Answer:
Fred is 31 years old and Natalie is 14 years old.
Step-by-step explanation:
Given:
If you add Natalie's age and Fred's age, the result is 45.
If you add Fred's age to 3 times Natalie's age, the result is 73.
Now, to find the age of Fred and Natalie.
Let the age of Fred be [tex]x.[/tex]
And the age of Natalie be [tex]y.[/tex]
As, given If you add Natalie's age and Fred's age, the result is 45.
[tex]x+y=45[/tex] ......(1)
Now, if you add Fred's age to 3 times Natalie's age, the result is 73.
[tex]x+3y=73[/tex] ......(2)
So, to solve the equations by using elimination method.
Now, subtracting both the equations (1) and (2):
[tex]x+y-(x+3y)=45-73[/tex]
[tex]x+y-x-3y=-28[/tex]
[tex]-2y=-28[/tex]
Dividing both sides by -2 we get:
[tex]y=14.[/tex]
Natalie's age = 14 years.
Now, to get the age of Fred by substituting the value of [tex]y[/tex] in equation (1):
[tex]x+y=45\\\\x+14=45[/tex]
Subtracting both sides by 14 we get:
[tex]x=31.[/tex]
Fred age = 31 years.
Therefore, Fred is 31 years old and Natalie is 14 years old.
ameson downloaded one digital song for $1.45, two digital songs for $2.90, and 5 digital songs for $7.25. Enter and solve an equation to find the cost to download 25 digital songsUse n for your independent variable and c for your dependent variable. The equation is Total cost of 25 songs is .
The equation is c = 1.45 n
Total cost of 25 songs is $36.25
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the rate of changeb is the initial value (value y at x = 0)∵ The cost of downloaded one digital song is $1.45
∵ The cost of downloaded two digital song is $2.90
∵ The cost of downloaded five digital song is $7.25
- There is a linear relation between the cost of downloading
the songs and the number of songs
∵ 2.90 = 2 × 1.45
∵ 7.25 = 5 × 1.45
∴ The total cost of downloaded songs is the product of the number
of songs and the cost per song
∵ The cost per song is 1.45
∵ n is the independent variable
∴ n represents the number of songs
∵ c is the dependent variable
∴ c represents the total cost of n songs
- Now we can write the linear equation
∴ c = 1.45 n
The equation is c = 1.45 n
∵ 25 digital songs downloaded
∴ n = 25
∵ c = 1.45 n
∴ c = 1.45(25)
∴ c = 36.26
Total cost of 25 songs is $36.25
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Use symbols Replace each with a number to make /24 >1/4 > 4/ a true statement
The numbers that replaces each blank to make the inequality a true statement are 48 and 32. The new inequality is 48/24 > 1/4 > 4/32.
In Mathematics and Euclidean Geometry, an inequality is a relation that compares two or more numbers and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).Based on the information provided, we can logically deduce the following incomplete inequality;
_/24 > 1/4 > 4/_
In order to make the left-hand side of the inequality true, we must have a number that is greater 1/4 or 0.25;
48/24 = 2
48/24 > 1/4
2 > 0.25 (True)
In order to make the right-hand side of the inequality true, we must have a number that is less than 1/4 or 0.25;
4/32 = 0.125
1/4 > 4/32
0.25 > 0.125 (True).
In conclusion, any number that is greater than 1/4 would make the left-hand side of the inequality true while any number that is less than 1/4 would make the right-hand side of the inequality true.
Complete Question:
Use symbols. Replace each __ with a number to make _/24 >1/4 > 4/_ a true statement.
How many unique ways are there to arrange the letters in the word TIGER?
Answer:
120
Step-by-step explanation:
Because it is lol
120
What is the method of arranging object?The number of ways of arranging n unlike objects in a line is n! (pronounced ‘n factorial’). n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1.
In the words TIGER there are 5 letters T,I,G,E,R.
The number of unique ways are there to arrange the letters in the word TIGER=5!=5*4*3*2*1=120.
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The price of gasoline rose from $2.45 in May to $2.89 in August. Find the percent of increase. Round your answer to the nearest whole percent.
Answer:
The percent in increase is 18%.
Step-by-step explanation:
Given:
The price of gasoline rose from $2.45 in May to $2.89 in August.
Now, to find the percent of increase.
The price of gasoline in May = $2.45.
The price of gasoline in August = $2.89.
So, we get the price of increase:
[tex]2.89-2.45=\$0.44.[/tex]
Now, to get the percent increase:
[tex]\frac{0.44}{2.45} \times 100[/tex]
[tex]=0.179\times 100[/tex]
[tex]=17.9\%.[/tex]
The increase in percent nearest to whole = 18%.
Therefore, the percent in increase is 18%.
To find the percent increase in gasoline prices, you subtract the initial price from the final price, divide this difference by the initial price, and then multiply by 100 to get a percentage. In this case, the increase in price was about 18%.
Explanation:The first step to finding the percent of increase in the price is to subtract the initial price from the final price. So, $2.89 - $2.45 equals $0.44. This is the amount of the increase in price. Then, to find the percentage of this increase, we divide the increase by the initial price, and multiply by 100 to convert it into a percentage. So, ($0.44 / $2.45) * 100 equals about 18%. So the percent of increase in the price of gas from May to August is 18%.
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8(x+2)=56 HELP PLZZ ANYONE
Use the Distributive Property to solve the equation.
Answer:
x = 5
Step-by-step explanation:
1. 8 (x + 2) = 56 Distribute the 8
2. 8x + 16 = 56 Subtract 16 from both sides
3. 8x = 40 Divide both sides by 8
4. x = 5
I don't understand this question I'm supposed to be graphing
x+y is equal or less than 3 plz help
y≤ 3 when x is 0 and x≤ 3 when y is 0
The graph is attached in figure below
Step-by-step explanation:
We need to graph x+y is equal or less than 3
Writing in mathematical form:
[tex]x+y\leq 3[/tex]
For solving we find x and y intercepts
The y-intercept can be found by putting x=0, y is :
[tex]0+y \leq 3\\y\leq 3[/tex]
y≤ 3 when x is 0
The x-intercept can be found by putting y=0, x is :
[tex]x+y \leq 3\\x+0\leq 3\\x\leq 3[/tex]
x≤ 3 when y is 0
Plotting these values on the graph:
The graph is attached in figure below
Keywords: Solving inequalities
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GHI = JKL. Which statement is FALSE.!?
. Marcus has 50 tokens to spend at the school
carnival. The Ferris wheel costs 7 tokens and
the carousel costs 5 tokens. The inequality
7x + 5y = 50 represents the possible ways
Marcus could use his tokens on the two rides.
Is the ordered pair (6, 3) a solution for the
problem situation?
Answer:
The ordered pair (6,3) can not be a solution for the problem situation.
Step-by-step explanation:
Marcus has total 50 tokens to spend at the carnival.
Now, given that the Ferris wheel costs 7 tokens and the carousel costs 5 tokens.
So, if Marcus play the Ferris wheel for x times and the carousel for y times, the total expenditure will be given by
7x + 5y = 50 ............ (1)
Now, the ordered pair (6,3) i.e. x = 6 and y = 3 does not satisfy the above relation equation (1).
So, the ordered pair (6,3) can not be a solution for the problem situation. (Answer)
A function g(x) has x-intercepts at ( 1/2,0) and (6,0). Which could be g(x)?
g(x) = 2(x + 1)(x + 6)
g(x) = (x-6)(2x - 1)
g(x) = 2(x - 2)(x-6)
g(x) = (x + 6)(x + 2)
g(x) = (x-6)(2x - 1)
Step-by-step explanation:
when you expand, it will be 2x²-13x+6=0
when you factories the quadratic equations,
the answer will be 1/2 and 6
Answer:
g(x) = (x-6)(2x - 1)
Step-by-step explanation:
A delivery truck drove 203 miles in 3.5 hours. After unloading and loading new cargo, it traveled on another 243 miles for 4.5 hours.
What was the average speed of the truck over its entire route?
Round to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
203 miles in 3.5 hrs....and 243 miles in 4.5 hrs
totaling : (203 + 243) miles in (3.5 + 4.5) hrs = 446 miles in 8 hrs
speed = distance / time
speed = 446 / 8
speed = 55.75 mph <==
Jeremy rides his bike at a rate of 15 miles per hour. Below is a table that represents the number of hours and miles Kevin rides. Assume both bikers ride at a constant rate. Which biker rides at a greater speed? Include all of your calculations in your final answer.
Time in hours (x) Distance in miles (y)
1.5 17.25
2 23
3.5 40.25
4 46
The correct answer would be, Jeremy rides at a greater speed than Kevin.
Step-by-step explanation:
Jeremy rides at a rate of 15 miles per hour
Kevin rides at a rate given in the table
Let Y be the distance traveled by Jeremy
And X be the number of hours
Then for Jeremy:
y/x = 15/1
=> y= 15 x
For Kevin:
(46-23)/(4-2)
= 23/2
= 11.5
So for Kevin, Y = 11.5 x
So when Jeremy's and Kevin's rates are compared,
15 > 11.5
which means Jeremy rides at a greater speed.
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Whích strand of mRNA would be made during transcription using the DNA
strand shown below?
AGC GCT
O A. UCG CGU
O B. TCG CGA
O C. UCG CGA
O D. AGC GCT
In both DNA and RNA, pairs are formed between cytosine and guanine. In DNA, adenine pairs with thymine, but in RNA it pairs with uracil.
So the corresponding mRNA strand would be
C. UCG CGA
Answer:
UCG CGA
Step-by-step explanation:
What is the value of x in the solution to the system
Answer:
whats the equation???
Step-by-step explanation:
1. Greg Forrester's charge account statement showed a previous balance 20 points
of $152.35, a finance charge of $1.78, new purchases of $45.23 and $15.67,
a payment of $50.00, and a credit of $12.84. What is the new balance? *
O
O
$152.19
$152.51
$227.87
O
$277.87
Answer:
Option $152.19
Step-by-step explanation:
Data provided in the question:
Previous balance = $152.35
Finance charge = $1.78
New purchases of $45.23 and $15.67
Payment = $50.00
Credit = $12.84
Now,
New Balance
= [Previous balance + Finance charge + New purchases ] - [ Payments + Credits ]
= [ $152.35 + $1.78 + ($45.23 + $15.67) ] - [$50.00 + $12.84 ]
= $215.03 - $62.84
= $152.19
Hence,
Option $152.19
Give line XY with coordinates X(3,1) and Y(3,-3), find the length of line XY
Answer:
4 units
Step-by-step explanation:
Distance formula:
[tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]
[tex]length \: of \: line \: xy \\ = \sqrt{(3 - 3 )^{2} + (1 - ( - 3))^{2} } \\ = \sqrt{(1 + 3)^{2} } \\ \ = \sqrt{4^{2} } \\ = 4 \: units[/tex]
Or since both coordinates lie at x=3, the line is a vertical line so you can simply count the increase in y to find the distance of the line.
1-(-3)= 4 units
1
-
-x+y=-5
9x-y=-11
Answer:
look at the picture shown
3 hats and 2 scarves costs £12.
5 hats and 4 scarves costs £21.
Find the cost of a hat.
Find the cost of a scarf.
Answer: Hat: £3 Scarf: £1.50
Step-by-step explanation:
hope this helps
The cost of a hat is £2 and the cost of a scarf is £1.5, obtained by solving the system of simultaneous equations representing the cost relationships.
Explanation:To solve this problem, you need to use a method called simultaneous equations. We denote the cost of a hat as 'h' and the cost of a scarf as 's'.
Then, we write down two equations based on the problem:
3h + 2s = 12 (Equation 1) 5h + 4s = 21 (Equation 2)
From Equation 1, we express 'h' as (12 - 2s) / 3. Substituting this into Equation 2 leaves us with a sole variable 's', after calculating this equation, you obtain s = 1.5, Substituting s into the first equation, we get h = 2. So, the cost of a hat is £2 and the cost of a scarf is £1.5.
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URGENT 15 POINTS
What is the greatest possible probability in any experiment?
A. 9/10
B. 1
C. 10
D. 100
Answer:
B) GREATEST POSSIBLE PROBABILITY in any experiment is 1.
Step-by-step explanation:
The probability of any event E is given as:
[tex]\textrm{Probability of any event E} = \frac{\textrm{Number of favorable events}}{\textrm{Total Number of outcomes}}[/tex]
Let us assume the the number of TOTAL OUTCOMES of any event E = n
Now, if the event is a SURE EVENT, then all outcomes are favorable events.
So, the total number of maximum favorable events = n
[tex]\textrm{Probability of event E} = \frac{\textrm{Number of favorable events}}{\textrm{Total Number of outcomes}} = \frac{n}{n} = 1[/tex]
Hence, the GREATEST POSSIBLE PROBABILITY in any experiment is 1.
52.3 is what percent of 1046
Answer:
it is 5%
Step-by-step explanation:
What is the constant of proportionality Y/X
Please help! I will give brainliest to CORRECT ANSWER!!
Answer:
3.5/1
Step-by-step explanation:
(0,0)
(3.5,1)
If the length of the radius of a circle is doubled, how does that affect the circumference and area?
The circumference will be doubled if radius is doubled
The area will increase four times if radius is doubled
Step-by-step explanation:
We will solve the question in two parts.
One for circumference and one for Area
Circumference:
The formula for circumference is given by:
[tex]C = 2\pi r[/tex]
Here r is the radius.
Doubling the radius means that new radius will be 2r
The new circumference will be:
[tex]C_N = 2\pi (2r)\\C_N = 2(2\pi r)\\C_N = 2C[/tex]
Hence,
The circumference will be doubled if radius is doubled
Area:
The area of circle is given by:
[tex]A = \pi r^2[/tex]
Putting radius equal to 2r
[tex]A_N = \pi (2r)^2\\A_N = \pi (4r^2)\\A_N = 4(\pi r^2)\\A_N = 4A[/tex]
Hence,
The area will increase four times if radius is doubled
Keywords: Circle, area
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A Physician orders Amoxicillin 500mg by mouth every 8 hours for a patient to treat Bronchitis. The pharmacy has available 250 mg tablets.
How many tablets will you dispense for a 10-day supply?
Answer:
60
Step-by-step explanation:
2of the 250mg pills 3times a day=6 pills a day for 10 days = 60 pills
Which inequality is equivalent to
−4t≥28
?
Answer:
t ≤ -7
Step-by-step explanation:
−4t≥28
−4/4 * t ≥ 28/4
−1 * t ≥ 7
-t ≥ 7
t ≤ -7
HELP ME!!! IM STUCK
Answer:help with mine ples
Step-by-step explanation: beause i need it orther wise i fail
What is 10m-3(2m-9)=9(m-1)+1
Answer:
a linear equation with a solution of m = 7
Step-by-step explanation:
The equation is a linear equation in m.
Perhaps you want the value of m that is the solution to the equation.
10m -6m +27 = 9m -9 +1 . . . . . eliminate parentheses
4m +27 = 9m -8 . . . . . . . . . . . . collect terms
35 = 5m . . . . . . . . . . . . . . . . . . add 8-4m to both sides
7 = m . . . . . . . . . divide by the coefficient of m
The solution is m = 7.
What is 24 % 0.4 in mathematics
Solve the system of linear equations bus graphing
y=1/2x+3
y= -2/3x-5
(1,3)
Answer:
The solution of [tex]y = \frac{1}{2} x + 3[/tex] and [tex]y = -\frac{2}{3} x - 5[/tex] is (-6.857, -0.429)
Step-by-step explanation:
The solution of y = 1/2 x + 3 and y = -2/3 x -5
is (-6.857, -0.429) . The solution is shown in the graph attached.
936 + 97281= x? what is x?
Answer:
x=98,217
Step-by-step explanation:
936 + 97281 = x
x=98217
Answer:
936 + 97281 = 98,217
x = 98,217
You just need to add to find x
Emily served 15.08 ounces of soup to her family of 4. How much soup did each person eat?
Answer: 3.77 ounces is the correct answer hope this helps
Answer:
Step-by-step explanation:
Kathy found $0.29. Now she has a total of $1.00. How much money did Kathy have to start?
Answer:
71 cents
Step-by-step explanation: Well it would be $1.00 minus the 29 cents she just got So 100 minus 29 is 71 it’s easy to do it in your head just think of 100 minus 30 and it’s 70 then subtract 1 from 30 and add it to the 70
Answer:
$0.71
Step-by-step explanation:
make $1.00 "100"* and $0.29 "29"* and subtract 100 and 29 to get "71" then turn the "71" into $0.71**
* this is done by making it a percentage by moving two units to the right
** this is done by making it a decimal by moving to units to the left