A system of inequalities is shown. Which symbol could be written in both circles in order to represent this system algebraically? y 3x x –2 ≤ ≥ < >

Answer:

[tex]z=\frac{395.2-400}{\frac{8}{\sqrt{16}}}=-2.4[/tex]  

[tex]p_v =2*P(Z<-2.4)=0.0164[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly different from 400.  

[tex]395.2-1.96\frac{8}{\sqrt{16}}=391.28[/tex]    

[tex]395.2+1.96\frac{8}{\sqrt{16}}=399.12[/tex]

So on this case the 95% confidence interval would be given by (391.28;399.12)

Since the confidence interval not contains the value of 400 we can conclude that the true mean is different from 400 at 5% of significance.      

Step-by-step explanation:

1) Data given and notation  

[tex]\bar X=395.2[/tex] represent the sample mean  

[tex]\sigma=8[/tex] represent the population standard deviation  

[tex]n=16[/tex] sample size  

[tex]\mu_o =7.3[/tex] represent the value that we want to test  

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

2) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean pressure is different from 400, the system of hypothesis are :  

Null hypothesis:[tex]\mu = 400[/tex]  

Alternative hypothesis:[tex]\mu \neq 400[/tex]  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

3) Calculate the statistic  

We can replace in formula (1) the info given like this:  

[tex]z=\frac{395.2-400}{\frac{8}{\sqrt{16}}}=-2.4[/tex]  

4) P-value  

Since is a two sided test the p value would given by:  

[tex]p_v =2*P(Z<-2.4)=0.0164[/tex]  

5) Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly different from 400.  

6) Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]

Now we have everything in order to replace into formula (1):

[tex]395.2-1.96\frac{8}{\sqrt{16}}=391.28[/tex]    

[tex]395.2+1.96\frac{8}{\sqrt{16}}=399.12[/tex]

So on this case the 95% confidence interval would be given by (391.28;399.12)

Since the confidence interval not contains the value of 400 we can conclude that the true mean is different from 400 at 5% of significance.      

Answer:the price of one adult ticket is $24.5

the price of one youth ticket is $20.5

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one youth ticket.

One family spends $131 on 2 adult tickets and 4 youth tickets at an amusement park. This means that

2x + 4y = 131 - - - - - - - - - -1

Another family spends $139 on 4 adult and 2 youth tickets at the same park. This means that

4x + 2y = 139 - - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 2, it becomes

8x + 16y = 524

8x + 4y = 278

Subtracting

12y = 246

y = 246/12 = 20.5

Substituting y = 20.5 into equation 1, it becomes

2x + 4×20.5 = 131

2x + 82 = 131

2x = 131 - 82 = 49

x = 49/2 = 24.5

Answer:

[tex]y=-0.36x+12.6[/tex]

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(10, 9) and (35, 0)

substitute the values in the formula

[tex]m=\frac{0-9}{35-10}[/tex]

[tex]m=-\frac{9}{25}=-0.36[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

With the slope [tex]m=-0.36[/tex] and point (35,0) substitute in the equation and solve for b

[tex]0=-0.36(35)+b[/tex]

[tex]0=-12.6+b[/tex]

[tex]b=12.6[/tex]

therefore

The equation of the line in slope intercept form is

[tex]y=-0.36x+12.6[/tex]

Answer:

B, C and D.

Step-by-step explanation:

3m=36-6m

9m=36

m=4

-1/3m+2=-1

-1/3m=-3

m=9

So not it

B, c and d is the same as they all equal to 4.

Answer:

The answer to your question is b, c and d

Step-by-step explanation:

Equation given

                        3m = 36 - 6m

                        3m + 6m = 36

                        9m = 36

                          m = 36/9

                         m = 4

Equation a

                        -1/3 m + 2 = -1

                        -1/3 m = -1 - 2

                        -1/3 m = -3

                               m = -3 x -3

                              m = 9

Equation b

                       -2(-4m - 6.4) = 44.8

                            -4m - 6.4 = 44.8/-2

                            -4m = -22.4 + 6.4

                            -4m = -16

                                m = -16/-4

                               m = 4

Equation c

                       8m - 5 - 2m + 1 = 20

                       6m = 20 + 4

                        6m = 24

                          m = 24/6

                         m = 4

Equation d

                       7m + 6 = 9m - 2

                       7m - 9m = -2 - 6

                             - 2m = -8

                                 m = -8/-2

                                 m = 4

n is the initial amount

0.07 is the factor of increase

x is the number of years that the emails increased

answer: C

Answer:

Correct answer: Two point of intersection and one touch point.

Step-by-step explanation:

Cartesian form of parabola is: y= a(x-1)² + 5  and point named A(2,4)

when we replace the coordinates of the point A in the formula we get

a = - 1 and parabola is  y= - (x-1)² + 5 which means that it faces the opening downwards. The parabola touches the circle in vertex.

God is with you!!!

Answer:$1109.23 will be in the account after 9 years

Step-by-step explanation:

Initial amount deposited into the account is $400 This means that the principal

P = 400

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 12%. So

r = 12/100 = 0.12

It was compounded for 9 years. So

n = 9

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 400 (1+0.12/1)^1×9

A = 400(1.12)^9 = 1109.23$

According to marginal analysis in economics, the optimal consumption is where marginal cost equals marginal benefit. Given that the marginal cost is constant at $10 per sandwich, and marginal benefit decreases, the optimal consumption would be to eat two sandwiches.

In your scenario, you are trying to determine the optimal number of peanut butter and jelly sandwiches to consume given a constant marginal cost and a decreasing marginal benefit. This is essentially a problem in the domain of Economics, particularly concerning the concept of marginal analysis.

The principle of marginal analysis states that optimal consumption occurs at the point where marginal cost equals marginal benefit. In numerical terms, this translates to the following: a $10 cost for each sandwich equals a $10 benefit. Therefore, this is the optimal point of consumption, meaning that you would ideally consume two sandwiches.

This is the result of the economic theory of consumer behavior, which predicts that consumers seek to maximize their utility while considering their budget constraints. Any further sandwiches would result in a negative gain, or a loss, because the marginal cost would exceed the marginal benefit (as the benefit from the third sandwich decreases to $8, from the fourth to $6, and so on). It should be noted that this analysis assumes rational behavior and no external costs or benefits associated with the consumption of more sandwiches.

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Answer:

She is absolutely correct!

Step-by-step explanation:

Let the total no. of stickers with Lena be x.

If she sticks 5 stickers per page, the number of pages she will use=[tex]\frac{x}{5}[/tex]

If she sticks 10 stickers per page, the number of pages she will use=[tex]\frac{x}{10}[/tex]

We all know, that the smaller the denominator the larger the number.

Therefore, [tex]\frac{x}{5} >\frac{x}{10}[/tex]

Condition being that x is a positive quantity which it automatically is.

So, Lena is right in her reasoning that she will use more no. of pages.

Yes, Lena is correct because placing a smaller number of stickers per page (5 instead of 10) will indeed result in the use of more pages overall, as this reduces the stickers-to-page ratio.

The question is asking if Lena will use more pages for her stickers if she places 5 stickers on a page instead of 10. We are working with a simple division concept here. When you have a fixed number of items (stickers, in this case) and you use fewer items per group (or page), you will end up with more groups (or pages).

If Lena puts 5 stickers on each page as opposed to 10 stickers on a page, she will indeed need more pages because she’s placing fewer stickers on each page. For instance, if she has 20 stickers: with 5 stickers per page, she will need 4 pages (20 stickers / 5 stickers per page = 4 pages). On the other hand, with 10 stickers per page, she will only need 2 pages (20 stickers / 10 stickers per page = 2 pages). Therefore, placing fewer stickers on a page results in more pages being used.

The question is incomplete. Here is the complete question:

Suppose your school is having a talent show to raise money for new music supplies. You estimate that 200 students and 150 adults will attend. You estimate $200 in expenses. Write an equation to find what ticket prices you should set to raise $1000.

Answer:

[tex]200x+150y=1200[/tex]

Step-by-step explanation:

Let 'x' be price per student ticket and 'y' be the price per adult ticket.

Given:

Number of students = 200

Number of adults = 150

Total fund to be raised = $1000

Expenses cost = $200

Now, price of ticket for 1 student = 'x'

Therefore, price of tickets of 200 students = [tex]200x[/tex]

Price of ticket of 1 adult = 'y'.

Therefore, price of tickets of 150 adults = [tex]150y[/tex]

Now, total fund raised will be equal to the total money obtained from selling the tickets minus the expenses estimated.

∴ Total fund raised = Total money from tickets - Expenses.

⇒ [tex]1000=200x+150y-200[/tex]

⇒ [tex]200x+150y=1000+200[/tex]

⇒ [tex]200x+150y=1200[/tex]

Therefore, the equation to find what ticket prices you should set to raise $1000 is given as:

[tex]200x+150y=1200[/tex]

Answer:

it is D

Step-by-step explanation:

this is because D has integers which are multiples of 15 and are also even numbers

The set of numbers that would be included in the shaded portion of the Venn diagram is {30, 60, 90, 120}.

A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by intersections of the circles.

The universal set. ∪, is the set of all positive integers.

The multiples of 15 are;

15, 30, 45, 60, 75, ........

The odd multiplies of 15 are;

15, 45, 75, 105, ......

The even multiplies of 15 are;

30, 60, 90, and 120.....

Comparing the set of numbers that would be included in the shaded portion of the Venn diagram is a set of multiples of 30.

Hence, the set of numbers that would be included in the shaded portion of the Venn diagram is {30, 60, 90, 120}.

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Dana must pay $1238.75 upfront.

Step-by-step explanation:

Given,

Cost of car = $24,650

Sales tax = 3.5%

Amount of sales tax = 3.5% of cost of car

Amount of sales tax = [tex]\frac{3.5}{100}*24650[/tex]

Amount of sales tax = [tex]\frac{86275}{100}=\$862.75[/tex]

Amount of title and tag fees = $376

Total upfront amount = Amount of sales tax + Amount of title and tag fees

Total upfront amount = 862.75+376 = $1238.75

Dana must pay $1238.75 upfront.

Keywords: percentage, sales tax

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Answer:

option B. 18,12,12

Step-by-step explanation:

perimeter= 60 units

(consider a rectangle with sides a,b,c & d in order)

a= 18 units (given)

c=18 units (since opp. sides of a rectangle are equal)

now the remaining length= 60-(18+18)

                                          = 60 - 36

                                          = 24

so the sum of the remaining sides, ie, b+d= 24

since b and d are equal (opp.sides of a rect.)

b=d=24/2=12

therefore, b=12; c=18; d=12

i really hope i'm clear...but if i'm not then please do ask...

Answer:

Step-by-step explanation:

Perimeter of a plane shape is the distance around the shape. The formula for determining the perimeter of a rectangle expressed as

Perimeter = 2(length + width)

The rectangle has for side. Two parallel and opposite sides are equal. There, if the length of one side of the rectangle is 18 units, it means that the length of the opposite side is also 18 units.

Since the perimeter of the rectangle is 60 units, it means that

2(18 + W) = 60

18 + W = 60/2 = 30

W = 30 - 18 = 12

Therefore, the lengths, in units, of the other three sides are 18 , 12 and 12 units

Answer: radius of the circle is 8.5 units

Step-by-step explanation:

The diagram of the circle and the inscribed triangle is shown in the attached photo. Looking at the length of each side of the triangle given, the lengths form a Pythagorean triple. We can confirm by applying Pythagoras theorem

Hypotenuse^2 = opposite side^2 + adjacent^2. It becomes

17^2 = 8^2 + ``15^2

289 = 64 + 225

289 = 289

This means that the triangle formed is a right angle triangle.

According to Thales theorem,

The diameter of the circle always subtends a right angle to any point on the circle. Since the diameter is the longest side of the circle and the angles is formed on a point on the circle,

Diameter = 17

Radius = diameter/2 = 17/2 = 8.5

Answer:

8.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diagram of triangle AMK is shown on the attached photo. To determine AM, we would apply trigonometric ratio since triangle AMP is a right angle triangle.

Sin# = opposite/hypotenuse

Sin 72 = 10/AM

AMSin72 = 10

AM = 10/Sin72 = 10/0.9511

AM = 10.51

To determine MK,

Cos# = adjacent/hypotenuse

Cos 50 = 10/MK

MKCos50 = 10

MK = 10/Cos50 = 10/0.6428

MK = 15.6

AK = AP + KP

Tan# = opposite/adjacent

Tan 72 = 10/AP

AP tan 72 = 10

AP =10/tan72 = 10/ 3.0777 = 3.25

Tan 50 = KP/10

KP = 10tan50

KP= 10× 1.1918 = 11.918

Therefore,

AK = 3.25 + 11.918 = 15.168

To find AM, MK, and AK in triangle AMK, use trigonometry and given angle measurements. Subtract the measure of angle PMK from 180 degrees to find the measure of angle A. Then, use the sine rule to find AK and AM.

To find the lengths of AM, MK, and AK, we can use trigonometry and the given angle measurements. Firstly, we can find MK by subtracting the measure of angle PMK from 180 degrees to find the measure of angle A. Then, we can use the sine rule to find the lengths of AK and AM. Using the given information, we can set up equations and solve for the unknown lengths.

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Explanation:

Marginal distribution: This distribution gives the probability for each possible value of the Random variable ignoring other random variables. Basically, the values of other variables is not considered in the marginal distribution, they can be any value possible. For example, if you have two variables X and Y, the probability of X being equal to a value, lets say, 4, contemplates every possible scenario where X is equal to 4, independently of the value Y has taken. If you want the probability of a dice being a multiple of 3, you are interested that the dice is either 3 or 6, but you dont care if the dice is even or odd.

Conditional distribution: This distribution contrasts from the previous one in the sense that we are restricting the universe of events to specific condition for other variable, making a modification of our marginal results. If we know that throwing a dice will give us a result higher than 2, then to in order to calculate the probability of the dice being a multiple of 3 using that condition, we have two favourable cases (3 and 6) from 4 total possible results (3,4,5 and 6) discarding the impossible values (1 and 2) from this universe since they dont match the condition given (note that the restrictions given can also reduce the total of favourable cases).

The joint distribution calculates the probabilities for two different events (related to two different random variables) occuring simultaneously. If we want to calculate the joint probability of a dice being multiple of 3 and greater than 2 at the same time, our possible cases in this case are 3 and 6 from 6 possible results. We are not discarding 1 or 2 as possible results because we are not assuming, that the dice is greater than 2, that is another condition that we should met in the combination of events.

The concepts of conditional distribution, marginal distribution, and joint distribution are used in statistics to analyze relationships between two variables. The joint distribution represents frequencies or probabilities of different combinations of values, the marginal distribution focuses on each variable individually, and the conditional distribution focuses on subsets of the population based on a specific condition or value.

The conditional distribution, marginal distribution, and joint distribution are concepts used in statistics to analyze relationships between two variables in a dataset.

The joint distribution represents the frequencies or probabilities of different combinations of values for the two variables. It is typically presented in a two-way frequency table or as a joint probability function.

The marginal distribution focuses on the frequencies or probabilities of each variable individually, disregarding the other variable. It represents the disconditional distribution focuses on subsets of the population defined by a specific condition or value of one variable. It represents the tribution of one variable while ignoring the other.

The distribution of one variable within a specific condition or value of the other variable.

For example, in a two-way table with gender and favorite sport, the joint distribution represents the frequencies of males and females who prefer different sports. The marginal distribution represents the frequencies of males and females overall, ignoring their sport preferences. The conditional distribution represents the frequencies of different sports within each gender.

Answer:

a. (x + 4)² + (y – 7)² = 3²

Step-by-step explanation:

General equation for a circle is:

(x – h)² + (y – k)² = r²

h and k are the center (h, k), and r is the radius.

They want a center of (-4, 7) so h=-4 and k=7

They want a radius of 3 so r=3

plug it into the equation.

(x – h)² + (y – k)² = r²

(x – (-4))² + (y – (7))² = (3)²

(x + 4)² + (y – 7)² = 3²

Answer: (  x + 4 )² + ( y - 7 )² = 3²

Step-by-step explanation:

Formula for the equation of a circle centre  (a, b), radius r

 = ( x - a )² + ( y - b )² = r²--------------------------------------------------------1

 a = -4 and b = 7 while r = 3

Therefore substitute for a , b and r  in the equation 1 above to get the equation of the circle.

 ( x - (-4 ) )² + ( y - 7 )² = 3²

open the brackets through direct or indirect methods gives

( x + 4 )² + ( y - 7 )² = 9

x² + 8x + 16 + y² - 14y + 49 = 9

x² + y² + 8x - 14y + 16 + 49 - 9 = 0

x² + y² + 8x - 14 y + 116 = 0

Answer:

  2880

Step-by-step explanation:

Sunnyside has 3 of every 4 books, so has ...

  (3/4)(3840) = 2880 . . . books

Answer: 60

Step-by-step explanation:

let x="students enrolled in all three"

"170 are enrolled in both Math and English" __ so 170-x are enrolled in ONLY Math and English

"150 are enrolled in both History and English" __ so 150-x are enrolled in ONLY History and English

"300 are enrolled in Math and History" __ so 300-x are enrolled in ONLY Math and History

"500 students are enrolled in at least two of these three classes"

so (170-x)+(150-x)+(300-x)+x = 500

620-2x=500

120=2x

60=x

Final answer:

By applying the principle of inclusion-exclusion, we can find that 60 people are enrolled in all three classes: art, drama, and piano.

Explanation:

To solve the problem of determining how many people are enrolled in all three classes (art, drama, and piano), we use the principle of inclusion-exclusion. The principle allows us to find the number of individuals enrolled in at least one of the classes by adding the numbers enrolled in each pair of classes and then subtracting the number counted twice. The formula for three sets A, B, and C is given by:

[tex]|A \union\ B \union\ C| = |A| + |B| + |C| - |A \intersect\ B| - |B \intersect\ C| - |A \intersect\ C| + |A \intersect\ B \intersect\ C|.[/tex] We are given the following information:

170 people are enrolled in both art and drama

150 people are enrolled in both piano and drama

300 people are enrolled in both art and piano

Let X represent the number of people enrolled in all three classes. The sum of people enrolled in at least two classes is 500. So, we need to solve the equation:

170 + 150 + 300 - 2X = 500

620 - 2X = 500

X = (620 - 500) / 2

X = 120 / 2

X = 60

Therefore, 60 people are enrolled in all three classes: art, drama, and piano.

Final answer:

The expression for the total cost is (3 × $2.00) + (2 × $1.50). After performing the calculations, the total cost for Mark's pretzels and juice is $9.00.

Explanation:

To calculate the total cost of the pretzels and juice that Mark bought, we need to multiply the quantity of each item by its price and then add the totals for each item.

The expression for the pretzels is 3 bags × $2.00 per bag, which equals $6.00. For the juice, the expression is 2 bottles × $1.50 per bottle, which equals $3.00. The total cost is the sum of these two amounts, so we have:

Total Cost = Cost of Pretzels + Cost of Juice
= (3 × $2.00) + (2 × $1.50)
= $6.00 + $3.00
= $9.00

Therefore, the total cost for the pretzels and juice is $9.00.

Answer:

A. t=500/200

Step-by-step explanation:

If Distance = d

Product Rate = r

Time = t

and the equation states that;

d = r x t

then by dividing the equation by r we get;

t = d / r

By putting in the values of d = 500 and r = 200 in the above equation we get;

t = 500 / 200

Answer: B

Step-by-step explanation:

d = t * r

t = d/r

t = 500d/200

Answer:

Marcos Should invest with the first bank

Step-by-step explanation:

Formula for finding compound interest is: A = p(1+\frac{r}{n})^{nt}

where

A = the future value of the investment

P = the principal investment amount (the initial deposit)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested

If marcos choose to invest with the first bank

A = 15000(1+\frac{0.025}{12})^{12*3} = £16166.81

If he choose to invest with the second bank

His principal become 15570 in the first year because of the 3.8% offer from the bank and t becomes 2.

A = 15570(1+\frac{0.01}{12})^{12*2} = £15884.27

Comparing the future value of his investment from both bank, Marcos will get more interest from investing with the first bank.

Answer:

Marco should choose the first bank to get the most interest over 3 years (£1153.36)

Step-by-step explanation:

According to the question, Marco is trying to invest his savings of £15,000 in a bank for three (3) years.

Two banks presented an offer with different interest rates. Bank 1 offers 2.5% interes rate per year while Bank 2 offers 3.8% interest rate for the 1st year and 1% interest rate for subsequent years.

In order to calculate the interest amount offered by both banks, we use the formula:

I = P × R × T ÷ 100

Where P= Principal amount to be invested

R = interest rate

T= Time in years

I = Interest amount

We will calculate the interest amount for each year, hence, T is 1 for each year.

Bank 1:

For 1st year;

P= £15,000 , R= 2.5%, T=1

I = 15000 × 2.5 × 1 ÷ 100

I = 375

To get the principal amount for year 2, we add 15000 + 375 = 15375

2nd year;

P= £15,375 , R= 2.5%, T=1

I = 15375 × 2.5 × 1 ÷ 100

I = 384.375

Principal amount for year3= 15375 + 384.375= 15759.38

3rd year;

P= £15,759.38 , R= 2.5%, T=1

I = 15759.38 × 2.5 × 1 ÷ 100

I = 393.98

Amount for three years = 15759.38 + 393.98= £16153.36

Hence, for the first bank, a total amount of £16153.36 was realized after three years with a total interest amount of £16153.36 - £15000 = £1153.36

Bank 2:

For 1st year;

P= £15,000 , R= 3.8%, T=1

I = 15000 × 3.8 × 1 ÷ 100

I = 570

To get the principal amount for year 2, we add 15000 + 570= 15570

N.B: The interest rate has been reduced for following years

2nd year;

P= £15,570 , R= 1%, T=1

I = 15570 × 1 × 1 ÷ 100

I = 155.7

Principal amount for year3= 15570 + 155.7 = 15725.7

3rd year;

P= £15,725.7 , R= 1%, T=1

I = 15725.7 × 1 × 1 ÷ 100

I = 157.257

Amount for three years = 15725.7 + 157.257 = £15882.95

Hence, for the second bank, a total amount of £15,882.95 was realized after three years with a total interest amount of £15882.95 - £15000 = £882.95

The interest amount of Bank 1 (£1153.36) after three years of investing £15000 will be more than the interest amount (£882.95) of Bank2 after investing the same amount for 3 years. Hence, Marco should choose Bank 1 to invest his savings.

The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5

Step-by-step explanation:

Let,

Cost of each fried crab claw = x

Cost of each gumbo = y

According to given statement;

4x+4y=32     Eqn 1

2x+y = 12.5   Eqn 2

Multiplying Eqn 2 by 2

[tex]2(2x+y = 12.5)\\4x+2y=25\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1

[tex](4x+4y)-(4x+2y)=32-25\\4x+4y-4x-2y=7\\2y=7[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{7}{2}\\y=3.5[/tex]

Putting y=3.5 in Eqn 2

[tex]2x+3.5=12.5\\2x=12.5-3.5\\2x=9[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{9}{2}\\ x=4.5[/tex]

The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5

Keywords: linear equation, subtraction

Learn more about subtraction at:

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The price for each cup of gumbo is $3.5.

The student's question poses a system of linear equations problem where we need to determine the cost of each order of fried crab claws and each cup of gumbo. We can define two variables: let x be the price of an order of fried crab claws and y be the price of a cup of gumbo. The first condition gives us the equation 4x + 4y = 32, and the second condition gives us the equation 2x + y = 12.5. Solving the system of equations by multiplying the second equation by 4 and subtracting from the first one yields:

8x + 4y = 50

4x + 4y = 32

(8x + 4y) - (4x + 4y) = 50 - 32

4x = 18

x = 4.5

Thus, the price for each order of fried crab claws is $4.5. Now, substituting x in one of the equations to find y we get:

2(4.5) + y = 12.5

9 + y = 12.5

y = 12.5 - 9

y = 3.5

So, the price for each cup of gumbo is $3.5.

Answer:

the answer is closest to option d) $2800

Step-by-step explanation:

Assume,

Cost per square meter = y = 92$

Step 1:

For Sphere 1:

Circumference = C1 = 5.5 m

Formula for Circumference is;

C = 6.2832(R)

Where R = radius of sphere

Therefore for radius;

C1 = 6.2832(R1)

5.5 = 6.2832(R1)

R1 = 5.5/6.2832

R1 = 0.87 m

Formula for Area;

A1 = 4π(R1)²

Since,  

π = 3.14

Therefore;

A1 = 4*3.14*(0.87)²

A1 = 9.51 m²

Cost of finishing for sphere 1 will be;

X1 = 92*A1

X1 = 92*9.51

X1 = $875

Step 2:

For Sphere 2:

Circumference = C2 = 7.85 m

Formula for Circumference is;

C = 6.2832(R)

Where R = radius of sphere

Therefore for radius;

C2 = 6.2832(R2)

7.85 = 6.2832(R2)

R2 = 7.85/6.2832

R2 = 1.25 m

Formula for Area;

A1 = 4π(R2)²

Since,  

π = 3.14

Therefore;

A1 = 4*3.14*(1.25)²

A1 = 19.63 m²

Cost of finishing for sphere 1 will be;

X2 = 92*A2

X2 = 92*19.63

X2 = $1,806

Step 3:

Now for total cost;

X = X1 + X2

X = 875 + 1806

X = $2,681

Answer:D no correlation

Step-by-step explanation:because if you were to draw a straight line, it wouldn’t be near all of the lines

Answer:

1) [tex]31 < p<37[/tex]

For this case the values that satisfy the inequality are: 32,33,34,35,36

And we can analyze one by one the number:

[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1

[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1

[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1

[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1

[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1

So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.

2) For this cas this statement is FALSE, since we have a counterexample on this case:

[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1

And since we have one element that not satisfy the condition that's FALSE.

Step-by-step explanation:

For this question we need to use the following definition "If an integer p can b expressed as the product of two integers, each of which that is greater then 1, then the integer p can be considered as a composite number". And this number is not the same as prime number.

Part 1

[tex]31 < p<37[/tex]

For this case the values that satisfy the inequality are: 32,33,34,35,36

And we can analyze one by one the number:

[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1

[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1

[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1

[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1

[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1

So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.

Part 2

For this cas this statement is FALSE, since we have a counterexample on this case:

[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1

And since we have one element that not satisfy the condition that's FALSE.

Answer:

the answer is option C. 0.3(x+8,000)=0.2x+12,000

Step-by-step explanation:

Assume;

Purchase cost of car = x

Purchase cost of truck = y = 8000 + x

Selling price of truck = a =12000+b

Selling price of car = b

Since profit for truck is 30%, therefore;

a = 30%*y

a = (30/100)*y

a = 0.3y

Since profit for car is 20%, therefore;

b = 20%*x

b = (20/100)*x

b = 0.2x

Now take;

A = 0.3y

12000 + b = 0.3 (8000+x)

12000 + 0.2x = 0.3(8000+x)

OR

0.3(8000+x) = 0.2x +12000

Answer: 80

Step-by-step explanation:

Given : Number of married couples = 5

Number of people required = 3

Since , the committee does not include two people who are married to each other,

We consider 1 married couple as one people , then the number of ways to select 3 persons =[tex]^{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5\times4\times3!}{3!\times2}=10[/tex]

Also, chances of selecting any partner = 2  (either Husband or wife)

So for 3 persons the total chances =(2) (2) (2)

Total number of ways to form the committee so that the committee does not include two people who are married to each other= 10 x (2) (2) (2) =80

Hence, the number of committees are possible = 80

Answer: The ratios are proportional

Step-by-step explanation:

Tony tacos is selling 15 sodas for 10 dollars.

Nicks nachos is selling 30 sodas for 20dollars. The ratio of the number sodas sold by Tony tacos to the number of sodas sold by Nicks nachos is 15/30 = 1/2

The ratio of the cost of sodas sold by Tony tacos to the cost of sodas sold by Nicks nachos is 10/20 = 1/2

So the number of sodas sold is proportional to the cost.