3 siblings are 3 different ages. The oldest is twice the age of the middle sibling, and the middle sibling is six years older than one-half the age of the youngest sibling. Write a composite function that gives the oldest sibling's age in terms of theyoungest. Explain how you got your answer.

Answer:

center = (-8, 7)

radius = 8 units

Step-by-step explanation:

Equation of a circle: \((x-h)^2+(y-k)^2=r^2\)

(where (h, k) is the center of the circle and r is the radius)

Rewrite the given equation:

\(x^2+y^2+16x-14y+49=0\)

\(\implies x^2+16x+y^2-14y+49=0\)

\(\implies (x+8)^2-64+(y-7)^2-49+49=0\)

\(\implies (x+8)^2+(y-7)^2=64\)

Therefore:

Answer:

The circle is centered at (8,0)

The circle has a radius of 10 units.

Step-by-step explanation:

trust

Answer:

2 x 3 x 3

Step-by-step explanation:

Prime Factorization is finding which prime numbers multiply together to make the original number.

Prime numbers are whole numbers greater than 1 that cannot be made by multiplying other whole numbers: 2, 3, 5, 7, 11, 13, 17, 19 ... etc.

Factors are the numbers you multiply together to get another number.

To find the prime factors of 18:

Start with dividing the number by the first prime number, 2.

So can 18 be divided by 2?  Yes:  18 ÷ 2 = 9   ⇒  So 2 is a factor.

However, 9 is not prime number.  Can 9 be divided by 2 and give us a whole number? No, as 9 ÷ 2 = 4.5 and 4.5 is not a whole number.

So let's try dividing 9 by the next prime number, 3:  9 ÷ 3 = 3.

We can now stop as we divided by the prime number 3 AND the result is a prime number.

Therefore, the prime factorization of 18 = 2 x 3 x 3

As two of the factors are the same (3) , we can also write this using exponents:  18 = 2 x 3²

The total number of coins in Lucy's coin collection is equal to 80 coins.

Given the following data:

To the total number of coins in Lucy's coin collection:

Since the percentage of the quarters in Lucy's coin collection is equal to fifteen percent (15%) of the total number of coins. Thus, we would multiply the total number of coins by 15% and equate it to 12 quarters.

Total number of coins:

\(\frac{15}{100} \times C = 12\\\\15C=12 \times 100\\\\15C =1200\\\\C=\frac{1200}{15}\)

C = 80 coins.

Read more on word problem here: https://brainly.com/question/24604067

Answer:

80 coins

Step-by-step explanation:

Let the total number of coins be C.

Given the following data:

Percentage of quarters = 15%

Total number of quarters = 12 quarters

To the total number of coins in Lucy's coin collection:

Since the percentage of the quarters in Lucy's coin collection is equal to fifteen percent (15%) of the total number of coins. Thus, we would multiply the total number of coins by 15% and equate it to 12 quarters.

Total number of coins:

C = 80 coins.

So the total number of coins in Lucy's coin collection is 80 coins.

Answer:

I mean, I think it varies by house and by location but a general range would be:

Min: 64 *F

Max: 74 *F

The expression, \(y^{-8}\), can be rewritten as positive exponents as 1/\(y^{8}\).

According to the question,

We have the following expression:

\(y^{-8}\)

Now, we know that if a power of a number is in negative and we have to convert the power into positive then the complete term is inversed and the term then has positive exponents.

(More to know: numbers with same base in multiplication will result in addition of exponents.)

For example, \(y^{-2}\) can be rewritten using positive exponents as 1/\(y^{2}\).

In the same, the given expression can be rewritten using positive exponents as:

1/\(y^{8}\)

Hence, the correct option is C (the third one).

To know more about exponents here

https://brainly.com/question/15993626

#SPJ1

Step-by-step explanation:

since there is no graph it's a bit hard to answer this question, but I'll try. I can help solve the equation that represents the ratio of the two numbers:

(x + 1/2)/y = 1/3

This can be simplified to:

x + 1/2 = y/3

To graph this equation, you would need to plot points that satisfy the equation. One way to do this is to choose a value for y and solve for x. For example, if y = 6, then:

x + 1/2 = 6/3

x + 1/2 = 2

x = 2 - 1/2

x = 3/2

So one point on the graph would be (3/2, 6). You can choose different values for y and solve for x to get more points to plot on the graph. Once you have several points, you can connect them with a line to show the relationship between x and y.

(Like I said, it was a bit hard to answer this question, so I'm not 100℅ sure this is the correct answer, but if it is then I hoped it helped.)

Answer:

D = 1,7,10

Step-by-step explanation:

-7 = 2x - 9

x = 1

5 = 2x - 9

x = 7

11 = 2x - 9

x = 10

the domain of (1,7,10)

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

Learn more about Kristine from

https://brainly.com/question/27244350

#SPJ11

Answer:

39.9 grees

Step-by-step explanation:

Since 4.2 kribs = 18 grees

Then,

1 krib = 18/4.2 grees

9.3 kribs = (18/4.2) x 9 3

9.3 kribs = 39.9 grees.

1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

For similar question on probability.

https://brainly.com/question/30599894

#SPJ11

Answer: 3.4 x 10^-4 (aka 10 to the negative 4th power)

Step-by-step explanation:

A sample of 68  is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean for the standard deviation of 40 hours

Since a level =1-0.96/2 =0.02, here the  Z value of 1-a = 1-0.02= 0.98 , for which z=2.055 .Now we know that the formula for margin is:

M = z*σ/√n, where σ is the standard deviation and n is the sample size since we are provided with the standard deviation of  40  and M=10. so,

=> 10= 2.055*40/√n

=>10√n= 2.055*40

=>√n =  82.2/10

=>n=67.6 ,which is almost  68

To know more about standard  deviation refer to the  link brainly.com/question/23907081

#SPJ4

Answer:

y>2x+1

Step-by-step explanation:

The GPA of a student who studies for 15 hours a week is 2.935.

What is a GPA?

Grade point average, or GPA, is a conventional method of evaluating academic performance in the United States on a scale of 0 to 4.

How to calculate GPA?

To calculate your GPA, divide the total number of grade points earned by the total number of letter-graded units undertaken.

Here,

We have an equation y = 0.164x + 0.475

put x= 15

we get,

y = 0.164* 15 + 0.475

y = 2.935

Hence, The GPA of a student who studies for 15 hours a week is 2.935

To learn more about the GPA from the given link

https://brainly.com/question/14626093

#SPJ13

The moment-generating function for y is given as eⁿᵇ - eⁿᵃ / n(b-a) and derivation of  moment-generating function of y is e-1/t

Given that,

The interval (0, 1) is covered by a uniform distribution of y, and a > 0 is a constant.

The moment generating function is eⁿᵇ - eⁿᵃ / n(b-a)

The given interval is (0,1)

Here a =0;

         b=1;

Now substitute the values of a and b in the above moment generating function we get,

y=eⁿᵇ - eⁿᵃ / n(b-a)

y=e^1-e^0/t(1-0)

y= e-1/t

Therefore, the derivation of the moment generating function is e-1/t

Learn more about moment-generating function here:

brainly.com/question/15061360

#SPJ4

Answer:

124568

865421

Step-by-step explanation:

please give 5 stars then i will say the rest

Answer:

y = x - 3

Step-by-step explanation:

Equation of line in slope point form is given as:

y - y_1 = m(x - x_1)

\(y - y_1 = m(x - x_1) \\ y - 2 = 1(x - 5) \\ y - 2 = x - 5 \\ y = x - 5 + 2 \\ y = x - 3 \\ \)

Answer:

\(T_n = -97n\)

Step-by-step explanation:

The actual sequence is: -97, -194, -291, -388

Required

Determine the nth term

nth term of an arithmetic progression is:

\(T_n = T_1 + (n - 1)d\)

Where

\(T_1 = First\ Term = -97\)

\(d = Common\ Difference = -194 - (-97) =-97\)

So:

\(T_n = T_1 + (n - 1)d\) becomes

\(T_n = -97 + (n - 1) * -97\)

\(T_n = -97 -97n + 97\)

Collect Like Terms

\(T_n = -97n + 97-97\)

\(T_n = -97n\)

Hence, a term of the sequence is:

\(T_n = -97n\)

Answer:

0.3 per ounce

4.80 / 16 = 0.3

0.3 × 16 = 4.80

The mean of the original data set is: mean = (338 + 318 + 353 + 313 + 318 + 326 + 307 + 317 + 311 + 311) / 10 = 323.2

To find the five-number summary, we need to order the data set from smallest to largest:

{307, 311, 311, 313, 317, 318, 318, 326, 338, 353}

The five-number summary is as follows:

Minimum: 307

First quartile (Q1): 311

Median (Q2): 317.5 (average of the 5th and 6th values)

Third quartile (Q3): 326

Maximum: 353

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). In this case:

IQR = Q3 - Q1 = 326 - 311 = 15

To identify any outliers, we need to calculate the lower and upper bounds:

Lower bound = Q1 - 1.5 × IQR = 311 - 1.5 × 15 = 289.5

Upper bound = Q3 + 1.5 × IQR = 326 + 1.5 × 15 = 347.5

Any values that are less than the lower bound or greater than the upper bound are considered outliers. In this case, there are no outliers.

Removing outliers will not affect the median or quartiles, but it will affect the mean. In this case, since there are no outliers, removing values will not affect the mean. The mean of the original data set is:

mean = (338 + 318 + 353 + 313 + 318 + 326 + 307 + 317 + 311 + 311) / 10 = 323.2

Learn more about data set here:

https://brainly.com/question/16300950

#SPJ11

Answer:

A or the first answer is correct

Step-by-step explanation:

3650 - 2000 = 1650

1650 / (divided by) 150 = 11

you can also check your work by doing 150 *(times) 11 = 1650

1650 + 2000 = 3650

Hello.

In order to find the slope of the given line, we should use the slope formula:

\(\mathrm{\displaystyle\frac{y2-y1}{x2-x1}}\)

y₂= the y-coordinate of the second point (6

y₁= the y-coordinate of the first point (-14)

x₂=the x-coordinate of the second point (-10)

x₁=the x-coordinate of the first point (-4)

Let's plug in the values and solve:

\(\mathrm{\displaystyle\frac{6-(-14)}{-10-(-4)}=\frac{6+14}{-10+4} =\frac{20}{-6} =-\frac{20}{6} =-\frac{10}{3} }\)

Answer:

\(\Large\boxed{\sf{\displaystyle-\frac{10}{3} }}\)

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

a) the solution of the differential equation is x = (1/sin(√3)t) + (2 cos(√3)t/sin(√3)t)

b) the solution of the differential equation is x = sin(t) + 2 cos(t)

a) Given differential equation is x''+x'+3x=0

The initial conditions are x(0)=1 and x'(0)=2

We have to solve the differential equation using Laplace transform.

So, applying Laplace transform on both sides, we get:

L{x''+x'+3x} = L{0}L{x''}+L{x'}+3L{x} = 0

(s^2 L{x}) - s x(0) - x'(0) + sL{x} - x(0) + 3L{x} = 0

(s^2+1)L{x} - s - 1 + 3L{x} = 0(s^2+3)

L{x} = s+1L{x} = (s+1)/(s^2+3)

L{x} = (s/(s^2+3)) + (1/(s^2+3))

Taking inverse Laplace on both sides, we get:

x = (1/sin(√3)t) + (2 cos(√3)t/sin(√3)t)

Thus, the solution of the differential equation is x = (1/sin(√3)t) + (2 cos(√3)t/sin(√3)t)

b) Given differential equation is x''+x=sin(t)

The initial conditions are x(0)=1 and x'(0)=2

We have to solve the differential equation using Laplace transform.

So, applying Laplace transform on both sides, we get:

L{x''}+L{x} = L{sin(t)}(s^2 L{x}) - s x(0) - x'(0) + L{x}

= L{(1/(s^2+1))}s^2 L{x} + L{x}

= (s^2+1)L{(1/(s^2+1))}L{x}

= 1/(s^2+1)L{x}

= (1/(s^2+1)) + (2s/(s^2+1))

Taking inverse Laplace on both sides, we get:

x = sin(t) + 2 cos(t)

Thus, the solution of the differential equation is x = sin(t) + 2 cos(t)

To know more about differential equation, visit:

https://brainly.com/question/32645495

#SPJ11

Answer:

$16.50

Step-by-step explanation:

$27.50/5=5.5

5.5*3=16.5

Answer:

What we can do is calculating what one bag cost. If we know that 5 cost 27.50 dollars, to know how much does one cost we only divide:

27.50/5 = 5.50 dollars

Now, we know how much does one bag cost, so we multiply it by three:

5.50 * 3 = 16.50

Now, we know 3 bags cost 16.5 dollars

Expanding the equation gives us the final quadratic equation is 5x^2 - 15x - 30 = 0.

The quadratic equation with roots −3 and 6 can be written in the form:

(x - r1)(x - r2) = 0,

where r1 and r2 are the roots of the equation. Substituting the given roots, we have:

(x - (-3))(x - 6) = 0,

which simplifies to:

(x + 3)(x - 6) = 0.

To include the leading coefficient of 5, we can multiply both sides of the equation by 5:

5(x + 3)(x - 6) = 0.

Expanding the equation gives us the final quadratic equation:

5x^2 - 15x - 30 = 0.

For more such questions on quadratic equation , Visit:

https://brainly.com/question/1214333

#SPJ11

Answer:

y = 5x

Because the slope is 5 and the y-intercept is 0.

Step-by-step explanation:

https://brainly.com/question/21273710

Need the slope only as y intercept is already 0 .

Slope:-

Equation of line

We introduced three conditions that should be met before we construct a confidence interval for an unknown population proportion: Random, Normal, and Independent.

There are three crucial requirements that must be met in order to establish a confidence interval. These are Independent, Random, and Normal.

Any survey is carried out objectively.

It is required to assure randomness. An independent choice is equally likely to be made in a random sample. Similar to how the confidence interval is built, normal is used to confirm which phenomena are being employed or to correct the approach if necessary. In a similar vein, independent is crucial because it contains the facts to be analyzed. For the purpose of calculating the standard deviation, independent is used.

Therefore, it's crucial to consider the Random, Normal, and Independent criteria while building a confidence interval.

To know more about random, normal and independent conditions, visit:

https://brainly.com/question/14093158

#SPJ4

A graphical plot with sales on the Y axis and time on the X axis is a:

a. Scatter diagram.

Using a single variable on each axis, the scatter diagram plots pairings of numerical data in an effort to identify any relationships between them. A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the more highly correlated the data is. You may also visualise the strength of any relationship. If the researcher believes there may be a correlation, a line of greatest fit can also be drawn on the graph.

Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

Thus, correct option: a

To know more about Scatter diagram refer to:

https://brainly.com/question/6592115

#SPJ4

Answer:

Infinitely many solutions

Step-by-step explanation:

Since you already have y isolated in one equation, you can plug it in and use it in the other equation

2y = 8x + 12

2(4x + 6) = 8x + 12

8x + 12 = 8x + 12

Get the x's to one side

12 = 12

Meaning you have infinitely many solutions.

Try plugging in any x value you can think of and the left side will always equal the right side. so

x = 0 --> 8(0) + 12 = 8(0) + 12

12 =12

x = 1 --> 8(1) + 12 = 8(1) + 12

20 = 20

and so on.

I graphed it here for you and the 2 functions are on top of each other which means at every x value y = 4x + 6 is equal to 2y = 8x + 12