A prime number is an integer greater than 1 with exactly two different positive factors, 1 and the number itself. There are three children in a family. Each of their ages is a prime number. The sum of their ages is 41 and at least two of the children have ages that differ by 16. Determine all possibilities for the ages of the children.

Answers

Answer 1

Answer:

Hence,

a=19,b=19,c=3

a=11,b=7,c=23

Step-by-step explanation:

[tex]Let\ their\ ages\ be\ a,b\ and\ c\ respectively, where\ a,b,c\ are\ primes\\Hence,\\a+b+c=41\\b-c=16\\Listing\ out\ all\ the\ primes\ from\ 0\ to\ 41\ we\ get:\\2,3,5,7,11,13,17,19,23,29,31,37,\\Hence,\\Lets\ seperate\ out\ the\ primes\ who\ differ\ by\ 16 :\\3\ and\ 19, 7\ and\ 23\ ,[/tex]

Hence,

[tex]Lets\ consider\ this\ set\ as\ b,c:\\Hence,\\To\ find\ a \\a=41-(b+c)\\Hence, By\ doing\ this\ indiviually\ we\ get:\\[/tex]

[tex]a=41-(19+3)\\a=41-22\\a=19\\Hence, a=19,b=19,c=3[/tex]

[tex]a=41-(23+7)\\a=41-30\\a=11\\Hence, a=11,b=7,c=23[/tex]


Related Questions

What is the quotient of x and three increased by 12 = 20

Answers

Answer:

x= 24

Step-by-step explanation:

Quotient means divide, increased means add

x/3 + 12 =20

Subtract 12 from each side

x/3 +12-12 = 20-12

x/3=8

Multiply each side by 3

x/3 * 3 =8*3

x= 24

Answer:700 / n, the quotient of 700 and a number. 2w, two times a ... h - 3, three less than a number ... 20 + m, 20 more than a number. x - 12, a number decreased by 12.

Step-by-step explanation:

True or False?
2^3 < 3^2​

Answers

Answer:

True

Step-by-step explanation:

[tex]2^{3} <3^{2} \\2*2*2<3*3\\8<9[/tex]

Answer:

True

Step-by-step explanation:

The table shows the prices of some candy items at a store. Jake selected 1.6 pounds of Fruit Chews and 2.6 pounds of Jelly Beans. The sales tax for his purchase was $0.52. .Item. .Price Per Pound. .Fruit Chews. $4.70 .Jelly Beans. $2.35 .Chocolate. $3.50 .If Jake had $25 to spend at the candy store, how much money did Jake have left after his purchase?

Answers

Answer:

The amount of money Jake had left after his purchase is $10.85

Step-by-step explanation:

The amount of Fruit Chews Jake selected = 1.6 pounds

The amount of Jelly Beans Jake selected = 2.6 pounds

The sales tax = $0.52

The amount of money Jake had to spend = $25

The table of values are;

Price Per Pound     [tex]{}[/tex]                  

Fruit Chews = $4.70

Jelly Beans = $2.35

Chocolate = $3.50

The amount of money Jake had to spend $25

The total amount of the candies Jake bought = 1.6 × $4.70 + 2.6 × $2.35 = $13.63

The total amount Jake spent = The total amount of the candies Jake bought + The sales tax

The total amount Jake spent = $13.63 + $0.52 = $14.15

The amount of money Jake had left after his purchase = The amount of money Jake had to spend - The total amount Jake spent

The amount of money Jake had left after his purchase =  $25 - $14.15 = $10.85

The amount of money Jake had left after his purchase = $10.85.

There are 6 people in George's family. How much did George's mom pay for tickets? Show how you found your solution.

Answers

Answer:

$75

Step-by-step explanation:

To find out how much George's mom paid for the 6 tickets, first find the unit rate, that is cost per ticket.

The unit rate/constant of proportionality between cost of tickets (y) and number of tickets (x) can be calculated using the coordinates of any points on the graph.

Using (4, 50), this means that 4 tickets cost $50.

Unit rate/constant of proportionality = y/x = 50/4 = 12.5

This means a ticket costs $12.5.

Therefore, 6 tickets would cost:

6 tickets × $12.5 = $75.

George's mom paid $75 for the tickets?

Tom have 47 quaters his dad gave him 14 how many top have in all

Answers

Answer:

61 or 33

Step-by-step explanation:

47+14=61 or 47-14 =33

Answer:

I can help

Step-by-step explanation:

Quarters in help is 61 but in money its $16. Hope this helps.

The probability that Terry buys a sandwich is 0.4.
The probability that Terry gets the bus is 0.9.
Assuming the events are independent, what is the probability that Terry buys a sandwich and gets the bus?

Answers

Answer:

The probability that Terry buys a sandwich and gets the bus is 0.36

Step-by-step explanation:

When two events are called independent, it means that the happening of one event doesn't affect the happening of other event.

Let A be the event that Terry buys a sandwich

Let B be the event that Terry gets the bus

Then

[tex]P(A) = 0.4\\P(B) = 0.9[/tex]

When two events are independent, their probabilities are multiplied i.e.

[tex]P(A\ and\ B) = P(A) * P(B)\\= 0.4 * 0.9\\= 0.36[/tex]

Hence,

The probability that Terry buys a sandwich and gets the bus is 0.36

PLZZZZ HELP ME!!!!! factor 15x + 81

Answers

Answer: 3(5x+27)

Step-by-step explanation:

15 and 81 are both divisible by 3.

Answer:

-5.4

Step-by-step explanation:

x= -81/15= -5.4

find the area of the figure. (sides meet at right angles.) 2m 2m 2m 2m 3m 7m 7m 7m ​

Answers

The answer is 43 square meters

3 and 4 plz help me im nice

Answers

Answer:

3. 7.2

4. 20

Step-by-step explanation:

You guys are life savers but does anyone know the answers to these questions? I’m so confused rn

Answers

Answer:

The third choice

Step-by-step explanation:

We need to find the slope and y-intercept of the line and then put it into y = mx = b form. To find the slope, pick a point on the line; I will use (-2, 5); count how many units up you need to go to get to the next point on the line, which in this case it would be 3. The count how many to the right or left you would need to go, which is 1 to the left. Moving left means a negative, so it is -1. Your slope fraction would be [tex]\frac{3}{-1}[/tex] , since slope is rise over run. You can sub this fraction in for m in y = mx + b, which will give you a revised equation of y = -3x = b. To find the y intercept, or b, just find the point where the line crosses the y-axis, which is -1. So, the equation is now y = -3x - 1.The correct answer is third choice.

Find the area of the circle.

Answers

Answer:

8.938

Step-by-step explanation:

Answer:

dont at me if its wrong but i think its the second one

Step-by-step explanation:

Find the value of X in the triangle

Answers

Answer:

             44°

Step-by-step explanation:

[tex]m\angle BAC=180^o-124^o=56^o\\\\\overline{AB}=\overline{BC}\quad\implies\quad m\angle BCA=m\angle BAC=56^o\\\\m\angle ABC=180^o-2\cdot56^o=68^o[/tex]

[tex]m\angle DBE=m\angle ABC=68^o[/tex]   {vertical angles}

[tex]\overline{BD}=\overline{DE}\quad\implies\quad m\angle DEB=m\angle DBE=68^o\\\\m\angle x=180^o-2\cdot68^o=44^o[/tex]

The table below represents the number of hours a student worked and the amount of money the student earned. What is the initial amount this student is paid? (Base pay, when number of hours, h = 0) I’LL PAY YOU 30 DOLLARS IN CASHAPP RIGHT NOW WHEN YOU DO IT!

Answers

i think it's (h= $6.25) because if you divide all y's by x you will get 6.25 every time. so the answer is most likely $6.25

The initial amount this student is paid is 0 and this can be determined by using the two-point slope form of the line.

Given :

The given table represents the number of hours a student worked and the amount of money the student earned.

The following steps can be used in order to determine the initial amount this student is paid:

Step 1 - The two-point form of the line can be used in order to determine the initial amount this student is paid.

Step 2 - So, the linear equation that represents the given situation is:

[tex]\rm \dfrac{d-50}{h-8}=\dfrac{93.75-50}{15-8}[/tex]

Step 3 - Simplify the above expression.

[tex]\rm \dfrac{d-50}{h-8}=6.25[/tex]

d - 50 = 6.25h - 50

d = 6.25h

Step 4 - Now, substitute the value of (h = 0) in the above expression.

d = 0

Therefore, the correct option is D) There is no base pay.

For more information, refer to the link given below:

https://brainly.com/question/11897796

A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 15 ​minutes, and then flies directly back to the hive at 16 feet per second. It is away from the hive for a total of 20 minutes.
b. How far is the flowerbed from the​ hive?

Answers

Answer:

Multiply 20

answer:[tex]20^{2}[/tex] feet

Step-by-step explanation:

Express the tangent of

Answers

Answer:

Step-by-step explanation:

TANGERINES

Answer:

of what ? finish the question

Find the third, fifth, and tenth terms of the sequence described by the rule.
A(n)= -5+ (n - 1)(6)
A(3) =
(Simplify your answer.)
A(5) =
(Simplify your answer.)
A(10) =
(Simplify your answer.)

Answers

A(3)= 6
A(5)= -19
A(10)= -49

Rich and Betsy Cuik started a small business. They manufacture a microwavable coffee-to-go cup called Cuik Cuppa Coffee. It contains spring water and ground coffee beans in a tea-bag-like pouch. Each cup costs the company $1.00 to manufacture. The fixed costs for this product line are $1,500. Rich and Betsy have determined the demand function to be q = -1,000p + 8,500, where p is the price for each cup.
Write the expense equation in terms of the demand, q.
Express the expense equation found in part (a) in terms of the price, p.

Answers

Answer: E= 1.00q + 1,500

Step-by-step explanation:

At a fair there are 18 game booths and 27 food booths. The fee for a food booth is $75 plus $5 per day. The fee for a game booth is $50 plus $8 per day. The fair lasts for d days, and all of the booths are rented for the entire time. Write and simplify an expression for the amount in dollars that the company is paid.

Answers

Answer:$$4444

Step-by-step explanation:

Write a linear function f with f(0) = 2 and f(2)=4.
f(x) =

Answers

Answer:

f(x) = x + 2

Step-by-step explanation:

(0, 2)

(2, 4)

Slope m = (4 - 2) / (2 - 0) = 1

y - 2 = 1(x - 0) ⇔ y = f(x) = x + 2

1. What is the m value (slope) and the b value (y-intercept)
in the equation y = 4x - 2 (m=
b=
2. What is the formula for slope?

Answers

[tex]y=4x-2[/tex]

m = 4 and b = -2

Formula to find slope can be meant 2 ways.

( 1 ) m = rise/run

( 2 ) [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] if it's a small text then it's m = y2-y1 / x2-x1

Misha found that the equation –|2x – 10| – 1 = 2 had two possible solutions: x = 3.5 and x = –6.5. Which explains whether or not her solutions are correct?

She is correct, because both solutions satisfy the equation.
She is not correct, because she made a sign error.
She is not correct, because there are no solutions.
She is not correct, because there is only one solution: x = 3.5.

Answers

She is not correct, because there are no solutions.

Explanation: If you isolate the absolute value by adding 1 both sides of the equation, you get -|2x-10|=3. There are no solutions, because the left side of the equation will always be negative and will never equal 3.

She is not correct, because there are no solutions. (Option C).

What is an equation?

An equation refers to any mathematical statement that contains the equality sign. Now we can see in the equation that there is a negative sign before the absolute value.

Now we have;

–|2x – 10| – 1 = 2

–|2x – 10| = 3

This is not possible because the absolute value does not return a negative value and the expression can never equal 3.

Thus, she is not correct, because there are no solutions.

Learn more about equation:https://brainly.com/question/10413253?

#SPJ9

identify an equation in slope-intercept form the line parallel to y=-3x+7that passes through (2,-4)

Answers

Answer:

y=-3x+2

Step-by-step explanation:

Same slope = parallel. You can aso double check this answer by either graphing using the desmos online graphing calculator or by plugging in the point into the equation y = -3(2) + 2 --> y = -6 + 2 --> y = -4, so we are correct.

Answer:

y=-3x+2

Step-by-step explanation:

In this equation the slope is the same as the original equation (-3), but has a different y-intercept meaning that this line is parallel. As for satisfying the requirement that the line is parallel and passes through (2,-4), I plugged the coordinates into the equation y=-3x+b to get  -4=-3(2)+b, and then found what b would have to equal to make the equation true.

(plus I put my answer into a graphing calculator to check my work)

help me someone solve this​

Answers

It’s b because the line passes through the y-axis at 1.

i really need help i have 1 minute to complete!!!!!

Answers

Answer:

8 angles are formed, and if angle one is 105° then angles 4, 5, and 8 are also 105°. and angles 2, 3, 6, and 7 would be 75°

de un numero se sabe que si a su cuadrado le restamos su mitad, se obtiene el mismo numero, Cuál es?

Answers

Answer:

2

Step-by-step explanation:

el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2

Answer: 2

Step-by-step explanation : el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2    Espero que ayude Ten un día maravilloso :)

What is the slope of the line that passes through the points (-6 , -4) and ( -12 , -4)? Write in simplest form plssss!

Answers

Answer:

the slope is zero

Step-by-step explanation:

Answer:

I think that: slope (m) = 0

Step-by-step explanation:

the equation of slope is m = y2-y1/x2-x1

so, y2 = -4, y1 = -4, and x2=-12, and x1= -6

Just substitute them into the equation:

m = -4 - -4 / -12- -16

m = 0

The slope is equal to 0

I hope this helps!

A function f(x)is graphed on the coordinate plane.

What is the function rule in slope-intercept form?



Enter your answer in the box.

f(x)=

Answers

Answer:

[tex]f(x)=2x+1[/tex]

Step-by-step explanation:

At x=0, the y is at 1  

at x=1, y went up to 3

the change between 3 and 1 is 2 therefore the equation is

[tex]f(x)=2x+1[/tex]

I hope this helps you and good luck!

Pls help ASAP!

What postulate are the triangles congruent by?

Answers

Answer:

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

- klhat percentage of 40 is 8?​

Answers

Step-by-step explanation:

8/40 x 100% = 20%

Topic: percentage

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

Geometric Series (attached image) muiltx choice

WILL GIVE THANKS !!

Answers

Answer:

Step-by-step explanation:

(B). - 28.7

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