Who is the pattern made from sticks how many sticks would be in pattern number 6 in triangles 6 is the first and it adds 4 to make two

Answers

Answer 1

The number of sticks in pattern 6 is; 26

The nth term of the sequence formed is; aₙ = 4n + 2

How to find the arithmetic sequence?

From the attached image, we see that;

Number of sticks in pattern 1 is 6

Number of sticks in pattern 2 is 10

Number of sticks in pattern 3 is 14

Thus, the sequence will be;

6, 10, 14, ...

This is an AP because the difference is 4.

The formula for the nth term of an AP is;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

In our sequence, first term; a = 6

Common difference; d = 10 - 6 = 4

Thus, the equation for the nth term is;

aₙ = a + (n - 1)d

aₙ = 6 + (n - 1)4

aₙ = 6 + 4n - 4

aₙ = 4n + 2

Now, substitute n = 6 in the above equation to find the number of sticks in pattern 6. This gives;

a₆ = 4(6) + 2

a₆ = 26

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Who Is The Pattern Made From Sticks How Many Sticks Would Be In Pattern Number 6 In Triangles 6 Is The

Related Questions

initial investment $ 415,000 $ 230,000 $ 720,000 $ 945,000 present value of future cash flows 765,000 415,000 1,200,000 1,560,000

Answers

Is Shaylee able to invest in all of these projects simultaneously is no. Since the company has limited excess of money i.e. 2 Million to invest.

What is probability index?

The present value of benefits for each dollar of investment is calculated using the profitability index approach. In other words, it involves the ratio that is produced by comparing the ratio of the initial investment to the present value of future cash flows from a project.

A solid investment is one with a profitability index of greater than 1.0, with higher values indicating more alluring enterprises.

The ratio between the initial investment and the present value of future cash flows is measured by the profitability index (PI). The index can be used to rate investment projects and display the value produced per investment dollar.

Profitability Index = Present Value of Cash INflows / Present Value of Cash Outflows

Project : Profitability Index

A : 1.8434 (765,000 / 415,000)

B : 1.8043 (415,000 / 230,000)

C : 1.6667 (1200,000 / 720,000)

D : 1.6508 (1560,000 / 945,000)

Order of Preference

Project - Order of Preference

A - First Preference

B - Second Preference

C - Third Preference

D - Fourth Preference

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coordinate geometry find the coodinates of the centroid of each triangle with the given vertices geometry answers

Answers

The Coordinates of the centroid of a triangle with the given vertices are (0, 4), (8, 10) and (6, 1) is (14/3, 5) and Centroid of triangle with vertices (1,5),(3,8),(0,2) is (4/3, 5).

What is Centroid of a triangle?

The centroid of a triangle is one of the point where all three medians of the triangle intersect. The median is a line segment drawn from one vertex to the midpoint on the opposite side. Triangle centroid divides each median into individual words in a 2:1 ratio. The centroid is usually at 2/3 of the median.

If the three vertices of a triangle are A(x₁,y₁) B(x₂,y₂), C(x₃,y₃), the centroid of the triangle is given by the formula :

G(x₁+x₂+x₃/3, y₁+y₂+y₃/3 ).

We have , two triangles with vertices,

a) triangle whose vertices are A(0, 4), B(8, 10) and C(6, 0). So, the coordinates of the centroid of a triangle whose vertices are (0, 4), (8, 10) and (6 , 1) are ( (0+8+6)/3 , (4+10+1)/3 ) or (14/3, 5).

b) triangle whose vertices are P(1, 5), Q(3,8) and R(0, 2). So, the coordinates of the centroid of a ∆PQR are ( (1+3+0)/3 , (5+8+2)/3 ) or (4/3, 5).

Hence, the required coordinates of Centroid are (14/3, 5), (4/3, 5).

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Complete question:

Coordinate geometry find the coodinates of the centroid of each triangle with the given vertices are a) (0, 4), (8, 10) and (6, 1)

b) (1,5),(3,8),(0,2)

help math. Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answers

The linear function is y = 5x + 12 and the number of customers after 3 and 4 hours are 27 and 41 respectively.

Linear Function

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line.

m = slopeb = y-intercept

Using the data in the table, we can write can a linear function to represent it.

Taking two points;

A = (0, 12)B = (1, 17)

The slope of the line is calculated as;

m = y₂ - y₁ / x₂ - x₁

m = 17 - 12 / 1 - 0

m = 5 / 1

m = 5

Using the value of the slope to calculate the y - intercept.

y = mx + b

17 = 5(1) + b

17 = 5 + b

b = 17 - 5

b = 12

The linear function is written as y = 5x + 12

a) The number of customers in the store after 3 hours is

y = 5x + 12

y = 5(3) + 12

y = 15 + 12

y = 27

b) The number of customers in store after 4 hours is

y = 5x + 12

y = 5(4) + 12

y = 20 + 12

y = 41

The linear function to model the table is y = 5x + 12

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researchers wanted to check if carpeted rooms in hospitals contained more bacteria than uncarpeted rooms. to determine the amount of bacteria in a room, researchers pumped the air from the room over a petri dish for eight carpeted and eight uncarpeted rooms. colonies of bacteria were allowed to form in the 16 petri dishes. the results are presented in the table. (measured as bacteria per cubic foot) carpeted: 11.8, 10.8, 8.2, 10.1, 7.1, 14.6, 13.0, 14.0 uncarpeted: 12.1, 12.0, 8.3, 11.1, 3.8, 10.1, 7.2, 13.7 do carpeted rooms have more bacteria than uncarpeted rooms at a

Answers

No , the carpeted rooms does not have more bacteria than uncarpeted rooms .

Given ,

α=0.05

n1=8

n2 = 8

mean = ∑x / n

x1 = 11.8+10.8+7.1+14.6+8.2+10.1+13.0+14.0 / 8 = 11.2

and

x2 =12.1+12.0+3.8+10.1+8.3+11.1+7.2+13.7 /8 = 9.78

Variance ,

s1  =2.6

s2 = 3.2

HYPOTHESES

H0 : μ 1 =μ 2

H1 : μ 1  ≠μ 2

​Either the alternative hypothesis or the null hypothesis applies to the claim. The equality must be present in the null hypothesis. The alternative hypothesis declares the opposite of the null hypothesis if the claim is the null hypothesis.

On calculating we get the test statistic t as,

t = 1.771

The null hypothesis is rejected if the test statistic's value falls within the rejection zone.

0.956<1.771,

therefore , fail to reject H .

Therefore , there is no support for the null hypothesis , so we accept the alternate hypothesis as true.

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Amy finished her chemistry assignment in 1/5 hours. Then she completed her history assignment in 3/4 hours.

Answers

The total time taken by Amy to complete her assignments is 19/20 hours.

What is addition?

Addition is one of the four basic operations of arithmetic, Addition in maths is a process of combining two or more numbers.

Given that, Amy finished her chemistry assignment in 1/5 hours. Then she completed her history assignment in 3/4 hours.

Total time taken by Amy = Time taken for chemistry assignment + Time taken for history assignment

= 1/5+3/4 = (15+4)/20

= 19/20

Hence, The total time taken by Amy to complete her assignments is 19/20 hours.

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Identifying subgroups of the overall marketplace based on factors such as age or income level is considered:

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Demographic segmentation is considered for identifying subgroups of the overall marketplace based on factors such as age or income level.

A precise method of identifying an audience is known as demographic segmentation. It is based on information such as age, gender, marital status, family size, income, education, race, occupation, nationality, and/or religion. It is one of the four primary categories of marketing segmentation and is possibly the most used approach.

By concentrating on specific qualities that may represent relevant markets for a firm, demographic segmentation joins consumers and potential customers together. The five primary demographic subgroups are :

Agegenderoccupationcultural background family status

Demographic segmentation is the process of dividing a market into subgroups based on factors such as age, gender, income level, education level, and geographic location. This is a common way for businesses to identify and target specific groups of consumers who are likely to be interested in their products or services. By understanding the characteristics of different demographic segments, businesses can tailor their marketing efforts and products to better meet the needs and preferences of these groups. This can help businesses to effectively reach and engage their target audience, and ultimately increase sales and profits.

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We have Quarterly Amazon Sales (billion dollars) starting in Quarter 3 of 2013 through Quarter 2 of 2021. In Quarter 2 of 2021 the Amazon Sales was 96.1 billion dollars. Use the output provided below to report the updated forecast for the Amazon Sales for Quarter 3 of 2021. The variable time period is coded in the following way: Start with t = 1 for Quarter 3 of 2013, t = 2 for Quarter 4 of 2013. The value of t will increase by 1 for each subsequent quarter. In this example we have created indicator variables for Quarters 1, 2 and 3. Quarter 4 is the baselevel. Using the output here for the model accounting for trend and seasonality as well as the output for the AR(1) model report the updated forecast for Amazon Sales in Quarter 3 of 2021. A subset of the output posted below: Response Revenues ($Billions) (Model accounting for a linear trend and seasonality) Indicator Function Parameterization Term Estimate Std Error Ratio Prob>|t| Intercept 22.67 2.170013 8.15 <0001* Time period 2.538 0.114582 19.54 <.0001* Quarter[1] - 10.44 2.376946 -4.39 0.0003* Quarter[2] -11.156 2.385217 -4.68 0.0001* Quarter[3] -8.773 2.290687 -3.83 0.0010* Bivariate Fit of Residual Revenues ($Billions) 2 By Lag residuals (AR(1) Model output) Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -0.0856 0.479018 -0.18 0.8598 Lag residuals 0.762 0.132836 5.74 <.0001 The Updated forecast for the Amazon Sales accounting for Trend, Seasonality and Adjusted for the Serial Correlation using the AR(1) model is: _________ billion dollars. If the answer is 75.2432 billion dollars just type 75.2432 Record your answer with at least 4 decimal places.

Answers

The AR(1) model was used to create an updated forecast for Amazon sales that account for trend, seasonality, and serial correlation is 97.6510

Accounting and revenue

Accounting is the recording of financial transactions along with storing, sorting, retrieving, summarizing, and presenting the results in various reports and analyses.Revenue in accounting refers to the entire amount of money made through selling products and services from a company's core operations. Revenue is another term for a company's earnings, also known as sales or turnover.

Given that:

Equation of regression

Revenue = 22.67 + 2.538*t - 10.44*Q1 + 11.156*Q2- 8.77*Q3

t = 1 for the third quarter of 2013.

t = 33 for the third quarter of 2021

Revenue = 22.67 + 2.538*33 - 8.77 = 97.6510 billion dollars.

Therefore, Revenue = 97.6510 billion dollars

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It would he quite risky for you to insure the life of a 21 -year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain $\$ 1250 dollars in premiums. But if he were to die, you would lose almost \$ 100,000$. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21 -year-old men. (b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the investment. We can measure the great risk of insuring $\mathrm{u}$ single person's life in Exercise 14 by computing the standard deviation of the income $Y$ that the insurer will receive. Find or using the distribution and mean found in Exercise 14.

Answers

The standard deviation of the income that the insurer will receive can be determined which is 9708 using the distribution and mean.

Given in the question that the high probability would gain  in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.

According to the information, the gain around is 1250

Amount would lost in case of death is 100000.The expected value with its probability is:

E(X) = ∑x ×P(x)

=(-99750) × 0.00183 + ...+ (1250) × 0.99058

= 303.35

The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is

The standard deviation of Y can be determined as

α = under root {∑x2 × P(x) - (∑x × P(x) }

= 9708

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A chain restaurant hires a new vice president with vast experience in the industry. The new vice president claims that based on his observations in the industry that if the company offers a rewards program to its diners then sales will increase by an average of at least $600 per restaurant per week. The executive management team decides to pilot a rewards program in a few areas and evaluate the impact after one year. Below are the sales changes (sales for the week compared to the same week the previous year) for a sample of restaurants. You can copy the data into Excel to complete this problem. There are 35 observations; be sure to copy all of them. a) To conduct a test of the vice president's claim the appropriate null hypothesis is the population mean does not equal 600. b) The point estimate for the mean change in sales is Select) c) The standard deviation for the change in sales is (Select) d) The estimated standard error for this problem is [Select] e) The appropriate test statistic for this problem is Select) f) The appropriate p-value for this hypothesis test is g) Based on your results and using a 0.05 level of significance for your test you [Select] the null hypothesis.
Previous question

Answers

On solving the provided question, we can say that  - h1: μ < $600 and mean - 1/35 X 20307 = 580.2

What is null hypothesis ?

According to a well-known statistical theory known as the null hypothesis, there is no statistically significant association between any two sets of observable data and measurable events.

By putting X = sales change in $

Null hypothesis -

h0= μ ≥ $600

alternative hypothesis is

h1: μ < $600

where μ  is population mean change in sales per week

point estimate of mean change in sales  is

mean - 1/35 X 20307 = 580.2

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Darwin's age is 6 years greater than twice fiona's age.If darwin is 50 years old, how many years old is fiona

Answers

Answer:

22years old

Step-by-step explanation:

Let Fiona's age = x

Darwin age

2x+6 = 50

2x = 50 -6

2x = 44

x= 44/2

x = 22years old

Find the range for the measure of the third side of a triangle given the measure of two sides.
10.5 cm, 4 cm
Oa. 4 cm Ob. 4 cm >x> 10.5 cm
Oc. 6.5 cm >x> 10.5 cm
Od. 6.5 cm

Answers

Answer:

6.5 cm < x < 14.5 cm

Step-by-step explanation:

The length of the side of a triangle must be greater than the difference of the lengths of the other two sides and less than the sum of the other two sides.

Difference: 10.5 cm - 4 cm = 6.5 cm

Sum: 10.5 cm + 4 cm = 14.5 cm

Answer: 6.5 cm < x < 14.5 cm

A marketing company wanted to test what makes people purchase more cereal and they varied box size and flashy/simple graphics. Which of the following would be the main effects tested in this study? a. the results comparing each box size and comparing flashy vs Simple graphics b. behavior of purchasing cereal c. the results comparing each box size only d. the results comparing flashy vs. simple graphics only

Answers

Option A is correct that is the results comparing each box size and comparing flashy vs simple graphics.

Given this, a marketing firm tested several package variations, including size, complexity, and simplicity, to determine which would encourage customers to buy more cereal.

Which of the following would be the key conclusions of the study?

We are aware of this since we are comparing various box and graphic sizes.

When contrasting the sizes of each box and the flashy vs. simple images, the influence of the research can be noticed.

The comparison of the sizes of each box and the effectiveness of flashy vs. straightforward images shows that Option A is the best choice.

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What are the two equations to set up to solve the equation |2x - 5| = 7​

Answers

Answer:

To solve the equation |2x - 5| = 7, you can set up two equations, one for the positive solution and one for the negative solution.

For the positive solution, you can start by isolating the absolute value expression on the left-hand side of the equation: |2x - 5| = 7 can be rewritten as 2x - 5 = 7. Then, you can solve this equation by adding 5 to both sides to get 2x = 12, and then dividing both sides by 2 to get x = 6.

For the negative solution, you can start by noting that the absolute value of a number is equal to its opposite if it is negative, so |2x - 5| = 7 can be rewritten as -(2x - 5) = 7. This equation can be solved by multiplying both sides by -1 to get 2x - 5 = -7, and then adding 5 to both sides to get 2x = -2. Then, dividing both sides by 2 to get x = -1.

Therefore, the two equations to solve the equation |2x - 5| = 7 are 2x - 5 = 7 and 2x - 5 = -7.

Answer:

C

Step-by-step explanation:

To solve the equation |2x - 5| = 7, we need to set up two equations, one for the case where the absolute value is equal to the positive value of the expression inside the absolute value bars, and one for the case where the absolute value is equal to the negative value of the expression inside the absolute value bars.

The first equation we need to set up is 2x - 5 = 7. In this case, the absolute value is equal to the positive value of 2x - 5, so we can simply set the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:

2x - 5 = 7

The second equation we need to set up is -(2x - 5) = 7. In this case, the absolute value is equal to the negative value of 2x - 5, so we need to set the negative of the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:

-2x+5 = 7

We can use these two equations to solve for the value of x. To solve the first equation, we can simply add 5 to both sides to get 2x = 12, and then divide both sides by 2 to get x = 6. To solve the second equation, we can first distribute the negative sign to get -2x + 5 = 7, and then add 5 to both sides to get -2x = 2. Finally, we can divide both sides by -2 to get x = -1.

Therefore, the two solutions to the equation |2x - 5| = 7 are x = 6 and x = -1.

Alternative:

2x-5 = 7

2x-5 = -7

The following series are geometric series. Determine whether each series converges or not. For the convergent series, enter the sum of the series. For the divergent series, enter DIV. Also for each series, enter the first term a and the common ratio r. Determine whether the following series is convergent or divergent. If convergent find the sum, and if divergent enter DIV: 4 - 4/2+ 4/4 - 4/8 +... =

Answers

The given series is convergent and the first term is 4 and the common ratio is -0.5 and the sum of the series is 8/3 .

The given series is 4 - 4/2+ 4/4 - 4/8 +...

We can see that the first term of the geometric series is 4

Hence a = 4

The second term is  -4/2 and the third term is 4/4

Hence r = 4 ÷ (-4/2) = -4/2 ÷ 4/4 = - 1/2 or -0.5

Since the common ratio is less than 1 we can say that the series is convergent.

Now for a convergent series we know that the sum of the terms of the series is equal to

S = a / (1-r)

or, S = 4 / (1-(-0.5))

or, S = 4 / 1.5

or, S = 8/3

Hence the sum of the convergent series is 8/3 .

Both the ratio test and the root test are based on a comparison with a geometric series and hence function in comparable scenarios.

In fact, if the ratio test works (that is, if the limit exists and is not equal to 1), then so does the root test; the contrary is not true. The root test is thus more broad, although in practise, determining the limit for regularly encountered kinds of series is frequently challenging.

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The greater of two numbers is twice the lesser. If the greater is x, what is the lesser.

Answers

Answer:

1/2x

Step-by-step explanation:

Answer:

The lesser is x/2.

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

Let the numbers be x and y, where x is greater and y is lesser.

Given that x = 2y.

Find y:

x = 2y                 Divide both sides by 2x/2 = yy = x/2

at the beginning of her senior year maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?

Answers

Answer:

  $114

Step-by-step explanation:

You want to know the interest due on student loans of $5000 (subsidized) and $4500 (unsubsidized) with an APR of 5.05% when Maria starts making payments 6 months after graduation.

Subsidized

The government pays the interest for the first 6 months after graduation, so Maria owes no interest on her subsidized loan.

Unsubsidized

The interest is figured beginning at graduation. The formula is ...

  I = Prt . . . . . . P is the principal amount, r is the interest rate, and t is years

  I = $4500(0.0505)(1/2) = $113.625 ≈ $114

Maria will owe $114 in interest on her loans 6 months after graduation.

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help what is the value of y??? please help me!!

Answers

Answer: I think that y =18

Step-by-step explanation: I thought this bc the one across from it is also 18 and they look equal. I hope I helped

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x³-7x+11?
0 +1.1.1.5
O
11
0 + 3.1.1.5,
45, +11
5
0 0 ±, ±3. 1. ±1, , 25, ±11

Answers

Answer:

1/5

-1/5

11/5

-11/5

1

-1

11

-11

Step-by-step explanation:

The Rational Root Theorem states that if a polynomial equation with integer coefficients has a rational root, then that root must be of the form p/q, where p is a factor of the constant term (in this case, 11) and q is a factor of the leading coefficient (in this case, 5).

Using this information, we can determine that the potential rational roots of the polynomial f(x) = 5x³-7x+11 are all of the following:

1/5

-1/5

11/5

-11/5

1

-1

11

-11

Note that this list includes all possible rational roots of the polynomial, but not all of these roots will necessarily be actual roots. To determine which of these potential rational roots are actual roots, we would need to test them by plugging them into the polynomial and solving for x.

what would the graph of the equation look like? y= -3/5x + 3

Answers

The graph of the equation y=-3/5+3 will be a straight line

How to determine the graph of a straight line?

The graph of a straight line is always straight.  The equation is written in slope intercept for where -3/5 is the

The form of an equation in slope intercept form is y=mx+c

Here, m=-3/5

c=3

To draw the line, from the point 3 on the x-axis, rise negative 3 and run 5

The draw the line for form a straight line

Note that the formula for slope is

S=rise/run

In conclusion, the equation forms a straight line.

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whats the midpoint of (2,9) and (10,-8)

Answers

Answer:

(6, 0.5)

Step-by-step explanation:

midpoint = x1+x2/2 , y1+y2/2

midpoint = 2+10/2 , 9+(-8)/2

midpoint = 12/2, 1/2

midpoint = 6, 0.5

Let (x1,y1) be (2,9) and let (x2,y2) be (10,-8)

The formula for the midpoint of a line segment is

(x1+x2/2,y1+y2/2)

So we get

((2+10)/2, (9+(-8))/2)

This gives us

(12/2,1/2)

So the midpoint between these two points is

(6,0.5) hope this helps!

Given the function:
f(x) = 1/2 (3x+7)
What is the output of the function when the input is x = 9?
A 9
B 15
C 17
D 21

Answers

Answer: C

Step-by-step explanation:

It's easy! Don't worry!

f(x) = 1/2(3x+7)

f(9) = 1/2(3(9)+7)

f(9) = 1/2(27+7)

f(9) = 1/2(34)

f(9) = 17

Trust me when you finish algebra this stuff is cake not going to lie. I did it under a minute. ;)

Also, gl passing algebra!

Find the domain of the function f(x)=\sqrt{\sqrt{x^2-16}-3}$

Answers

We have to make sure that we are taking square roots of non-negative values to stay within the real number system.

You have to make sure x^2-16 ≥ 0 for the inner square root to stay in the real numbers.

You also have to make sure sqrt(x^2-16)-3 ≥ 0 for the outer square root to stay in the real numbers.

Solving x^2-16 ≥ 0 we have that x^2 ≥ 16, so either x≥4 or x≤-4.

Solving sqrt(x^2-16)-3 ≥ 0, we have

     sqrt(x^2-16) ≥ 3

              x^2-16 ≥ 9

                   x^2 ≥ 25

    either x ≥ 5 or x ≤ -5.

Since that second condition is more restrictive that x ≥ 4 or x ≤ -4, we can default to just using

   { x | x ≥ 5 or x ≤ -5 }

   (-infty, -5) U (5, infty)


6. Writing When you add a
one-digit number to a
decade number, what do you
notice about the ones place
digit of the sum?

Answers

When one adds a one digit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added.

What is a decade number?

It's important to bite that a decade number simply means the numbers that are counted when counting numbers by tens to 100.

In this situation, when one adds a one diigit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added. Any example will be:

= 10 + 2

= 12

In this case, the 2 is in the units value of the number

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Given that f is increasing, f is increasing, and that the range of g is included in f what can be said about f o g?

Answers

H(x) is a decreasing function too.  fog will be decreasing function.

An easy definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them.

                     In plain English, a function is an association between inputs in which each input is connected to precisely one output.

Let  h(x) = f(g(x))

 Hence,

        h'(x) = f'(g(x) ) . g(x)

  h'(x) = f'g(x)) . g(x)

 Now g(x) is a strictly decreasing function.

Then

  g'(x) < 0 for all real x.

Hence

     h'(x) < 0

since h'(X) = f'(g(X)) . g'(X) and g'(x) < 0

 Therefor h(x) is a decreasing function too.

 Hence fog will be decreasing function.

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Please help will mark brainily

Answers

Answer: C. 2x+3y=7.20  4x+2y=8.80

Step-by-step explanation: 2x and 4x = grapefruit,  3y and 2y = oranges

A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.


Servings Sauce (cups) Oregano (tsp)
5 15 two and a half
7


At this rate, how much sauce and oregano will be needed to make 7 servings?

Answers

Answer: To make 7 servings of the recipe, you will need:

Sauce: 7 servings * 15 cups/5 servings = <<7*15/5=21>>21 cups

Oregano: 7 servings * (2.5 tsp/5 servings) = <<7*(2.5/5)=1.75>>1.75 tsp

So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

Step-by-step explanation:

They will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, To make 7 servings of the recipe, you will need:

Sauce:

⇒ 7 × 15 /5

⇒ 21 cups

Oregano: \

⇒ 7 × (2.5 /5 )

⇒ 1.75 tsp

So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

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For purposes of making on-campus housing assignments, a college classifies its students as Priority A (seniors), Priority B (juniors), Priority C (freshmen and sophomores). Of the students who choose to live on campus, 10% are seniors, 20% are juniors, and the rest are underclassmen. The most desirable dorm is the newly constructed Gold dorm, and 60% of the seniors elect to live there. 15% of the juniors also live there, along with only 5% of freshmen and sophomores. What is the probability that the student lived in the Gold dorm and was an underclassmen? Round to three decimals.

Answers

The probability that the student lived in the Gold dorm and was an underclassmen is of:

0.035 = 3.5%.

How to obtain a probability?

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

The parameters for this problem are given as follows:

70% of the students are underclassmen. (freshmen and sophomores).Of the underclassmen students, 5% live in the gold dorm.

Hence the probability that the student lived in the Gold dorm and was an underclassmen is calculated as follows:

p = 0.7 x 0.05 = 0.035 = 3.5%.

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After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.6+4 /(t+4)^3 feet per year, where t is the time (in years).
(a) Find the number of feet that the tree will grow in the second year.
(b) Find the number of feet the tree will grow in the third year.

Answers

a.) 0.5367 feet

b.) 0.5223 feet'

Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).

The amount of growth can be gotten by integrating the given rate equation as shown:

[tex]\int\limits {0.5} \, + \frac{6}{(t+4)^{3} } dt[/tex]

[tex]=\int\limits {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx[/tex]

[tex]=0.5t+\int\limits6u^{-3} du \, \,where \,u=t +4 \, and \, du=dt[/tex]

[tex]=0.5t+6*\frac{u^{-3} }{-2} + C[/tex]

[tex]=0.5t-3u^{-2}+C[/tex]

[tex]=0.5t-3(t+4)^{-2} +C[/tex]

a)  The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from  t =1 to t = 2

[tex]\int\limits^2_1 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \, =[0.5t-3(t+4)^{-2} ][/tex]

[tex]=[0.5(2)-3(2+4)^{-2} ]-[0.5-3(5)^{-2} ][/tex]

[tex]=\frac{11}{12}-\frac{1}{2}-\frac{3}{25}[/tex]

[tex]=0.9167-0.5+0.12[/tex]

[tex]=0.5367[/tex]

b)  The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from  t =2 to t = 3

[tex]\int\limits^3_2 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \,[/tex]

[tex]=[0.5t-3(t+4)^{-2} ][/tex]

[tex]=[1.5-\frac{3}{49} ]-[1-\frac{1}{12} ][/tex]

=1.439-0.9167

=0.5223 feet

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Write a polynomial of least degree with roots 0, 4, and 9

Answers

Answer:

Your Polynomial: [tex]x^3-13x^2+36x=0[/tex]

Step-by-step explanation:

Given information: 0 , 4 , 9

0 -> x = 0 -> (x - 0) = 0

4 -> x = 4 -> (x - 4) = 0

9 -> x = 9 -> (x - 9) = 0

(x - 0)(x - 4)(x - 9) = 0

x * (x - 4) * (x - 9) = 0

(x^2 - 4x) * (x - 9) = 0

x^3 - 9x^2 - 4x^2 + 36x = 0

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = Vf. (If the vector field is not conservative,enterDNE) F(x, y, z)= i + sin(z)j + y cos(z)k, f(x, y, z) =​

Answers

The function f such that F = ∇f does not exist, and the answer is DNE (does not exist).

What is a vector field?

Generally, To determine whether or not the vector field is conservative, we need to check if its curl is zero. The curl of the given vector field is:

curl(F) = ∇ x F

          = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k

Substituting in the values of the components of F, we get:

curl(F) = (-cos(z))i + (0)j + (-y sin(z))k

Since the curl of the vector field is nonzero, the vector field is not conservative.

Therefore, the solution is DNE, and the function f such that F = f does not exist (does not exist).

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