job is option A which is  y=200x.

Given a graph showing the amount of money that Janice saves each week from her summer job.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation and cubic equation.

Equation can be formed from any two points present on the graph with the help of following formula:

[tex](y-y_{1})=(y_{2} -y_{1} ) /(x_{2} -x_{1} )*(x-x_{1} )[/tex] where [tex](x_{1} ,y_{1} ),(x_{2} ,y_{2} )[/tex]are the points.

So,we have to find points first which are (6,1200),(7,1400)

Put the values in the formula:

(y-1200)=(1400-1200)/(7-1)*(x-1200)

y-1200=200/1(x-6)

y-1200=200(x-6)

y-1200=200x-1200

y=200x-1200+1200

y=200x

Hence the equation shows the amount of monet that Janice saves each week from her summer job is option A which is y=200x.

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Complete the following proof.
Prove: In an equilateral triangle the three medians are equal.
+a
e-(.*)-(
2a
P=
- (0 + 2ª + )-( ₂² )-(.)
?
2
0+
2-(+)-()
|− a)² + (
R-
C(a. b)
PC
=
(2a, 0)
√3 (with side - 2a)
QA-
- √(₁-2)* ·-(- -)
J(J
9a² 8²
a² (√3)²
B
(Height of equalateral A = b)
X
RB
a²3
√3
(²-²)² + (- - -)*
-J* · ·
()*(3
√√3

Answers

The median of an equilateral triangle are equal has been proved.

How to proof the triangle?

The medians are given as AD, BE, and CF.

Let AB = AC = BC = x unit.

In triangles, BFC and CEB, we've

BF = CE.

ABC = ACB since they're both 60°

BC = BC

By SAS congruence,

BFC = CEB = BE = CF.

Similarly, we've AB = BE

Therefore, AD = BE = CF

median of an equilateral triangle are equal has been proved.

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HELP!!!!!!!!!!!!!!!!!!!! I WELL GIVE BRAINLIST AND 100 point if answered in less the 20 mins

If I have 419 assignments to do and i have pleated completed 79 how much work will I need to do every day to finish in one week

Answers

Answer:

10

Step-by-step explanation:

Answer:

You have to complete around 49 assignments everyday to finish in one week.

Step-by-step explanation:

• First, we have to calculate the number of assignments left to do:

Assignments remaining = 419 - 79

                                        = 340

• There are 7 days in a week, which means 340 assignments need to be completed in 7 days.

7 days  ⇒  340 assignments

1 day    ⇒   340 ÷ 7

            =    48.6

            ≅ 49 assignments

∴ You have to complete around 49 assignments everyday to finish in one week.

Were the non-violent, civil disobedience tactics used by civil rights leaders like dr. king effective at creating change and ending injustice? why or why not

Answers

Yes, the non-violent, civil disobedience tactics used by civil right leaders were effective to a great extent at creating change and ending injustice.

How were the civil disobedience tactics effective?

Martin Luther King, Jr.'s and other civil right leaders' leadership and vision were shaped by their steadfast faith in the efficacy of nonviolence and civil disobedience. Although it permitted civil rights protesters to avoid harsher legal penalties, it also had a deeper significance. America only learned about the effectiveness of nonviolent protest as a result of the work of Martin Luther King, Jr. and his civil disobedience allies.

Civil Disobedience Tactics

The Civil Rights Act of 1964 and the Voting Rights Act of 1965 were primarily made possible thanks to King. The Civil Rights Act outlawed discrimination on the basis of "race, color, religion, or national origin" in the workplace and in public places. African Americans' right to vote is safeguarded by the Voting Rights Act.

Inspired by Gandhi, King and other non-violent leaders, utilized civil disobedience to pressure governments to change. It manifested as widespread, nonviolent defiance of official orders. Civil disobedience is the act of refusing to comply with governmental orders or demands and remaining unaffected by the arrest and punishment that may follow.

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142857/500000 simplified

Answers

Using your own examples, explain why all statements are sentences but not all sentences are statements. Clearly indicate which type of non-statement you have used in each case. (Your response should be between 500 and 600 words).

Answer:

0.285714 -> 0.29

Step-by-step explanation:

The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.


Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?

y ≤ x^2 – 3
y > –x^2 + 2

Answers

The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution

How to modify the graphs

From the graph, we have:

f(x) = x² - 3

g(x) = -x² + 2

Next, we change the equations to inequalities as follows:

y ≤ x² - 3

y > -x² + 2

To modify the graph, we then perform the following transformations:

Shift the function g(x) down by 2 unitsReflect across the x-axisShift the function g(x) down by 3 units

How to identify the solution set

After the modifications in (a), we have:

y ≤ x² - 3 and y > -x² + 2

Substitute y > -x² + 2 in y ≤ x² - 3

-x² - 2 ≤ x² - 3

This gives

2x² ≤ - 1

Divide by 2

x² ≤ - 0.5

The square root of numbers less than 0 is a complex number

Hence, the set of inequalities do not have a solution

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Please help me on this geometry question

Answers

Answer:

? = 3

Step-by-step explanation:

given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is

[tex]\frac{?}{6}[/tex] = [tex]\frac{2}{4}[/tex] ( cross- multiply )

4? = 12 ( divide both sides by 4 )

? = 3

Answer:

3

Step-by-step explanation:

Because the triangles are similar

6/4 = (?+6)/(2+4)

6/4 = (?+6)/6

Cross multiply

36 = 4?+24

4?=12

?=3

Huan runs a business selling sweets. She is designing a container to hold the sweets. She uses rectangular pieces of cardboard measuring 20 cm by 30 cm. The mass of 1 square metre of the cardboard is 210 grams. She cuts a square from each corner of a piece of cardboard. She then folds the cardboard to make an open box. By changing the size of the square she cuts out, Huan can change the volume of the box.
(a) Work out the mass of the box made when she cuts a square of side 5cm from each corner.
(b) Huan cuts a square of side x from each corner of the cardboard.
(i) Explain why the volume of the box she makes is given by x(20-2x)(30-2x).
(ii) Explain why 0<x<10
(c) Huan wants to make a box with volume of at least 900cm3. She wants the mass of the box to be as small as possible.
By drawing a suitable graph, work out the mass of the box she will make ​

Answers

Answer:

d33z3 n0ts divided by ur m0m square root that x10 then divide by your d3pression.

Step-by-step explanation:

gotem

Given that 20=20+18+16+...+x, how many terms are on the right side of the equation

Answers

20 terms on the right side of the given equation [tex]20=20+18+16+...+x[/tex].

How we find the sum of n terms?

The first n terms of the arithmetic sequence are added together to form the sum of the first n terms of AP.

Therefore, we can only evaluate the sum of n terms in a sequence if we are aware of the type of sequence it is. Usually, when calculating the sum of an n-number of terms, we take into account arithmetic progression. The common distinction between each following term and each preceding term remains unchanged throughout this progression. Natural numbers are an illustration of Arithmetic Progression, where the common difference is 1. We must therefore be familiar with the formula in order to calculate the sum of natural numbers.

We can use formula for sum of n terms-

[tex]S = \frac{n}{2}(2a + (n-1)d)[/tex]

where, S- sum of n terms

n- number of terms

a- first term

d- difference between two consecutive terms

Here, S= 20 , a = 20, d= -2

we have to find n,

[tex]S = 20 = \frac{n}{2}(2(20) + (n-1)(-2)) \\20 = \frac{n}{2}(40-(2n-2))\\40 = n(40-2n+2)\\40 = 42n-2n^2\\2n^2 -42n +40 = 0[/tex]

solving this quadratic equation-

[tex]2n^2 -42n +40 = 0\\2n^2 -40n-2n+40=0\\2n(n-20)-2(n-20) = 0\\(2n-2)(n-20)=0[/tex]

when,

[tex]2n-2 = 0\\n=1[/tex]

When,

[tex]n-20=0\\ n=20[/tex]

as we can see that there are more than 1 terms present in the series so answer will be 20 terms.

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As a server or bartender, it is a good practice a. to have multiple interactions with patrons to evaluate their moods and needs. b. sample the patrons' drink to determine how strong they are. c. to not take patrons' drink orders too quickly upon arrival. d. to only serve the patrons one alcoholic drink every 90 minutes.

Answers

It is a good practice for a server or bartender to not take patrons' drink orders too quickly

Who is a bartender or server?

A bartender a person who prepares or serves alcoholic and some non-alcoholic beverages from behind a bar.

Below are some of the duties or responsibilities of a bartender:

Greet customers and create a welcoming atmosphere.Use a till to take orders and payments.Handle cash.Serve drinks at the bar or at the table.Keep the bar clean and well stocked.Give advice on drinks to suit customers' tastes.Collect glasses and wash up.

So therefore, it is a good practice for a server or bartender to not take patrons' drink orders too quickly

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Sketch the curve y = \sqrt{x+3} .
Find the area bounded by the curve, X-axis and Y-axis.
I get the first part but not the second part.

Answers

The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

How to determine the area bounded by the curve, x-axis and y-axis?

The curve is given as:

y = √(x + 3)

The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0

When y = 0, we have:

0 = √(x + 3)

This gives

x = -3

So, we set up the following integral

A = ∫ f(x) d(x) (Interval a to b)

This gives

A = ∫ √(x + 3) d(x) (Interval -3 to 0)

When the above is integrated, we have:

A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)

Expand

A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]

This gives

A = 1/3 * 2(3)^3/2

Apply the law of indices

A = 2(3)^1/2

Rewrite as:

A = 2√3 or 3.46

Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

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Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease. Suppose also that the incidence of the disease is 1%. If a person tests positive for the disease, what is the chance that they have the disease

Answers

If the test gives positive results for 95% of those having disease and correctly gives negative results for 90% of those who don't have disease and the incidence of the disease is 1% then the chance of having disease is 0.0105.

Given that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease.

We have to calculate the chance of having disease.

Probability that test is correct in determining the disease when person is suffering from it is 0.95.

Probability that test is not correct in determining the disease when person is suffering from it is 1-0.95=0.05.

Probability that test is correct in determining that the person is not suffering from disease  when person is not suffering from it is 0.90.

Probability that test is not correct in determining that the person is not suffering from disease  when person is not suffering from it is 1-0.9=0.10.

The chance of having disease is equal to incidence of disease multiplied by probabilities that the test has corectly determined disease when personis suffering from it and when test is not able to determine the disease when person is suffering from it.

Chance=0.01*0.95+0.01*0.10

=0.0095+0.001

=0.0105.

Hence the chance of having disease is 0.0105.

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how to solve for x in graphic sketch ​

Answers

Yes you can you can solve for x in graphic sketch

The Bay announced it would open a 9000-plus square metre freestanding store in the new West Grand Promenade. This would be the largest store on the promenade, with other smaller stores selling food, tires, and shoes. How else can this particular Bay store be described

Answers

This Bay store can also be described as a big box retailer store.

Big Box Retailer

A big box retailer is a physically enormous retail store that is typically a component of a chain of stores (also known as a hyper store, supercenter, superstore, or megastore). By extension, the phrase, big box retailer can also refer to the business that runs the store.

The Bay Store as a Big Box

There are numerous retail chains that only operate in Canada, aside from the large American big box retailer stores like Walmart Canada and the formerly-existent Target Canada. These include places like Hudson's Bay by Home Outfitters, Loblaws by Real Canadian Superstore, Rona, Winners by HomeSense, Canadian Tire by Mark's & Sport Chek, Shoppers Drug Mart, Chapters by Indigo Books and Music, Sobeys, and several others.

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