Every two years, a manufacturer's total yearly sales decline 20%. She sells 400 total units in her first year. Rounded to the nearest unit, how many total units will she sell her ninth year?

Answers

Answer 1

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ p=period \end{cases}[/tex]

we know, the first year she sold 400 units, thus year 0, 400 units, t = 0, A = 400.

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\to &400\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &0\\ p=period \end{cases} \\\\\\ 400=I(1-r)^{\frac{0}{p}}\implies 400=I\cdot 1\implies 400=I[/tex]

therefore then

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &400\\ r=rate\to 20\%\to \frac{20}{100}\to &0.20\\ t=\textit{elapsed time}\\ p=period\to &2 \end{cases} \\\\\\ A=400(1-0.2)^{\frac{t}{2}}[/tex]

now, how many units will it had decreased by the 9th year? t = 9

[tex]\bf A=400(1-0.2)^{\frac{9}{2}}[/tex]

Answer 2

146.54 units are the total units will she sell her ninth year.

Here, we have,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

where,

A = amount

I = initial amount

r = rate

t = time

p = period

we know, the first year she sold 400 units,

thus year 0, 400 units, t = 0, A = 400.

so, we get,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

=> 400 = I × 1

=> 400 = I

therefore then, when, rate = 20 %

we get,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

[tex]= > A = 400(1-0.2)^{t/2}[/tex]

now, how many units will it had decreased by the 9th year? t = 9

so, we get,

[tex]= > A = 400(1-0.2)^{9/2}[/tex]

=> A = 146.54

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Related Questions

One pound of grapes costs $1.55. Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of 3.5 pounds of grapes?

A First one
B second one
C third one
D last one

Answers

1.55 / 1 = x / 3.5....$ 1.55 to 1 lb = $ x to 3.5 lbs

first one <==

it could have also been : 1 / 1.55 = 3.5 / x...but that is not an answer choice

Answer:

Step-by-step explanation:

One pound of grapes costs $1.55. To find the amount x of 3.5 pounds of grapes we would have to multiply 1.55 by 3.5. This would give us the amount x we would have to pay for them.

If we examine the 4 equivalent radios shown in the pictures, we will see that the first one correctly shows this equivalency.

[tex]\frac{1.55}{1} = \frac{x}{3.5}[/tex]

The other 3 pictures show radios that would give us x = 3.5 / 1.55 (second and third) or x = 1.55 / 3.5 (fourth picture).

Therefore, the correct answer would be a)

jeff finds some bugs. he finds 10 fewer grasshoppers than crickets. he finds 5 few crickets than ladybugs. if jeff finds 5 grasshoppers. how many ladybugs does jeff find? how many crickets does he finds?

Answers

Answer:
Jeff finds 15 crickets
Jeff finds 20 ladybugs

Explanation:
Assume that the number of grasshoppers is x, the number of crickets is y and the number of ladybugs is z

We are given that:
1- Number of grasshoppers is 10 less than number of crickets.
This means that:
x = y - 10 .............> equation I

2- Number of crickets is 5 less than number of ladybugs.
This means that:
y = z - 5 ..............> equation II

3- Jeff found 5 grasshoppers.

Substitute with value of grasshoppers in equation I to get the number of crickets as follows:
x = y - 10
5 = y - 10
y = 10 + 5
y = 15 crickets

4- Now we know that the number of crickets is 15, substitute with that value in equation II to get the number of ladybugs as follows:
y = z - 5
15 = z - 5
z = 15 + 5
z = 20 ladybugs

Based on the above:
number of crickets is 15
number of ladybugs is 20

Hope this helps :)

Jeff found 15 crickets and 20 ladybugs

Let the number of grasshoppers be x

Let the number of crickets be y

Let the number of ladybugs be z

If Jeff finds 10 fewer grasshoppers than crickets, hence x = y - 10

If he finds 5 few crickets than ladybugs, hence y = z - 5

If jeff finds 5 grasshoppers, hence x = 5

Since x = y - 10

5 = y - 10

y = 5 + 10

y = 15

Similarly since y = z - 5

15 = z - 5

z = 15 + 5

z = 20

This shows that Jeff found 15 crickets and 20 ladybugs

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Consider the function h(x) = arcsin x) considering the input of h... i) ...which is a valid unit of measure for the input quantity

Answers

Given the function [tex]h(x)=\arcsin(x) [/tex]

Part a:

Considering the input of h

i.) A valid unit of measure for the input quantity is Seconds

ii.) The possible input values, i.e. the domain of h are -1 ≤ x ≤ 1

Part B:

i.) A valid unit of measure for the output quantity is the Radians.

ii.) The possible output values, i.e. the range of h is 0 ≤ h ≤ 2π

Part C:

i.) [tex]\arcsin\left(\sin\frac{\pi}{3}\right)=\frac{\pi}{3}[/tex]

ii.) [tex]\arcsin\left(\sin\frac{2\pi}{3}\right)=\frac{2\pi}{3}[/tex]

iii.) [tex]\arcsin\left(\sin\frac{7\pi}{6}\right)=\frac{7\pi}{6}[/tex]

iv.) [tex]\arcsin\left(\sin\frac{7\pi}{4}\right)=\frac{7\pi}{4}[/tex]

which of the following equations represents a direct variation?

A y=x -1
B y=×/3
C y = x + 5
D y = 2x-3

Answers

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x , and y = 6 when x = 2 , the constant of variation is k = = 3 . Thus, the equationdescribing this direct variation is y = 3x .

The equation represents a direct variation is y = x/3. So option (b) is correct.

A direct variation is a relationship between two variables where one variable is a constant multiple of the other. To identify a direct variation, we look for equations in the form y = kx, where k is a constant.

Let's analyze each equation:

A) y = x - 1

This equation doesn't represent a direct variation because it includes a constant term (-1) in addition to the variable x.

B) y = x/3

This equation represents a direct variation because it's in the form y = kx, where k = 1/3.

C) y = x + 5

Similar to option A, this equation doesn't represent a direct variation because it includes a constant term (+5) in addition to the variable x.

D) y = 2x - 3

Similar to option A, this equation doesn't represent a direct variation because it includes a constant term (-3) in addition to the variable x.

Therefore, the correct answer is B) y = x/3, as it represents a direct variation.

186.302 in expanded form

Answers

100 + 80 + 6 + .3 + .002

A business bought a lot of 2,500 lamps for fifty thousand dollars and wants to to sell them at 15% prfit. How much should each lamp cost?

Answers

Let L = how much is lamp should cost

L = [(50,000)(0.15) + 50,000]/(2500)

Calculate the right side of the equation to find your answer.

So 15% of 50000=7500 The answer is 7500

what do Subway fraction and a whole number it is 5/6 x 36

Answers

The answer to this question is 221/6 I believe

The graph of the function f(x) = (x − 3)(x + 1) is shown.

Which describes all of the values for which the graph is positive and decreasing?

A.all real values of x where x < −1
B.all real values of x where x < 1
C.all real values of x where 1 < x < 3
D.all real values of x where x > 3

Answers

There's an error in the graph, but the answer is A.

Answer:

The correct option is A.

Step-by-step explanation:

The given function is

[tex]f(x)=(x-3)(x+1)[/tex]

Equate f(x)=0 to find the x-intercepts of the function.

[tex]0=(x-3)(x+1)[/tex]

[tex]x=3,-1[/tex]

The x-intercepts of the function are -1 and 3. From the below graph it is clear that,

In x<-1, the function is positive and decreasing.

In -1<x<1, the function is negative and decreasing.

In 1<x<3, the function is negative and increasing.

In x>3, the function is positive and increasing.

Therefore the correct option is A.

Two vectors are given by a with arrow = 3 î + 6 ĵ and b with arrow = -1 î + ĵ. (a) find a with arrow ✕ b with arrow.

Answers

Given that vectors are [tex]\vec a = (3, 6, 0)[/tex] and [tex]\vec b = (- 1, 1, 0)[/tex], the cross product of the two vectors are [tex]\vec a \times \vec b = (0, 0, 9)[/tex].

How to determine the cross product of two vectors

Vectorially speaking, cross product is a operation between two 3-dimension vectors to generate a third vector perpendicular to the two former. If we know that [tex]\vec a = (3, 6, 0)[/tex] and [tex]\vec b = (- 1, 1, 0)[/tex], then the cross product is:

[tex]\vec a \times \vec b = \left|\begin{array}{ccc}\hat{i}&\hat {j}&\hat{k}\\3&6&0\\-1&1&0\end{array}\right|[/tex]

[tex]\vec a \times \vec b = (0, 0, 3 + 6)[/tex]

[tex]\vec a \times \vec b = (0, 0, 9)[/tex]

Remark

The statement is incomplete and there is no possibility to complete it. Hence, we decided to consider the given statement as complete.

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Final answer:

The cross product of vectors a and b is found by creating a matrix with the vectors' components and calculating its determinant. The result in this case is -3î.

Explanation:

To find the cross product of vectors a = 3 î + 6 ĵ and b = -1 î + ĵ, you have to follow the matrix method. We list the unit vectors î, ĵ at the top of our matrix, and then add the components of vectors a and b underneath.

⟮ î ĵ ⟯
⟮ 3 6 ⟯ (from vector a)
⟮ -1 1 ⟯ (from vector b)

We calculate the determinant of this matrix using the rule of Sarrus. The resulting vector will be î(y1*z2 – z1*y2) - ĵ(x1*z2 – z1*x2) which, when plugging in our values, gives 3î - 6î. Therefore, a✕b equals -3î.

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Express the decimal number 100 in all radices from 2 to 9

Answers

A decimal number can be converted into diffrent radices by continuos division and recording the remainders.

Part 1

To convert the decimal number 100 to radix 2, we have:

[tex] \frac{100}{2} =50 \ remainder \ 0 \\ \\ \frac{50}{2} =25 \ remainder \ 0 \\ \\ \frac{25}{2} =12 \ remainder \ 1 \\ \\ \frac{12}{2} =6 \ remainder \ 0 \\ \\ \frac{6}{2} =3 \ remainder \ 0 \\ \\ \frac{3}{2} =1 \ remainder \ 1 \\ \\ \frac{1}{2} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 2 is 1100100

Part 2:

To convert the decimal number 100 to radix 3, we have:

[tex]\frac{100}{3} =33 \ remainder \ 1 \\ \\ \frac{33}{3} =11 \ remainder \ 0 \\ \\ \frac{11}{3} =3 \ remainder \ 2 \\ \\ \frac{3}{3} =1 \ remainder \ 0 \\ \\ \frac{1}{3} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 3 is 10201

Part 3:

To convert the decimal number 100 to radix 4, we have:

[tex]\frac{100}{4} =25 \ remainder \ 0 \\ \\ \frac{25}{4} =6 \ remainder \ 1 \\ \\ \frac{6}{4} =1 \ remainder \ 2 \\ \\ \frac{1}{4} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 4 is 1210

Part 4:

To convert the decimal number 100 to radix 5, we have:

[tex]\frac{100}{5} =20 \ remainder \ 0 \\ \\ \frac{20}{5} =4 \ remainder \ 0 \\ \\ \frac{4}{5} =0 \ remainder \ 4[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 400

Part 5:

To convert the decimal number 100 to radix 6, we have:

[tex]\frac{100}{6} =16 \ remainder \ 4 \\ \\ \frac{16}{6} =2 \ remainder \ 4 \\ \\ \frac{2}{6} =0 \ remainder \ 2[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 244

Part 6:

To convert the decimal number 100 to radix 7, we have:

[tex]\frac{100}{7} =14 \ remainder \ 2 \\ \\ \frac{14}{7} =2 \ remainder \ 0 \\ \\ \frac{2}{7} =0 \ remainder \ 2[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 202

Part 7:

To convert the decimal number 100 to radix 8, we have:

[tex]\frac{100}{8} =12 \ remainder \ 4 \\ \\ \frac{12}{8} =1 \ remainder \ 4 \\ \\ \frac{1}{8} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 144

Part 8:

To convert the decimal number 100 to radix 9, we have:

[tex]\frac{100}{9} =11 \ remainder \ 1 \\ \\ \frac{11}{9} =1 \ remainder \ 2 \\ \\ \frac{1}{9} =0 \ remainder \ 1[/tex]

Starting from the bottom we collate the remainders.

Therefore, the value of decimal number 100 in radix 5 is 121

Calculate the quotient and remainder of 19 divided by 7.

Answers

If you want the remainder then it will look like this: 2R5. But if you want the decimals then it is 2.71428571, to be exact. Hope this helps.

A group of friends is collecting aluminum for a recycling drive.Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon.The weight of each person's donation is shown in the table.

A. order the weights of the donations from greatest to least.

B. Which of the friends will receive a free movie coupon? Which will not?

C.What if? Would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum? Explain

Brenda. Claire Jim. Micah

4.3. 5.5. 6 1/6. 15/4

Peter
4 3/8

Answers

Answer:

Brenda Claire Jim Micah Peter

4.3 5.5 6 1/6 15/4 4 3/8

4.3 5.5 6.17 3.75 4.375 (all values in decimal)

A. order the weights of the donations from greatest to least.

6.17 , 5.5 , 4.375 , 4.3 , 3.75

B. Which of the friends will receive a free movie coupon? Which will not?

As given - Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon.

So, Brenda, Claire, Jim and Peter will receive coupons and Micah will not receive.

C.What if? Would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum?

Micah got 3.75 pounds and if he got 0.5 pounds more, then he would have;

[tex]3.75+0.5=4.25[/tex] pounds

Then he would have got the coupon as a minimum of 4.25 pounds is required.

Use integers to represent the values in the statement.The hightest elevation in a country is Mt.Snowy with an altitude of 15178 feet.The lowest elevation in the country is Green Valley with an altitude of 237 feet below sea level

Answers

the lowest elevation can be represented in integers like this: -237 feet
because it is below sea level, it is negative
the highest elevation can be expressed like so: 15178 feet

Answer:

Integers include positive Natural Numbers and Negative Natural numbers along with number which has no value called Zero.

Positive Integer=1,2,3,4.........Infinity

Negative Integer= -1,-2,-3,-4,...... -Infinity

Height of Mt.Snowy which is above sea level can be represented in terms of Integers = + 15,718 feet

Height of Green Valley which is above sea level can be represented in terms of Integers = + 237 feet

As, both Mountain snowy and Green valley are above sea level , so it will be represented by positve Integers.

I need help fast!! Having trouble with this!!

Answers

THE ANSWER TO THIS PROMBLEM IS A

d = 8t

if t = 0 then d =0
if t =1 then d =8x1 = 8
if t = 2 then d = 8x2 = 16

answer is C.
d = 8t

Donna opens a certificate of deposit (CD) with $2,000. The bank offers a 3% interest rate. If the account compounds quarterly, which of the following equations represents the future value of the account, after 1 year?

Answers

1) Quaterly interes = 3% / 4 = 0.03 / 4

2) Values:

after 1 quarter: 2000 (1 + 0.03/4)

after 2 quarters: 2000 (1 + 0.03/4)^2

after 3 quarters: 2000 (1 + 0.03/40^4

after 4 quarters = 2000 (1 + 0.03/4)^4

You could have used the future value formula directly:

A = C * (1 + r/n) ^ n*t

where r = 3% = 0.03

n = number of periods in a year: 4

t = number of years = 1

C = initial investment = 20000

=> A = 2000 (1 + 0.03/4)^4

Answer: option D. A = 2000 ( 1 + 0.03 /4) 4

There are two less nickels than dimes, and as many quarters, as nickels and dimes together. The total amount of money is $5.25. How many quarters, dimes, and nickels are there?

Answers

n=d-2
q=n+d =>q=(d-2)=q=2d-2
25q+5n+10d=525
replace q and n with d
25(2d-2) +5(d-2)+10d=525
50d-50+5d-10+10d=525
65d=585
d=9
n=7
q=16

Find the probability and interpret the results. if convenient, use technology to find the probability. during a certain week the mean price of gasoline was $2.715 per gallon. a random sample of 32 gas stations is drawn from this population. what is the probability that the mean price for the sample was between $2.691 and $2.732 that week? assume sigmaσequals=$0.049

Answers

From the given question:

[tex]\mu=\$2.715 \\ \\ \sigma=\$0.049[/tex]

The probability of a normally distributed data between two values (a, b) is given by:

[tex]P(a\ \textless \ \bar{x}\ \textless \ b)=P\left( \frac{b-\mu}{\sigma/\sqrt{n}} \right)-P\left( \frac{a-\mu}{\sigma/\sqrt{n}} \right)[/tex]

Thus,

[tex]P(\$2.691\ \textless \ \bar{x}\ \textless \ \$2.732)=P\left( \frac{\$2.732-\$2.715}{\$0.049/\sqrt{32}} \right)-P\left( \frac{\$2.691-\$2.715}{\$0.049/\sqrt{32}} \right) \\ \\ =P(1.963)-P(-2.771)=0.97515-0.0028=\bold{0.97235}[/tex]

Final answer:

To find the probability of the sample mean price being between $2.691 and $2.732, calculate the Z-scores for each bound and use a Z-table or statistical software. This utilizes the central limit theorem and the concept of Z-scores in statistics.

Explanation:

The question is about finding the probability that the mean price for a sample of 32 gas stations was between $2.691 and $2.732, assuming the population mean was $2.715 and standard deviation was $0.049. To solve this, we use the Z-score formula for each sample mean, Z = (X - μ) / (σ/√n), where μ is the population mean, σ is the population standard deviation, and n is the sample size. Then, we find the area between these Z-scores using a Z-table or statistical software to get the probability.

To calculate:

For $2.691: Z = ($2.691 - $2.715) / ($0.049/√32) = -3.44For $2.732: Z = ($2.732 - $2.715) / ($0.049/√32) = 2.45

Refer to a Z-table or software with these Z-scores to find the probability of the sample mean price being between $2.691 and $2.732. This method exemplifies how statisticians use Z-scores and the central limit theorem to estimate probabilities relating to sample means.

Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month. The bike Jane wants is $1,536 at the local bike shop.

Which equation represents this situation, and after how many months, t, will Jane have enough money to purchase the bike?

A, 3(2)t = 1,536; t = 11
B, 3(1.2)t = 1,536; t = 35
C, (3 · 2)t = 1,536; t = 9
D, 3(2)t = 1,536; t = 9

Answers

the Answer is D)
i just did the math. plug 3(2)^9 in to a calculator!

Answer:

Hence, option: D is true.

D) 3×(2)^t = 1,536; t = 9

Step-by-step explanation:

Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month.

he bike Jane wants is $1,536 at the local bike shop.

The equation that represents this situation, and after how many months, t, will Jane have enough money to purchase the bike is:

D) 3×(2)^t = 1,536; t = 9

since in the first month the cost is:

[tex]C_1=3\times 2[/tex]

in next month the cost is:

[tex]C_2=3\times 2\times 2\\\\C_2=3\times 2^2[/tex]

in t=3 months the expression is:

[tex]C_3=3\times 2^2\times 2\\\\C_3=3\times 2^3[/tex]

Hence in general we say:

[tex]C_t=3\times 2^t[/tex]

Hence,

[tex]3\times 2^t=1536\\\\2^t=\dfrac{1536}{3}\\\\2^t=512\\\\2^t=2^9\\\\t=9[/tex]

Hence, option: D is true.

D) 3×(2)^t = 1,536; t = 9

A given line has the equation 10x + 2y = −2.

Answers

what variable are u solving for?

Answer:

5x+y=12

Step-by-step explanation:

How do I answer question #9

Answers

add 6,3, and 5 together to get. 14. subtract 14 and 26. you get 12 left over. 12 mm less rain is the answer

Hello ItzJibblez!

STEPS
1. First you will add 6 mm+ 3 mm + 5 mm = 14
2. Then you subtract 26 - 14 = 12.

So the answer to your amazing question is 14 mm!

Have an awesome day!!!

Which is another way to name UST? TSR TSU USR UTS

Answers

Another was to name it is <TSU.

TSU is the correct answer

Use the graph of y = tan x to find all values of x, 0 ≤ x ≤ 2π, for which the following is true.

tan x is undefined

Answers

check the picture below, notice the red asymptotic lines.

now, recall that

[tex]\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \\\\\\ tan\left( \frac{\pi }{2} \right)=\cfrac{sin\left( \frac{\pi }{2} \right)}{cos\left( \frac{\pi }{2} \right)}\implies \stackrel{und efined}{tan\left( \frac{\pi }{2} \right)=\cfrac{1}{0}} \\\\\\ tan\left( \frac{3\pi }{2} \right)=\cfrac{sin\left( \frac{3\pi }{2} \right)}{cos\left( \frac{3\pi }{2} \right)}\implies \stackrel{und efined}{tan\left( \frac{\pi }{2} \right)=\cfrac{-1}{0}}[/tex]

Which equation has a y-intercept of 0?

A) y = 7x + 1

B) y = -3x

C) y = 4x - 4

D) y = x + 5

Answers

The answer would be B because, unlike the others, it only shows the slope.

Compare all of these equations to y = mx + b. The "b" represents the y-intercept. The correct answer here is the equation that has no "b." This means that b = 0.

all real numbers that are less than or equal to -27?in interval notation.

Answers

All real numbers that are less than or equal to -27?in interval notation.

(-∞, -27]

Final answer:

The set of all real numbers less than or equal to -27 in interval notation is (-∞, -27].

Explanation:

The set of all real numbers that are less than or equal to -27 can be represented in interval notation as (-∞, -27]. In interval notation, a square bracket indicates that the endpoint is included in the set. In this case, -27 is included because the question states 'less than or equal to.' The symbol '-∞' represents negative infinity, indicating that there is no lower bound on the set.

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Which ordered pairs in the form (x, y) are solutions to the equation 7x−5y=28 ?Solation 7x−5y=28 ? A. (−6, −14) B. (7,9) C. (4,10) D.(-1,-7)

Answers

Probe every pair:

pair       x          y           7x - 5y

A. (-6,-14)    -6 -14    7(-6) - 5(-14) = -42 + 70 = 28 => it is a solution

B. (7,9)           7          9          7(7) - 5(9) = 49 - 45 = 4 => not a solution

C. (4,10)        4          10        7(4) - 5(10) = 28 - 50 = - 22 => not a solution

C. (-1,-7)        -1          -7       7(-1) - 5(-7) = -7 + 35 = 28 => it is a solution

Answer: option A. (-6,-14) and option D. (-1,-7)

!!!!PLEASE HELP!!!!

Joe purchased a tray of 48 petunias to plant in his garden. The graph shows points representing the number of flowers left to plant at several different times while Joe is planting.

Select from the drop-down menus to complete the equation, in standard form, that represents the relationship between the number of petunias left to plant, y, and the time, x, Joe has spent planting.

Answers

Required equation is y - 36 = (24 - 36)/(2 - 1) (x - 1)

y - 36 = -12(x - 1)

y - 36 = -12x + 12

12x + y = 12 + 36

12x + y = 48

Answer:

12x + y = 48

Step-by-step explanation:

Find the inverse laplace transform of the function by using the convolution theorem. f(s) = 1 s5(s2 + 1)

Answers

By the convolution theorem,

[tex]f(t)=(g*h)(t)=\displaystyle\int_{\tau=0}^{\tau=t}g(\tau)h(t-\tau)\,\mathrm d\tau\implies F(s)=G(s)H(s)[/tex]

where [tex]F(s),G(s),H(s)[/tex] are the respective Laplace transforms of [tex]f(t),g(t),h(t)[/tex].

We have

[tex]F(s)=\dfrac1{s^5(s^2+1)}=\dfrac1{4!}\dfrac{4!}{s^5}\times\dfrac1{s^2+1}[/tex]

If we let [tex]G(s)=\dfrac{4!}{s^5}[/tex] and [tex]H(s)=\dfrac1{s^2+1}[/tex], then clearly [tex]g(t)=t^4[/tex] and [tex]h(t)=\sin t[/tex], so by the convolution theorem,

[tex]f(t)=\dfrac1{4!}t^4*\sin t=\displaystyle\frac1{24}\int_{\tau=0}^{\tau=t}\tau^4\sin(t-\tau)\,\mathrm d\tau=\frac{t^4}{24}-\frac{t^2}2+1-\cos t[/tex]

If two lines are perpendicular, which statement must be true? A.The slopes of the two lines are equal. B.The slopes of the two lines are undefined. C.The slopes of the two lines are zero. D.The slopes of the two lines are negative reciprocals.

Answers

Answer:

Option D is correct that is The Slopes of two lines are negative reciprocals.

Step-by-step explanation:

Perpendicular lines are the lines which intersect each other at right angle or make 90° angle with each other.

we that the Slope of perpendicular lines are equal to -1

Therefore, Option D is correct that is The Slopes of two lines are negative reciprocals.

Answer:

The answer to your question is D. The slopes of the two lines are negative reciprocals.

Step-by-step explanation:

Hope this helps have a great day :D

What is the constant of proportionality I. The equation y=5x?

Answers

Answer:

The value of the constant of proportionality is [tex]k=5[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

The value of the constant k is equal to the value of the slope

In this problem we have

[tex]y=5x[/tex] ------> is a linear direct variation

The slope is [tex]m=5[/tex]

therefore

The value of the constant of proportionality is [tex]k=5[/tex]

The constant of proportionality on the equation is 5.

To obtain the constant of proportionality ;

We compare the general direct proportionality relation with the equation given.

The equation given : y = 5x

The direct relationship between y and x is :

y α x

y = kx - - - (1)

Where, y and x are variables and k is the constant of proportionality.

Comparing equation (1) with the equation given :

y = kx

y = 5x

We can observe that, k in the equation (1) equals to 5 in the given equation.

Hence, the constant of proportionality is 5

Learn more : https://brainly.com/question/11388407

how do i figure out 3/4 of 640 fraction

Answers

640/4 x 3 = 480

answer
3/4 of 640 = 480

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