If the father is 22 years older than his son, and the sum of their ages is 38 years, we can set up the following equations to represent this information:
Copy code
father + son = 38
father = son + 22
We can solve for the father's and son's ages by substituting the second equation into the first equation:
Copy code
(son + 22) + son = 38
2 * son + 22 = 38
2 * son = 16
son = 8
Therefore, the son's age is 8 years, and the father's age is 8 + 22 = <<8+22=30>>30 years.
Answer:
16
Step-by-step explanation:
son=38-22
son=16
hope am correct
If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours
Answer:
9 workers
Step-by-step explanation:
15 workers = 48 hrs build
x workers = 30 hrs build
cross multiply
15 × 30 = x × 48
450 = 48x
x =
[tex] \frac{450}{48} [/tex]
x = 9.37
so it will take approximately 9 workers to build a wall for 30hrs
i hope this helped
Sunny runs at a steady rate, and Moonbeam runs m times as fast, where m is a number greater than 1. If Moonbeam run to overtake Sunny a head start of h meteres, how many meters must Moonbeam run to overtake Sunny? ( Give your ansewr as an expression in terms of h and m.)
Hint : Let s be Sunny's rate. In terms of m and s, at what rate does Moonbeam catch up to Sunny?
Answer:
4 hours
Step-by-step :
If Sunny runs twice as fast as Moonbeam
Given the assumed data:
Sunny's speed = 12m/h
Moonbeam's speed= 6m/h
Therefore, if they run for 2 hours, Sunny would have covered 12 * 2 = 24 miles
While Moonbeam would have covered 6 *2 = 12 miles in the same 2 hours.
This given illustration shows that given that all parameters are equal, except the x2 speed of Sunny to that of Moonbeam, he would always be 2x faster than Moonbeam.
If they run for 4 hours, Sunny would have covered 12 * 4 = 48 miles
While Moonbeam would have covered 6 *4 = 24 miles in the same 4 hours.
HHHHEeeelllpppPPp
The graph shows the height, y, in meters, of a rocket above sea level in terms of the time
seconds, since it was launched. The rocket landed at sea level.
What does the x-intercept represent in this situation?
A
the height from which the rocket was launched
B the time it took the rocket to return to sea level
C. the total distance the rocket flew while it was in flight
D. the time it took the rocket to reach the highest point in its fight
Your dog has a mass of 45.5 lb. what is the dog’s mass in kilograms? (note: 1 lb = 0.45 kg.)
If the mass of dog is 45.5 lb then the mass in kilogram is 20.475 Kg .
In the question ,
it is given that ,
the mass of the dog is = 45.5 lb ,
we have to convert the given mass of dog into Kilogram .
For that we will need the conversion rate ,
the conversion rate to convert mass from lb to Kilogram is given as , 1 lb is = 0.45 kg ,
So , 45.5 lb in Kilogram will be equal to = 45.5 × 0.45 ,
After multiplication ,
we get ,
mass = 20.475 Kg .
Therefore , the mass in Kilogram is 20.475 Kg .
Learn more about Conversion here
https://brainly.com/question/4911126
#SPJ4
The area of a rectangle is 105 sq in and the length of one side is 7 in. What is the length of the perimeter?.
The perimeter of the rectangle is 44cm
Given:
Area: [tex]Area = 105cm^{2}[/tex]
width: [tex]w= 7 cm[/tex]
To find the perimeter first we need to find the length of the rectangle.
We find it with the formula for the area of a rectangle:
[tex]Area = width*length[/tex]
so clearing for length:
[tex]length = \frac{area}{width}[/tex]
substituting known values:
[tex]length = \frac{105}{7} \\length = 15 cm[/tex]
And now we can calculate the perimeter:
[tex]perimeter = 2(width + length)\\\\perimeter = 2(7cm + 15cm)\\\\perimeter = 44cm[/tex]
Hence , the perimeter of the rectangle is 44cm
Learn more about Perimeter of rectangle at :
https://brainly.com/question/19819849
#SPJ4
There are some coloured pins in a bag. The pins can be green,yellow, purple, or grey. A pin is going to be taken at random from the bag. The table shows the probabilities of picking a purple or grey pin.
The probability of picking a green pin is three times the probability of picking a yellow one.
a)Complete the table.
There are 14 purple pins in the bag.
b)Work out how many green pins are in the bag
a) Green is 0.3, Yellow is 0.1
b) There are 12 green pins in the bag
Given,
In the question:
There are some colored pins in a bag. The pins can be green, yellow, purple, or grey. A pin is going to be taken at random from the bag.
The table shows the probabilities of picking a purple or grey pin.
The table is not given in the question :
So, The table is :
Colors: Green Yellow Purple Grey
Probability: 0.35 0.25
To find the :
a)Complete the table.
There are 14 purple pins in the bag.
b)Work out how many green pins are in the bag.
Now, According to the question:
The probability is the ratio between the possible outcomes over the total outcomes:
The value of the probability of possible outcomes is greater than 0 and smaller than 1 (0 < P < 1)
The sum of the probabilities of all outcomes must equal 1.
A bag contains some green, yellow, purple and grey pins
∵ The probability of picking a purple pin P(purple) = 0.35
The probability of picking a grey pin P(grey) = 0.25
→ The total of all possible outcomes is 1
The sum of the probability of green and yellow pins = 1 - 0.35 - 0.25
The sum of the probability of green and yellow pins = 0.4
P(green) + P(yellow) = 0.4 ⇒ (1)
∵ The probability of picking a green pin is 3 times the probability
of picking a yellow pin
P(green) = 3 P(yellow) ⇒ (2)
→ Substitute (2) in (1)
3 P(yellow) + P(yellow) = 0.4
4 P(yellow) = 0.4
→ Divide both sides by 4
P(yellow) = 0.1
The probability of picking a yellow pin is 0.1
→ Substitute P(yellow) in (20 by 0.1
P(green) = 3(0.1)
P(green) = 0.3
The probability of picking a green pin is 0.3
Green = 0.3, Yellow = 0.1
There are 14 purple pins in the bag
P(purple) = 0.35
0.35 of purple pins = 14
→ To find the total number of pins in the bag divide 14 by 0.35
The total number of pins = 14 ÷ 0.35
The total number of pins = 40 pins
P(green) = 0.3
The number of green pins = 0.3 × 40
The number of green pins = 12 pins
Hence, There are 12 green pins in the bag.
Learn more about Probability at:
https://brainly.com/question/11234923
#SPJ4
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answer:12.9
Step-by-step explanation:
Sheila made 51 cookies. Her sister made 27 cookies. Her brother ate 3 cookies. The remaining cookies will be sold in packages containing 5 cookies each. How many packages of cookies will be made?
How many packages of cookies will be made?
15
Step-by-step explanation:
Sheila made 51 cookies… Sister make 27 cookies ( add them )
78…..
Brother ate 3 cookies..
78 - 3 =
75..
75/5 =
15
Create a proportion using the form = to represent the following word problem. 78% of what number is 42?.
Therefore the solution to this question of proportion, 78% of what number is 42 is 53.84.
What is proportion?In general, the word "proportion" is used to describe a part, share, or amount that is compared to an entire. Two ratios are in proportion, according to the definition of proportion, when they are equal. Two ratios or fractions being equal is expressed by an equation or a statement.
Here,
If 78% of x (any number) equals 42, then we need to set this up as an equation in order to figure it out.
1) Writing down 78% as a fraction. Taking into account that we refer to a product when we say 78% of some amount (x).
78%=78/100 \s=>78x/100=42
2) Afterward, we can continue:
100*78x/100=42*100
78x=4200
x=4200/78
x=53.84
Therefore the solution of 78% of what number is 42 is 53.84.
To know more about proportion , visit
https://brainly.com/question/18255679
#SPJ4
Grady marks down some $4.09 pens to $3.59 for a week and then marks them back up to $4.09. Find the percent of increase and the percent of decrease to the nearest tenth. Are the percents of change the same for both price changes? If not, which is a greater change? Complete the explanation, and round your percents to the nearest tenth.
The first change was
a decrease
of
0.1
% and the second change was
an increase
of
%. The two percent changes
are not
the same, and the
second
percent change is greater.
The solution is the two percent changes are not the same, and the second percent change is greater
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage
Given data ,
Let the initial value of the pens = $ 4.09
Let the final value of the pens = $ 3.59
So , the percentage change is calculated by
Percentage decrease = ( ( final value - initial value ) / initial value ) x 100
Substituting the values in the equation , we get
Percentage decrease = ( ( 3.59 - 4.09 ) / 4.09 ) x 100
Percentage decrease = ( -0.5 / 4.09 ) x 100
Percentage decrease = -0.122249 %
Therefore , the approximate percentage decrease = -0.1 %
Now ,
The value of the pens is increased to = $ 4.09
So , the percentage change is calculated by
Percentage increase = ( ( final value - initial value ) / initial value ) x 100
Substituting the values in the equation , we get
Percentage increase = ( ( 4.09 - 3.59 ) / 3.59 ) x 100
Percentage increase = ( 0.5 / 3.59 ) x 100
Percentage increase = 0.13927 %
Therefore , the approximate percentage increase = 0.1 %
Hence , the two percent changes are not the same, and the second percent change is greater
To learn more about percentages click :
https://brainly.com/question/12861068
#SPJ1
100 Points + brainliest if correct and well explained:
An equation is shown:
−np − 3 = 7(c − 4)
Which of the following solves for n?
n = the quantity 7 times c minus 31 all over negative p
n = the quantity 7 times c minus 25 all over negative p
n = the quantity 7 times c plus 31 all over p
n = the quantity 7 times c plus 25 all over p
The value for n is n = the quantity 7 times c minus 25 all over negative p.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
−np − 3 = 7(c − 4)
Now, solving for n
-np - 3 = 7c - 28
-np = 7c - 28 + 3
-np = 7c -25
-n = 1/p( 7c- 25)
n= 1/ (-p) (7c- 25)
So, the value for n is n = the quantity 7 times c minus 25 all over negative p.
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ2
nothing to hard just please give correct answer!!
The equation of the first graph is
y > 2x - 4
The equation of the first graph is
y ≥ -x + 4
How to get the equations of the linesThe graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m calculating using the points on the graph (0, -4) and (2, 0)
m = (y₀ - y₁) / (x₀ - x₁)
m = (-4 - 0) / (0 - 2)
m = (-4) / (-2)
m = 2
c = y intercept, from the graph
c = -4
The equation of the line is y = 2x - 4
shading above the line is greater than and dotted lines means it does not have equal to
hence y > 2x - 4
for the second graph
the slope, m calculating using the points on the graph (0, 4) and (4, 0)
m = (y₀ - y₁) / (x₀ - x₁)
m = (4 - 0) / (0 - 4)
m = (4) / (-4)
m = -1
c = y intercept, from the graph
c = 4
The equation of the line is y = -x + 4
shading above the line is greater than and solid lines means there is equal to in the inequality
hence y ≥ -x + 4
Learn more about linear functions at:
https://brainly.com/question/29323505
#SPJ1
find y when x = 10 if y =8 when x = 20
Answer:
ANS:- Y =4
Step-by-step explanation:
x =20 half x =10
y = 8 half y = 4
I WILL MARK AS BRAINLIST PLEASE. Write the equation of the line in fully simplified slope-intercept form
Answer:
y= -5x-8
Step-by-step explanation:
Slope-intercept form equation: y=mx+b
b is where the line meets the y line. So it meets it at the number "-8". Then with the mx in the equation, you find that by doing rise over run. I got 5/-1, which goes to just plain old -5.
I hope this helps!!!
x can be 1,2,3,4
If x = 1, x?=-150
If x = 2, x?=-50
If x = 3, x?=50
If x = 4, x?=150
(x? Has to be the same in all questions)
Answer:
x=1
Step-by-step explanation:
because x has to be same in all number
A bag contains 14 red tiles, 20 blue tiles, and 16 green tiles. A tile is randomly drawn from the bag, the color recorded, and then the tile placed back in the bag. If this procedure is done 40 times, how many times do you expect to draw a blue tile?
12
Therefore the required probability as a total number of the expected draw of blue tiles will be 16.
What is Probability?Probability = the number of possible paths to success / The total number of outcomes. That is a chance of getting an event
What is the formula for probability?The formula for calculating an event's probability is the ratio of favorable outcomes to the total number of outcomes. Probabilities are always between 0 and 1. Probability = Number of Favorable Outcomes / Total Number of Outcomes is the general probability formula.
Given:
Number of red tiles = 14
Number of blue tiles = 20
Number of green tiles = 16
total number of tiles = 14+20+16=50
P(blue) = number of blue tiles / total number of tiles
= 20/50
=2/5
40 times the procedure is repeated
so, answer=(2/5)*40 = 16
Therefore the required probability as a total number of the expected draw of blue tiles will be 16.
To know more about probability visit:
https://brainly.com/question/14210034
#SPJ1
3) Kevin made $9 per hour working as a
lifeguard. How many hours did he work
this week if his weekly pay before
deductions was $288? Define a variable
and write an equation. Solve the equation.
Answer: 9x = 288, 32 hours
Step-by-step explanation:
x can be the variable and it represents the hours he worked. 9 is the amount made each hour, so it is multiplied by x. 288 is the total made, so 9x=288.
9x = 288 Divide by 9 on both sides to isolate x
x = 32 hours. Kevin worked 32 hours this week
Answer:32
Step-by-step explanation: 32x9=288
The equation x² - 4x + y2-2y = 16 describes a circle. What is the y-coordinate of
the center of the circle?
Answer:
1
Step-by-step explanation:
→ Complete the square
( x - 2)² - 4 + ( y - 1 )² - 1 = 16
→ Simplify
( x - 2 )² + ( y - 1 )² = 21
→ Find centre
( 2 , 1 )
3/48
X
у
Find Lx and LY
Answer:
3/48
Step-by-step explanation:
i need you help mate
if the a horizon in a soil sample measures 3 inches, and the rate of top soil for temperate deciduous forest (where the soil was sampled) is 1 in/225 years, how long did it take for this horizon to develop?
The time taken by the horizon to develop is calculated with the half-life which is 675 years.
Organic matter particles have more negatively charged particles, which hold on the positively charged particles.
The organic matter in the soil affects the water holding capacity of the soil. Thus is if there are more organic matter, this means that the organic matter is more. Thus the farmer has to add more organic matter.
In order to reduce the the acidity, the farmers add Calcium oxide, Calsium hydroxide and so on.
The horizon s formed after years of sediment formation. Thus the process can take years.
This is the half-life of the soil and with the formula of half-life we get 225 * 3 = 675 years.
Therefore, the time taken by the horizon to develop is 675 years.
To know more about horizons, refer: https://brainly.com/question/28812370
#SPJ4
hello can someone please help me solve this question:
graph 4x+6y>=10
>= meaning greater than or equal to
Explanation is there for your question
How many solutions does this system of equations have? y=-1/3x+7 y=-2x^3+5x^2+x-2 A. no solution B. 1 solution C. 2 solutions D. 3 solutions
The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution thus option (B) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In other words, the equation must be constrained with some constraints.
As per the given equations,
y = (-1/3)x + 7 and y = -2x³ + 5x² + x - 2
The graph of both equations has been plotted below,
The number of points where both curves cut each other = 1
Thus, the number of solutions = 1
Hence "The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution".
For more about the equation,
brainly.com/question/10413253
#SPJ1
Answer:
1 solution
Step-by-step explanation:
Plato/Edmentum
a survey is carried out at uiuc to estimate the proportion of students who like to wear costumes on halloween. 1000 students participated in the survey. if you were to create a confidence interval with 98% confidence and a 4% margin of error, what would be the population sd?
The population standard deviation sd would be 0.543 .
Given :
a survey is carried out at uiuc to estimate the proportion of students who like to wear costumes on halloween. 1000 students participated in the survey. if you were to create a confidence interval with 98% confidence and a 4% margin of error .
we know that
margin of error = z * s / [tex]\sqrt{n}[/tex]
Z score at 98% = 2.326
0.04 = 2.326 * s / [tex]\sqrt{1000}[/tex]
0.04 * [tex]\sqrt{1000}[/tex] = 2.326 * s
1.264 = 2.326 * s
s = 1.264 / 2.326
s = 0.543
Learn more about the confidence here:
https://brainly.com/question/13242669
#SPJ4
Solve the equation 20 + 0.44x = 19 + 1.69x.
By solving the given equation 20 + 0.44x = 19 + 1.69x we get x=0.8.
What is meant by an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.
Given,
20 + 0.44x = 19 + 1.69x
20-19=1.69x-0.44x
1=1.25x
x=0.8
Therefore, by solving the given equation 20 + 0.44x = 19 + 1.69x we get x=0.8.
To know more about equation, visit:
https://brainly.com/question/29657983
#SPJ1
I don't know how to do 2x-y=3
Answer:
x=2 y=1
Step-by-step explanation:
Answer:
y=2x-3
Step-by-step explanation:
Literal Equations
help asap !!
Answer:
Step-by-step explanation:
y = 6x - 12
6x - 12 = y
6x = y + 12
x = (y + 12)/6
5. Use the given process data to construct a control chart for p.
A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected
and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below.
4756831244562
Select the correct lower control limit.
lower control threshold for the data is LCL = -0.007
How does lower control limit work?The lower control limit on a control chart is the value below which any particular data point would be deemed to be out of statistical control owing to specific cause variation. It is represented by a line below the centerline.
The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]
To date,
Size of sample = n
Sample size is 12 samples.
Televisions with defects = X
We have a sample defect = p
p chart week with n = 200
x = 4, 7, 5, 6, 8, 3, 12, 4, 4, 5, 6, 2.
P = x/n
p = 4/200 = 0.02
p = 7/200 = 0.035
p = 5/200 = 0.025
p = 6/200 = 0.03
p = 8/200 = 0.04
p = 3/200 = 0.015
p = 12/200 = 0.06
p = 4/200 = 0.02
p = 4/200 = 0.02
p = 5/200 = 0.025
p = 6/200 = 0.03
p = 2/200 = 0.01
total will be 0.33
p bar = 0.33/12
p bar = 0.0275
The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]
LCL = 0.0275 - 3[tex]\sqrt{ 0.0275 (1- 0.0275/200}[/tex]
LCL = -0.007
To know more about lower control limit click :
brainly.com/question/13861213
#SPJ1
Please Solve question
The component form of two vectors 2u - v is (10, 0), no magnitude in the second direction.
What is a vector?A vector is a quantity that has both magnitude and direction.
Given are two vectors u = (4, - 1) and v = (-2, - 2).
∴ The value of 2u - v in component form is 2(4, - 1) - (-2, - 2).
2u - v = (8, - 2) - (-2, - 2).
2u - v = (8+2, - 2+2).
2u - v = 10
learn more about vectors here :
https://brainly.com/question/13322477
#SPJ1
HELP ASAP
Equation in picture
Answer:1/2
Step-by-step explanation:
3/4+(-1/2)-(-1/4)
3/4-1/2+1/4
1-1/2=1/2