a+b+c=68
b-3=a
c-5=b
now just solve the system of equations, substitue so that there are only b's in the equation:
a+b+c=68
(b-3) + b + (b+5) = 68
3b=66
b=22
Therefore Barbara is 22
The required age of barbar is 22 years.
Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Alice, Barbara and Carol are a, b and c.
Age Alice is 3 years younger than Barbara,
a = b - 3 - - - -(1)
Age Barbara is 5 years younger than Carol
b = c - 5
c = b + 5 - - - -(2)
Together the sisters are 68 years old i.e.
a + b +c =68
From equation 1 and 2
b - 3 + b + b +5 = 68
3b + 2 = 68
3b = 66
b = 33
Thus, the required age of barbar is 22 years.
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Write an algebraic expression yo find the number of seconds in n minutes
Answer:
60n seconds
Step-by-step explanation:
In 1 min, there are 60 seconds
So,
1 min = 60 secs
For n minutes, it becomes:
=> 60n seconds
The hourly revenue of a certain clothes manufacturer is represented by the function f(x) = -0.082x2 + 7.3x + 3.6 for the domain [0, 89]. According to this model, what is the maximum revenue this clothes manufacturer can have in an hour?
Answer:
166.07
Step-by-step explanation:
since the domain is [0,89] means the maximum amount is when x=89
vertex is where it reached the maximum amount:(44.512,166.07)
Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$[tex]Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$[/tex]
Answer:
Step-by-step explanation:
common denominator
[tex](\sqrt(2)+1)(\sqrt(2)-1) = (\sqrt{2})^2-1^{2}=2-1 = 1[/tex]
Add with common denominator
[tex]\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.[/tex]
[tex]= \frac{{\sqrt2-1}}{1} + \frac{\sqrt2+1}{1}[/tex]
[tex]=2* (\sqrt2)[/tex]
Two sides of a square are divided into fourths and another side of the square is trisected, as shown. A triangle is formed by connecting three of these points, as shown. What is the ratio of the area of the shaded triangle to the area of the square? Express your answer as a fraction.
==========================================================
Explanation:
Let's say this is a 1 by 1 square. The area is 1*1 = 1 square unit. Whatever the area of the triangle is, we divide it over 1 and it will yield the same value as the area of the triangle. In other words, the area of the triangle will be the answer.
Along the top we have 3 ticks to indicate the top segment has been cut into 3+1 = 4 equal parts. The horizontal distance from the the vertical side of the triangle to the peak of the triangle is 3/4 units. This is because we travel 3 ticks out of 4 total. So this is the height when we consider the vertical segment of the triangle to be the base.
The base is 1 unit as it spans the original square's side length
base = 1
height = 3/4
area of triangle = (1/2)*(base*height)
area of triangle = (1/2)*(1*3/4)
area of triangle = 3/8
ratio of triangle area to square area = (triangle area)/(square area)
ratio of triangle area to square area = (3/8)/1
ratio of triangle area to square area = 3/8Answer:
3/8
Step-by-step explanation:
let side of square=x
Area of a square =x^2
height of a triangle= 3x/4 ( 4/4=1/4) since height is only 3x/4 from the square)
( base =x same side as a square)
Area of a triangle=1/2 bh=1/2(x*3x/4)= 3x^2/8
the ratio of shaded triangle to the area= (3x^2/8)/x^2=3x^2/8x^2=3/8
On your own sheet of paper, make a stem-and-leaf plot of the following set of data and then find the range of the data.
Answer:
Step-by-step explanation:
The given set of data is 83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92.
Now the stem - leaf plot will be,
5 4
6 0 1 2 2
7 1 2 4 6 8
8 2 3 4 6 7
9 0 2 5 5 9
Since range of the data = Highest term of the data - Lowest term of the data
= 99 - 54
= 45
Therefore, range of the data set is 45.
The range of the data is 45.
The calculation is as follows:As we know that
Since range of the data = Highest term of the data - Lowest term of the data
= 99 - 54
= 45
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Plz help urgently i dont know how to do it
Answer:
11
Step-by-step explanation:
1650/15/10 = 11
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
One fifth of the square of a number
Answer:
The statement, one fifth of the square of a number is written as
[tex] \frac{1}{5} {x}^{2} [/tex]
Hope this helps you
What the correct answer now
Answer:
14.3
Step-by-step explanation:
first find length of VW
10/sin 119 = VW/ sin 26
VW = 5
angle V = 180 - 119 - 26 = 35
then area = 1/2 ab sin C
1/2 (10)(5) sin 35 = 14.33941.....
There are 30 children in a nursery at least one adult needs to be with eight children in the nursery work out the least number of adults needed in the nursery
Answer:
4 adults
Step-by-step explanation:
There will be 3 people handling eight children each and one person handling 6 children in a total of 30 children
Plz help I don't know what the answer is
Answer:
1) Is 180
2) Is 5
Step-by-step explanation:
express 1023.4567 correct to 3 significant figures
Answer:
1020
Step-by-step explanation:
well, the first three significant figures stops at the 102, so round the 1023.4567 to a whole number which just becomes 1023
then, round the answer so you only have the 102, so you would round down since 4 or less, which 3 is less than 4, you round down, and you would get 1020
that last 0 is not a significant figure because it does not have a decimal point or any other number following after it--any 0s at the end of a number are not significant if there is no decimal point or other number after them.
find the value of n if (81)^5/n = 243
Answer:
N = 14348907
Step-by-step explanation:
81^5 = 3486784401
3486784401/243 = 14348907
Double Check
3486784401 / 14348907=243
So N = 14348907.
A jar contains only pennies, nickels, and dimes. The number of dimes is one more than the number of nickles, and the number of pennies is six more than the number of nickels. How many of each denomination are in the jar, if the total value is $4.80?
Answer:
Nickels=29
Dime=30
Pennies=35
Step-by-step explanation:
Nickels=$0.05
Dime=$0.10
Pennies=$0.01
Total value=$4.80
Let quantity of
Pennies=p
Nickels=n
Dimes=d
d=n+1
p=n+6
0.01 *[n + 6] + 0.05n + 0.10*[n+1] =4.80
Open parenthesis
0.01n+0.06+0.05n+0.10n+0.10=4.80
0.16n+0.16=4.80
0.16n=4.80-016
0.16n=4.64
n=29
Pennies=n+6
=29+6
=35
Dime=n+1
=29+1
=30
Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+__
Answer:
37
Step-by-step explanation:
Solve for x using the Quadratic Formula: x2 + 2x + 1 = 0 x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
x = 2
x = 1
x = 0
x = −1
Answer:
x = - 1Step-by-step explanation:
x² + 2x + 1 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
a = 1 , b = 2 , c = 1
We have
[tex]x = \frac{ - 2± \sqrt{ {2}^{2} - 4(1)(1)} }{2(1)} \\ \\ x = \frac{ - 2 ± \sqrt{4 - 4} }{2} \\ \\ x = \frac{ - 2 ± \sqrt{0} }{2} \\ \\ x = - \frac{2}{2} \\ \\ x = - 1[/tex]
Hope this helps you
Which set of events is an example of dependent events?
A. Rolling an odd number, and then rolling an even number.
B. You choose a number from 1 to 50 from a hat, replace it, and then draw a second number.
C. You choose a marble from a bag, don't replace it, and then choose another marble.
D. You roll a 4, and then spin yellow on a spinner.
C.
Because the marble is not replaced and that affects the next event where another marble is chosen.
Dependent events:
It is the event where one event outcome is dependent on the other event outcome.
Independent events:
It is the event where one event outcome is not dependent on the other event outcome.
You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
Option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Dependent events:
It is the event where one event outcome is dependent on the other event outcome.
Independent events:
It is the event where one event outcome is not dependent on the other event outcome.
Now,
A. Rolling an odd number, and then rolling an even number.
This is an independent event.
B. You choose a number from 1 to 50 from a hat, replace it, and then draw a second number.
This is an independent event.
C. You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
D. You roll a 4 and then spin yellow on a spinner.
This is an independent event.
Thus,
You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
Option C is the correct answer.
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Use the cubic model y = 10x3 − 12x to find the value of y when x = 9.
Answer:
7182
Step-by-step explanation:
All you shoud do is to replace x by 9
● y = 10 * 9^3 -12*9
● y = 7182
Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $124 $256 $118 $441 $122 $335 $340 $191
Answer:
$122.1
Step-by-step explanation:
We are given the following data in the question
$124, $256 , $118, $441, $122, $335, $340, $191
Step 1
Find the mean
Mean = Sum of Terms / Number of Terms
Number of Terms = 8
Mean = ($124 + $256 + $118 + $441 + $122 + $335 + $340 + $191 )/ 8
Mean = $1927/8
= $240.875
Approximately to 1 decimal place
$240.9
Step 2
Standard deviation formula
S = √( x - μ)²/ N - 1),
N = Number of terms
μ = Mean
S = √[($124 - $240.9)² + ($256 - $240.9)² + ($118 - $240.9)² + ($441 - $240.9)² + ($122 - $240.9)² + ($335 - $240.9)² + ($340 - $240.9)²+ ($191 -$240.9)²/ 8 - 1]
S = $122.0895
Approximately to 1 decimal place
S = $122.1
Therefore, the standard deviation for the given data is $122.1
SOMEONE PLEAE HELP ME! Person who gets it correct will gain the BRAINLIEST!
Answer:
Third option is the right choice.
Step-by-step explanation:
[tex]y=a(b)^x[/tex] where "b", is the common ratio.
The common ratio for third table is constant for all the terms.
Best Regards!
The owner of a health food store is developing a new product that consists of peanuts and raisins. Raisins cost \$2.50$2.50dollar sign, 2, point, 50 per pound and peanuts cost \$3.50$3.50dollar sign, 3, point, 50 per pound. The owner wants to create 202020 pounds of the product that cost \$3.03$3.03dollar sign, 3, point, 03 per pound. Which of the following systems of equations can be used to determine the number of pounds of peanuts, ppp, and the number of pounds of raisins, rrr, that should be combined?
Answer:
9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product
Step-by-step explanation:
The cost of raisins is $2.5 per pound and the cost of peanut per pound is $3.50.
Let r represent the number of raisin pound and p represent the number of peanut pound. Since 20 pounds of a new product that consists of peanuts and raisins need to be produced, it can be represented by the equation:
p + r = 20 (1)
The new product would cost $3.03, therefore:
3.5p + 2.5r = 3.03(20)
3.5p + 2.5r = 60.6 (2)
We have to solve equation (1) and (2) simultaneously. First multiply (1) by 2.5 to get 2.5p + 2.5r = 50. Subtract 2.5p + 2.5r = 50 from equation (2):
p = 10.6 pound
Put p = 10.6 in equation (1)
10.6 + r = 20
r = 20 - 10.6 = 9.4
r = 9.4 pound
9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product
Answer:
p + r = 20
[tex]\frac{3.50p+2.50r}{20}[/tex] = 3.03
Step-by-step explanation:
The total cost of the product when the peanuts and raisins are combined is:
3.50p + 2.50r
To obtain the per pound cost, this expression needs to be divided by the number of total pounds, 20.
[tex]\frac{3.50p+2.50r}{20} =3.03[/tex]
**KA's explanation**
do side lengths 8,7 and 15 create a triangle ?
Answer:
Yes
Step-by-step explanation:
To make a triangle the 2 smaller sides must join together to become greater than or equal to the biggest side.
8+7=15
Therefore,
side lengths 8, 7, and 15 do create a triangle.
Hope this helps
Answer:
No, this can cannot create a triangle because to create a triangle you need two sides greater than one of the side and since 8+7=15 and 15 cannot be equal to 15 and it had to be more than 15 or so.
Possible ways to create triangle
a+b>c
a+c>b
b+c>a
Step-by-step explanation:
Find the legs of a 30° -60°-90° triangle whose hypotenuse is:
10 in.
PLEASE ANSWER ASAP IM really STRUGGLING!!
You use Pythagoras' Theorem and the theorem of 30-60-90 triangle
2^2(3-8)÷5-1 please help
Answer:
-5
Step-by-step explanation:
2^2*(3-8)÷5-1
4*(-5)÷4
-20÷4
=-5
Answer:
-5
Step-by-step explanation:
Firstly 2^2=4, 4(3-8)=4*(-5)= -20, -20/5 -1= -4-1= -5
Solve for x 65 10 55 8
Answer:
Hey there!
60=0.5(55+5x+15)
120=5x+70
50=5x
x=10
Hope this helps :)
Answer:
Answer is 8
Step-by-step explanation:
2.) Calculate x, to the nearest tenth of a meter
Answer:
63.4°
Step-by-step explanation:
The following data were obtained from the question:
Opposite = 6 cm
Adjacent = 3 cm
Angle x =?
The value of angle x can be obtained as follow:
Tan x = Opposite/Adjacent
Tan x = 6/3
Tan x = 2
Take the inverse of Tan.
x = Tan¯¹ 2
x = 63.4°
Therefore, the value of angle x is 63.4°
Answer:
63.4°
Step-by-step explanation:
What happens to the diagonal of a rectangle when the rectangle is reflected across a line of symmetry? What does this suggest about the diagonals of rectangles?
When you reflect a diagonal over a line of symmetry, the diagonal will land perfectly on the other diagonal (and vice versa). This suggests that one diagonal is a mirror copy of the other.
Another way to put it: The vertex points of the rectangle will swap when we reflect over a line of symmetry. A diagonal is simply the opposite vertex points joined together. So this is why the diagonals swap places (because the vertices line up perfectly when you apply the reflection).
A shape with a line of symmetry will land on itself, when reflected across the line of symmetry. The true statements are:
The diagonals of the rectangle will land perfectly on each otherThe diagonals of a rectangle are lines of symmetryFrom the question, we understand that; the rectangle is reflected across the line of symmetry
When this is done, the half of the rectangle will land directly on the other half.
This means that, the diagonal of the rectangle will land perfectly on the other diagonal
The statement above suggests that, the diagonal of a rectangle is also a line of symmetry of the rectangle.
Read more about lines of symmetry and diagonals at:
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An airline company advertises that 100% of their flights are on time after checking 5 flights from yesterday and finding that these 5 were on time a) What is population of interest? b) What is the sample? c) Was this a representative sample? Explain. d) How should the company determine the percentage of their flights that are on time?
a) The population is all of the flights belonging to the particular airline. It's not all flights in general because the airline does not have control over a rival company's flight schedule.
------------------
b) The sample is the 5 airlines the company selected. Ideally the sample should represent the population as much as possible. The larger the sample, the more representative the sample is.
------------------
c) No, the sample is likely not representative because one day of flight does not represent the entire lifetime of all flights done so far for that company. This particular day could have been a very good day with good weather, which may explain why the 5 flights were all on time.
------------------
d) It would be better for the company to select the days at random and sample all of the flights for those particular days chosen. This is a cluster sample. Each cluster is a day. Also, I think more flights should be sampled. Five flights does not seem like enough.
steven wants to buy a 495 steven has no money saved,but will be able to deposit 40 into a savings account when he receives his paycheck each Friday however before steven can buy the bike he must give his sister 65 that he owes her
Answer:
14 paychecks
Step-by-step explanation:
$495 + $65 = $560
$560 / 40 = 14
Therefore , he must save for 14 paychecks
Hope this helps and pls mark as brainliest :)
Answer:
14
Step-by-step explanation:
$495 + $65 = $560
$560 / 40 = 14
He must save for 14 paychecks.
Hope this help
Mark me BRAINLIEST
Tysm
Solve for x. (x+2)/3+(2x-4)/4=3
Answer:
x=4
Step-by-step explanation:
First you need to factor the equation. You can do this by multiplying the numbers by eachother so they have a denominatior of 12.
You would come out to have this...
((x+2)*4)/12 + ((2x-4)*3)/4=3
At this point you can combine the numerators over the common denominator.
((x+2)*4+(2x-4)*3)/12=3
You can now rewrite the equation into factored form.
5x-2/6=3
Multiply both sides of the equation by 6.
5x-2=18
move the terms not containing x to the right
5x=20
and divide by 5
x=4
(३) एक शब्द में उत्तर लिखो:
१. कवि की जिह्वा पर इसके गीत हों -
२. मातृभूमि के चरण धोने वाला
३. मातृभूमि के सपूत -
४. प्रतिदिन सुनने/सुनाने योग्य नाम -
५. मातृभूमि के चरणों में इसे नवाना है
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