Baby Kana's parents measure her height every month. H(t)H(t)H, left parenthesis, t, right parenthesis models Kana's height (in centimeters) when she was ttt months old. What does the statement H(160)=150H(160)=150H, left parenthesis, 160, right parenthesis, equals, 150 mean?

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

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: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:

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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Question is Incomplete,Complete question is given Below.

Ben earns $9 per hour and $6 for each delivery he makes. he wants to earn more than $155 in an 8-hour workday. what is the least number of deliveries he must make to reach his goal?

Answer:

Ben must make at least 14 Deliveries to achieve his goal.

Step-by-step explanation:

Hourly Rate = $9 per hour

Cost of each Delivery = $6

Number of hours to be worked = 8 hours.

Money needs to be earned =$155

we need to find the number of deliveries he must make to reach his goal.

Solution :

Let number of deliveries be 'x'.

Now we can say that Hourly rate multiplied by number of hours of work plus Cost of each delivery multiplied by number of deliveries should be greater than or equal to Money needs to be earned.

Framing in equation form we get;

[tex]9\times8+6x\geq 155[/tex]

Solving the equation we get;

[tex]72+6x\geq 155[/tex]

Subtracting both side by 72 using Subtraction property of Inequality we get;

[tex]72+6x-72\geq 155-72\\\\6x\geq 83[/tex]

Now Dividing both side by 6 using Division Property we get;

[tex]\frac{6x}{6} \geq \frac{83}{6} \\\\x\geq 13.83[/tex]

Hence Ben must make at least 14 Deliveries to achieve his goal.

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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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

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: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:

  2880

Step-by-step explanation:

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

  (3/4)(3840) = 2880 . . . books

Answer:

The probability of a successful event is the ratio of the number of successful events to the total number of events. In this case, a successful event is selecting a red marble from the box. The total number of events is the total number of marbles in the box:

Red marbles/Total number of marbles

4/12 divide

=1/3

The probability of her selecting a red marble is 1/3

The distribution of the marbles is given as:

Red = 4

Green = 8

The probability of selecting a red marble is:

P(Red) =Red/Total

So, we have:

P(Red) = 4/(4 + 8)

Evaluate

P(Red) = 1/3

Hence, the probability of her selecting a red marble is 1/3

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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.      

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:

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.

Answer:

The Company made 6 Bradley hats and 12 Karli hats.

Step-by-step explanation:

Given,

Total Amount of leather = 100 yards

Total number of hats = 19

Solution,

Let the number of Bradley hat be x.

And also let the number of Karli hat be y.

Total number of hats = 19

[tex]\therefore x+y=19\ \ \ \ \ equation\ 1[/tex]

Now, Bradly hats requires 4 yards and Karli hats requires 6 yards of leather.

So framing the above sentence in equation form, we get;

[tex]4x+6y=100\ \ \ \ \ equation\ 2[/tex]

Now, multiplying equation 1 by 4, we get;

[tex]4(x+y)=19\times4\\\\4x+4y=76\ \ \ \ \ equation\ 3[/tex]

Now we subtract equation 3 from equation 2, we get;

[tex](4x+6y)-(4x+6y)=100-76\\\\4x+6y-4x-4y=24\\\\2y=24\\\\y=\frac{24}{2}=12[/tex]

[tex]y=12[/tex]

On substituting the value of y in equation 1, we get the value of x.

[tex]x+y=19\\\\x+12=19\\\\x=19-12=6[/tex]

Hence The Company made 6 Bradley hats and 12 Karli hats.

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:

[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:

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: 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.

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:

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 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

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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: 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:

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

Answer:

[tex]10[/tex]

Step-by-step explanation:

Given that [tex]R,S,T[/tex] are mid points of the sides of the triangle [tex]ABC[/tex]

Perimeter of [tex]\Delta ABC=AB+AC+BC=20[/tex]

In the [tex]\Delta ARS\ and\ \Delta ABC[/tex]

[tex]\frac{AR}{AB}=\frac{1}{2} \ \ (as\ R\ is\ mid\ point\ of\ AB)[/tex]

[tex]\frac{AS}{AC}=\frac{1}{2} \ \ (as\ S\ is\ mid\ point\ of\ AC)[/tex]

[tex]\angle A=\angle A[/tex]

from [tex]SAS[/tex] these two triangles are similar

Hence

[tex]\frac{RS}{BC}=\frac{AR}{AB}=\frac{AS}{AC}=\frac{1}{2}[/tex]

[tex]RS=\frac{BC}{2}[/tex]

Similarly [tex]RT=\frac{AC}{2}\ and\ ST=\frac{AB}{2}[/tex]

[tex]Perimeter\ of \ \Delta RST=RS+ST+RT\\\\=\frac{BC}{2}+\frac{AR}{2}+\frac{AC}{2}   \\\\=\frac{AB+AC+BC}{2}\\\\=\frac{20}{2}\\\\ =10[/tex]

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 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.

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: