aryn needs enough mulch to cover a rectangle flower bed measuring 2 1/4 yd by 3 1/2yd each bag cover 3 square yds and cost $4 how many bags does she need and how much money she need

Answers

Answer 1

Answer:

cars are dum

Step-by-step explanation:


Related Questions

which of the following descriptions represent the transformation shown in the image? Part 1d​

Answers

Answer:

(C) Translation of 2 units right, 1 up, and a reflection over the y-axis.

Step-by-step explanation:

Ideally, we are looking for a reflection of the red image over the y-axis, and to do that, we can see how we need to move the black image.

In order for points Q and Q' to be a reflection of each other, they need to have the same y value, and be the exact same distance from the y axis, so the point that Q has to be at is (-1,-3).

Q is right now at (-3,-4) so we can translate this.

To get from -3 to -1 in the x-axis, we go right by 2 units.

To get from -4 to -3 in the y-axis, we go up one unit.

Now, if we reflect it, the triangles will be the same.

Hope this helped!

Answer:

C.

Step-by-step explanation:

When you study the images, it is clear that the black triangle has to be reflected over the y-axis to face the same direction as the red triangle. So, choice A is eliminated.

Once you reflect the black triangle across the y-axis, you have points at (-1, -1), (3, -4), and (3, -2). Meanwhile, the red triangle's coordinates are at (-3, 0), (1, -3), and (1, -1). From these points, you can tell that the x-values differ by 2 units and the y-values differ by 1 unit.

All of these conditions match the ones put forth in option C, so that is your answer.

Hope this helps!

Use all the information below to find the missing x-value for the point that is on this line. m = - 1 / 3 b = 7 ( x, 4 )

Answers

Answer:

[tex]\boxed{x = 9}[/tex]

Step-by-step explanation:

m = -1/3

b = 7

And y = 4 (Given)

Putting all of the givens in [tex]y = mx+b[/tex] to solve for x

=> 4 = (-1/3) x + 7

Subtracting 7 to both sides

=> 4-7 = (-1/3) x

=> -3 = (-1/3) x

Multiplying both sides by -3

=> -3 * -3 = x

=> 9 = x

OR

=> x = 9

Answer:

x = 9

Step-by-step explanation:

m = -1/3

b = 7

Using slope-intercept form:

y = mx + b

m is slope, b is y-intercept.

y = -1/3x + 7

Solve for x:

Plug y as 4

4 = 1/3x + 7

Subtract 7 on both sides.

-3 = -1/3x

Multiply both sides by -3.

9 = x

PLEASE HELP QUICK! Determine x value of: sqrt x + 8 - sqrt x - 4 = 2

Answers

Answer:

x=8

Step-by-step explanation:

[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:

8lb of the cheaper Candy

17.5lb of the expensive candy

Step-by-step explanation:

Let the cheaper candy be x

let the costly candy be y

X+y = 25.5....equation one

2.2x +7.3y = 25.5(5.7)

2.2x +7.3y = 145.35.....equation two

X+y = 25.5

2.2x +7.3y = 145.35

Solving simultaneously

X= 25.5-y

Substituting value of X into equation two

2.2(25.5-y) + 7.3y = 145.35

56.1 -2.2y +7.3y = 145.35

5.1y = 145.35-56.1

5.1y = 89.25

Y= 89.25/5.1

Y= 17.5

X= 25.5-y

X= 25.5-17.5

X= 8

WILL MARK BRAINLIEST If Alan and Zack can clean a room in 30 minutes when working together, and Alan cleans twice as fast as Zack, how long would it take Alan to clean the room by himself?

Answers

Answer:

45 min

Step-by-step explanation:

Here,

the we take the work as W and Alan's speed as A and Zack's speed as Z.

A = 2Z

W = 30 ( A+Z)

if the time for Alan to done cleaning alone is t then t = W ÷ A

t = ( 30 (A+(A÷2)))÷ A

t = 45 min

I am done .

The average weight of a person is 160.5 pounds with a standard deviation of 10.4 pounds. 1. What is the probability a person weighs more than 150.2 pounds

Answers

Answer:

0.8390

Step-by-step explanation:

From the question,

Z score = (Value-mean)/standard deviation

Z score = (150.2-160.5)/10.4

Z score = -0.9904.

P(x>Z) = 1- P(x<Z)

From the Z table,

P(x<Z) = 0.16099

Therefore,

P(x>Z) = 1-0.16099

P(x>Z) = 0.8390

Hence the probability that a person weighs more than 150.2 pounds = 0.8390

15x - 30 x 0 + 40 = 89

Answers

Answer:

x = 49/15

Step-by-step explanation:

15x - 30 x 0 + 40 = 89           PEMDAS

15x + 40 = 89        Isolate the variable

15x = 49      

x = 49/15

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 49/15 or 3 4/15 or 3.26

▹ Step-by-Step Explanation

15x - 30 * 0 + 40 = 89

15x - 0 + 40 = 89

15x + 40 = 89

15x = 89 - 40

15x = 49

x = 49/15 or 3 4/15 or 3.26

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the new equation, find x if the point P(x, 4) lies on the new line. y=3x-1 y=1/4 x+2

Answers

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]

Which Graph represents the solution to the compound inequality 4x +8< -16 or 4x + 8 > 4

Answers

Answer:

option 3

Step-by-step explanation:

4x+8<-16

x<-6

4x+8_>-16

x_>-1

(it's more and equal .so the circle has to be shaded and move to the right of -1)

Answer:C

Step-by-step explanation:

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of −7 and 6, and goes to −∞ as x→−∞.

Answers

Answer:

Step-by-step explanation:

Hello, because of the end behaviour it means that the leading coefficient is negative so we can construct such polynomial function as below.

[tex]\large \boxed{\sf \bf \ \ -(x+7)(x-6) \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The polynomial function will be f ( x ) = - x² - x + 42

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+ bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Given data ,

The polynomial function is of second degree with zeros of -7 and 6

So , x = -7 and x = 6

Let the function be f ( x ) where f ( x ) = ( x + 7 ) ( x - 6 )

Now , as x tends to infinity , the negative makes no such difference on the zeros of the function f ( x ) ,

And , f ( x ) = - ( x + 7 ) ( x - 6 )

Therefore , to find the polynomial function , f ( x ) = - ( x + 7 ) ( x - 6 )

f ( x ) = - [ x² - 6 x + 7 x - 42 ]

        = - [ x² + x - 42 ]

        = - x ² - x + 42

Hence , the polynomial function f ( x ) = - x ² - x + 42

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Question 16 (5 points)
Given the recursive formula shown, what are the first 4 terms of the sequence?

Answers

Answer:

i think its b

???

Step-by-step explanation:

im sorry if im wrong im not very confident on my answer :(

Answer:

D

Step-by-step explanation:

Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.

Find the probability of each event. A six-sided die is rolled seven times. What is the probability that the die will show an even number at most five times?

Answers

Answer:

[tex]\dfrac{15}{16}[/tex]

Step-by-step explanation:

When a six sided die is rolled, the possible outcomes can be:

{1, 2, 3, 4, 5, 6}

Even numbers are {2, 4, 6}

Odd Numbers are {1, 3, 5}

Probability of even numbers:

[tex]\dfrac{\text{Favorable cases}}{\text{Total cases }} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]

This is binomial distribution.

where probability of even numbers,  [tex]p =\frac{1}{2}[/tex]

Probability of not getting even numbers (Getting odd numbers) [tex]q =\frac{1}{2}[/tex]

Probability of getting r successes out of n trials:

[tex]P(r) = _nC_r\times p^r q^{n-r}[/tex]

Probability of getting even numbers at most 5 times out of 7 is given as:

P(0) + P(1) +P(2) + P(3) +P(4) + P(5)

[tex]\Rightarrow _7C_0\times \frac{1}{2}^0 \frac{1}{2}^{7}+_7C_1\times \frac{1}{2}^1 \frac{1}{2}^{6}+_7C_2\times \frac{1}{2}^2 \frac{1}{2}^{5}+_7C_3\times \frac{1}{2}^3 \frac{1}{2}^{4}+_7C_4\times \frac{1}{2}^4 \frac{1}{2}^{3}+_7C_5\times \frac{1}{2}^5 \frac{1}{2}^{2}[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (_7C_0+_7C_1+_7C_2+_7C_3+_7C_4+_7C_5)\\[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (1+7+\dfrac{7 \times 6}{2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6}{2})\\\Rightarrow \dfrac{120}{128} \\\Rightarrow \dfrac{15}{16}[/tex]

Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours

Answers

Answer:

3.27 hours

Step-by-step explanation:

Calculate the difference in speed and distance between the trains.

The relative speed:

101 - 90 = 11 mph

Difference in distance:

42 - 6 = 36 miles

[tex]time=\frac{distance}{speed}[/tex]

[tex]t=\frac{36}{11}[/tex]

[tex]t = 3.27[/tex]

Answer:

yeah she is correct

Step-by-step explanation:

Could someone answer the question with the photo linked below? Then explain how to solve it?

Answers

Answer:

b = sqrt(57)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

8^2 + b^2 = 11^2

64+ b^2 = 121

Subtract 64

b^2 = 121-64

b^2 =57

Take the square root of each side

b = sqrt(57)

Please answer this correctly without making mistakes.Please simplify the correct answer

Answers

Answer:

19/70 of NASA shuttle missions were carried out by Discovery.

9/140 of NASA shuttle missions were carried out by Challenger.

17/70 of NASA shuttle missions were carried out by Endeavour.

Step-by-step explanation:

Adding the number of missions carried out by NASA gives us 140 in total.

Discovery's total amount of missions simplified is 19/70.

Challenger's total amount of missions is already in the simplest form.

Endeavour's total amount of missions simplified is 17/70.

Answer:

81/140

Step-by-step explanation:

Well to find the fraction we first need to total amount of NASA missions.

38 + 32 = 70

70 + 34 = 104

104 + 27 = 131

131 + 9 = 140

Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.

38 + 9 + 34 = 81

Now we can make the following fraction,

81/140

This is already in simplest form.

Thus,

the answer is 81/140.

Hope this helps :)

A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?

Answers

Answer:

a) percentage of the employees that will experience lost-time accidents in both years = 1.2%

b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%

Step-by-step explanation:

given

percentage of lost time accident last year

P(L) = 8% = 0.08 of the employees

percentage of lost time accident current year

P(C) = 4% = 0.04 of the employees

P(C/L) = 15% = 0.15

using the probability

P(L ∩ C) = P(C/L) × P(L)

= 0.08 × 0.15 = 0.012 = 1.2%

percentage of the employees will experience lost-time accidents in both years = 1.2%

b) Using the probability of the event

P(L ∪ C) = P(L) + P(C) - P(L ∩ C)

= 0.08 + 0.04 -0.012 = 0.108 = 10.8%

percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%

A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total possible outcomes are there when choosing a marble from the bag?

Answers

Answer:

its 14/C

Step-by-step explanation:

i got i right on edg U^U

Answer:

16

Step-by-step explanation:

i did edge test yea dont  be imma fake :***    

write and equation to represent the following statement 28 is 12 less thank K. solve for K K =

Answers

Answer:

K = 40

Step-by-step explanation:

As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"

Hope it helps and pls mark as brainliest : )

Answer:

Equation : 28 = k - 12

K = 40

Step-by-step explanation:

28 is 12 less than k

Let's create an equation:

[tex]28 = k - 12[/tex]

Now, let's solve:

[tex]28 = k - 12[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - k = - 12 - 28[/tex]

Calculate the difference

[tex] - k = - 40[/tex]

Change the signs on both sides of the equation

[tex]k = 40[/tex]

Hope this helps...

Best regards!!

plzzzzz helpp j + 9 - 3 < 8

Answers

Answer:

j < 2

Step-by-step explanation:

Simplify both sides of the inequality and isolating the variable would get you the answer

The total cost of a sweater and a jacket was $71.55 If the price of the sweater was $3.19 less than the jacket, what was the price of the sweater? Express your answer as a simplified fraction or a decimal rounded to two places.

Answers

Answer: $34.18

Step-by-step explanation:

Let the cost of the Jacket = $x and

The cost of the sweater. = $y

Now total price. = $71.55.

So, $x + $y. = $71.55 -- 1

From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation

y = ( x - $3.19 )

Now substitute for y in the equation (1) above.

x + ( x - 3.19 ) = 71.55

Now solve the equation

x + x - 3.19 = 71.55

2x - 3.19. = 71.55

2x = 71.55 + 3.19

2x. = 74.74

x = 74.74/2

= $37.37. cost of the jacket

Now to determine the cost of the sweater,

$71.55 - $37.37 = $34.18

The cost of the sweater = $34.18.

Determine the t critical value for a lower or an upper confidence bound in each of the following situations. (Round your answers to three decimal places.)

a. Confidence level = 95%, df = 10
b. Confidence level = 95%, df = 15
c. Confidence level = 99%, df = 15
d. Confidence level = 99%, n = 5
e. Confidence level = 98%, df = 23
f. Confidence level = 99%, n = 32

Answers

Answer:

A. 1.812

B. 1.753

C. 2.602

D. 3.747

E. 2.069

F. 2.453

Step-by-step explanation:

A. 95% confidence level, the level of significance = 5% or 0.05

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182

B. 95% confidence interval = 0.05 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753

C. 99% confidence interval = 0.01 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602

D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747

E. 98% confidence interval = 0.02 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069

F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453

Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000. If a person is about to take the test what is the probability that he or she will make a score of 650 or more?

Answers

Answer:

0.0668 or 6.68%

Step-by-step explanation:

Variance (V) = 10,000

Standard deviation (σ) = √V= 100

Mean score (μ) = 500

The z-score for any test score X is:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = 650:

[tex]z=\frac{650-500}{100}\\z=1.5[/tex]

A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]

The probability is 0.0668 or 6.68%

The probability that he or she will make a score of 650 or more is 0.0668.

Let X = Scores made on a certain aptitude test by nursing students

X follows normal distribution with mean = 500 and variance of 10,000.

So, standard deviation = [tex]\sqrt{10000}=100[/tex].

z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].

The probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]

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find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2​

Answers

Answer:  A) N'=(-2, 2) M'=(-1, 0)  L'=(-5, -2)

Step-by-step explanation:

N = (-2, -4)      M = (-3, -2)       L = (1, 0)

Reflection over y = -1

N' = (-2, 2)      M' = (-3, 0)       L' = (1, -2)

Reflection over x = -2

N'' = (-2, 2) M'' = (-1, 0)  L'' = (-5, -2)

Question 10 of 10
Which set of polar coordinates are plotted in the graph below?

Answers

Answer:

(-2, -(2pi)/3)

Step-by-step explanation:

a p ex

In da pic :)))))))))

Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?

Answers

Step-by-step explanation:

brain list me please......

Answer:

Jacob:

Alive 69-70

alive 79-80

alive 62-63

alive 73-74

alive 78-Died 79

Carol:

alive 88-89

alive 67-68

alive 99-100

alive 73-74

alive 94- Died 95

Step-by-step explanation:

Harry is trying to complete his hill walking scouts badge. He is using a map with a scale of 1 cm : 2 km. To earn the badge he needs to walk 14 km. What is the distance he needs to walk on the map?

Answers

Answer:

7 cm

Step-by-step explanation:

14 / 2 = 7 cm

7cm is the distance Harry needs to walk on the map?

What is Distance?

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.

Given that,

Harry is trying to complete his hill walking scouts badge.

He is using a map with a scale of 1 cm : 2 km.

To earn the badge he needs to walk 14 km.

Let the distance he needs to walk on the map is x.

By given data we write an equation

1/2=x/14

Apply Cross Multiplication

14/2=x

7=x

Hence, 7cm is the distance he needs to walk on the map.

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Please help. I’ll mark you as brainliest if correct!

Answers

Answer:

CDs: $30,000bonds: $90,000stocks: $50,000

Step-by-step explanation:

You can let c, b, s represent the investments in CDs, bonds, and stocks, respectively.

  c + b + s = 170000 . . . . . . total invested

  0.0325c +0.038b +0.067s = 7745 . . . . . . . annual income

  -c + b = 60000

You can solve this set of equations using any of a number of methods, including on-line calculators, graphing calculators, scientific calculators, Cramer's Rule, substitution, elimination, and more. The solution is ...

  c = 30,000

  b = 90,000

  s = 50,000

Maricopa's Success invested $30,000 in CDs, $90,000 in bonds, and $50,000 in stocks.

Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The negative root of ex = 4 − x2

Answers

Answer:

x = -1.964636

Step-by-step explanation:

Given equation;

eˣ = 4 - x²

This can be re-written as;

eˣ - 4 + x² = 0

Let

f(x) = eˣ - 4 + x²    -----------(i)

To use Newton's method, we need to get the first derivative of the above equation as follows;

f¹(x) = eˣ - 0 + 2x

f¹(x) = eˣ + 2x         -----------(ii)

The graph of f(x) has been attached to this response.

As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.

Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0

From Newton's method,

[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]

=> When n=0, the equation becomes;

[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]

[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]

Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;

f(-2) = e⁻² - 4 + (-2)²

f(-2) = e⁻² = 0.13533528323

And;

f¹(2) = e⁻² + 2(-2)

f¹(2) = e⁻² - 4 = -3.8646647167

Therefore

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - -0.03501863503[/tex]

[tex]x_{1} = -2 + 0.03501863503[/tex]

[tex]x_{1} = -1.9649813649[/tex]

[tex]x_{1} = -1.96498136[/tex]         [to 8 decimal places]

=> When n=1, the equation becomes;

[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]

[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]

Following the same procedure as above we have

[tex]x_{2} = -1.96463563[/tex]

=> When n=2, the equation becomes;

[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]

[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]

Following the same procedure as above we have

[tex]x_{3} = -1.96463560[/tex]

From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately  -1.964636 to 6 decimal places.

Newton's method of approximation is one of the several ways of estimating values.

The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

The equation is given as:

[tex]\mathbf{e^x = 4 - x^2}[/tex]

Equate to 0

[tex]\mathbf{4 - x^2 = 0}[/tex]

So, we have:

[tex]\mathbf{x^2 = 4}[/tex]

Take square roots of both sides

[tex]\mathbf{ x= \pm 2}[/tex]

So, the negative root is:

[tex]\mathbf{x = -2}[/tex]

[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]

Differentiate

[tex]\mathbf{f'(x) = e^x +2x }[/tex]

Using Newton's method of approximation, we have:

[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]

When x = -2, we have:

[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]

[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]

So, we have:

[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -1.96498136}[/tex]

Repeat the above process for repeated x values.

We have:

[tex]\mathbf{x_{2} = -1.96463563}[/tex]

[tex]\mathbf{x_{3} = -1.96463560}[/tex]

Up till the 6th decimal places,

[tex]\mathbf{x_2 = x_3}[/tex]

Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

Read more about Newton approximation at:

https://brainly.com/question/14279052

The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.

Answers

Answer:

Hey there!

A=1/2bh

14=1/2(28)h

14=14h

h=1

Hope this helps :)

Answer:

the height is 1 inch

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

where b is the base

h is the height

From the question

Area = 14in²

b = 14 inches

So we have

[tex]14 = \frac{1}{2} \times 28 \times h[/tex]

which is

[tex]14 = 14h[/tex]

Divide both sides by 14

That's

[tex] \frac{14}{14} = \frac{14h}{14} [/tex]

We have the final answer as

h = 1

Therefore the height is 1 inch

Hope this helps you

and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern

Answers

Answer:

quadratic

Step-by-step explanation:

This graph has a parabola form wich is a propertie for qaudratic functions

Answer:

A

Step-by-step explanation:

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