Their ages are 5 years, 25 years
How to find their ages?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let L and Y represent the age of the older person and younger person respectively.
Using the given information, we can write:
L = 4Y + 5 --- (1)
L + Y = 30 --- (2)
From (2):
L = 30 - Y --- (3)
Put (3) in (1):
L = 4Y + 5
30 - Y = 4Y + 5
4Y + Y = 30 - 5
5Y = 25
Y = 25/5
Y = 5 years
Put Y = 5 into (3):
L = 30 - Y
L = 30 - 5
L = 25 years
Their ages are 5 years, 25 years
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Solve -27 19 - 2x.
Enter your responses in the boxes.
-27 19 - 2x
H
-27-
23
-
-www
= -2x
1 = x
19-
-2x
Answer:
Simplifying
-27 = 19 + -2x
Solving
-27 = 19 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
-27 + 2x = 19 + -2x + 2x
Combine like terms: -2x + 2x = 0
-27 + 2x = 19 + 0
-27 + 2x = 19
Add '27' to each side of the equation.
-27 + 27 + 2x = 19 + 27
Combine like terms: -27 + 27 = 0
0 + 2x = 19 + 27
2x = 19 + 27
Combine like terms: 19 + 27 = 46
2x = 46
Divide each side by '2'.
x = 23
Simplifying
x = 23
Select the correct answer.
Which expression is equivalent to sin (2x) cos x?
The equivalent trigonometric expression to sin(2x)cos(x) is given as follows:
sin(2x)cos(x) = 2sin(x)cos²(x).
How to obtain the equivalent trigonometric expression?The expression for this problem is defined as follows:
sin(2x)cos(x).
The trigonometric identity used to simplify sin(2x) is given as follows:
sin(2x) = 2sin(x)cos(x).
Hence the expression can be written as follows:
sin(2x)cos(x) = 2sin(x)cos(x)cos(x)
sin(2x)cos(x) = 2sin(x)cos²(x).
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1. Find the semester GPA for the following. Show or explain your work.
Class Credit Hours Grade
MAT 171 4 C
HEA 112 2 A
ENG 111 3 B
ACA 111 1 D
BIO 112 4 A
2. Annie is a junior at a local university. She has 80 credit hours and a GPA of 2.1.
She wants to raise her GPA for a scholarship this semester.
She takes 16 credit hours and makes all A's, earning a 4.0 for this semester.
Annie averages the previous GPA of 2.1 and the current semester GPA of 4.0. She adds 2.1 + 4.0, then divides by 2, obtaining 3.05.
She believes she should now have a GPA of 3.05.
Is her reasoning correct? Justify your answer with 2 - 3 sentences.
Answer:
aiaiiwakkaoajdjsjzjhsjaj
6) The sides of a triangle are 3x, 2 and 9. If you know that all the sides are whole numbers,
determine the value of x and the third side of the triangle. Is the triangle acute, obtuse, or
right?
The requried two sides are equal, this triangle is an isosceles triangle, which means that two of the angles are equal to 45 degrees or less, and the triangle is acute.
What is the isosceles triangle?A triangle with two sides and two congruent angles is called an isosceles triangle.
To determine the value of x and the third side of the triangle, we need to first ensure that the triangle is a valid triangle, meaning that the sum of the lengths of the two shorter sides must be greater than the length of the longest side.
In this case, the two shorter sides are 2 and 3x, and the longest side is 9. We have,
2 + 3x > 9
Solving for x, we get:
3x > 7
x > 7/3
Since x must be a whole number, the smallest possible value for x that would make the triangle valid is 3. With x = 3, the third side of the triangle would be 3 × 3 = 9, which is equal to the longest side.
Therefore, the triangle has sides 2, 9, and 9.
Since two sides are equal, this triangle is an isosceles triangle, which means that two of the angles are equal to 45 degrees or less, and the triangle is acute.
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how many groups of 1/2 in a 8
Answer:
Step-by-step explanation:
y=16. There are sixteen 1/2 in 8
PREMISES
y=8/.5
CALCULATIONS
y=8/.5
y=8(2)
y=
16
PROOF
If y=16, then the dependent value D(y) 8/.5 returns
y(.5)=8
Solve for x and simplify answer
4
\x=-18
3
The value of the variable is x = -6/9
What is a fraction?A fraction is defined as the part of a whole number.
The different types of fractions are;
Mixed fractionsSimple fractionsComplex fractionsImproper fractionsProper fractionsWe are given the equation:
4/x = -18/3
To make 'x' the subject, cross multiply
-18x = 12
Now, divide both sides by the coefficient of x, we get;
x = 12/-18
x = -6/9
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That standard deviation of the ages of class members is 14.8. Find the range of ages that are within one standard deviation of the mean age.
I am so confused… brainlest if you answer quick and correct.. Ty.
The range of ages that are within one standard deviation of the mean age are given as follows:
M - 14.8 ≤ M ≤ M + 14.8.
In which M is the mean age.
How to obtain the range?The standard deviation of a data-set is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations.
The values that are within one standard deviation of the mean M have the bounds given as follows:
Lower bound: M - 14.8 -> one standard deviation below the mean.Upper bound: M - 14.8 -> one standard deviation above the mean.More can be learned about the standard deviation of a data-set at https://brainly.com/question/475676
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If your car gets 33 miles per gallon, how much does it cost to drive 350 miles when gasoline costs $2.80 per gallon?
Answer:
$29.68 to drive 350 miles
Step-by-step explanation:
To find the cost of driving 350 miles, we first need to calculate the amount of gasoline required for driving 350 miles. We can use the formula:
gasoline = distance ÷ miles per gallon
Plugging in the given values:
gasoline = 350 ÷ 33
gasoline = 10.606060606060606
So, we need 10.61 gallons of gasoline to drive 350 miles.
Next, we multiply the amount of gasoline needed by the cost per gallon to find the total cost:
total cost = gasoline × cost per gallon
total cost = 10.61 × 2.80
total cost = 29.6780
Therefore, it would cost approximately $29.68 to drive 350 miles when gasoline costs $2.80 per gallon and your car gets 33 miles per gallon.
Answer: 350 mi * 1 gal / 33 miles * $2.80 / 1 gal = 29.69$
which means the cost is 2.8*(350/33)=29.69$
Step-by-step explanation:
Here, 2.80$/1 Gal.
Now we need to cancel out gallons, so we add a ratio with gallons.
2.80$/1 Gal. x 1 Gal/33 mi.
Now add the last data element to cancel out miles.
2.80$/1 Gal. x 1 Gal/33 mi. x 350 mi.
Cancelling out units and numbers gives,
(2.80$ x 350)/33. Continue reducing to an answer:
980$/33 = 29.69$
How do you solve the problem: 5/8 * a/b = - 1/4?
Answer:a=-2
b=5
Step-by-step explanation:
[tex]\frac{a}{b} =\frac{\frac{-1}{4} }{\frac{5}{8} } \\\frac{a}{b} =\frac{-1}{4}*\frac{8}{5}\\\frac{a}{b}=-2/5[/tex]
The tool crib is 144 inches. How many 12 inches pieces can you cut from it
Answer:
Step-by-step explanation:
12
144 divided by 12 is 12
Please help me I need help with algebra 2
Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:
p(x) = (x + 1) q(x)
for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:
p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0
So,
0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c
= -5 + 7 - 2 + 3 + c
= c = 3
So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.
In which quadrant does the point (-21 , 13) lie?
A fruit juice recipe calls for 5 parts orange juice and 6 parts pineapple juice. Which proportion can be used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice?
30 over 21 equals j over 100
6 over 5 equals j over 21
6 over j equals 5 over 21
5 over 6 equals j over 21
For given ratio of orange juice and pineapple juice i.e. 5/6, proportion used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
What exactly is a ratio?
Fractions are commonly used to describe ratios and proportions. A ratio is demonstrated when a fraction is expressed as a:b, whereas a percentage indicates that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.
We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.
As a result, when b is larger than zero, the ratio, such as a:b, defines the relationship between two variables. For example, the 2:4 ratio is expressed as 2:4 = 1:2.
Now,
Given that In recipe ratio of orange juice / pineapple juice =5/6
then to make a recipe with 21 L of pineapple juice, the orange juice (j)
needed will be
5/6=j/21
j=17.5 L
hence,
proportion used to find the amount of orange juice, j will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
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Answer: its D
Step-by-step explanation:
pls i belieive most of yall are npcs
if (x) - **4, g(x) = x= 2, and h(x) = 4x+1, what is (f• Hºg)(x)?
2x+16
o (fe hºg)(x) =
2x+4
o (fonog)(x)=
4x-3
o (f• hºg)(x)- Ax=1
4x-5
o (f• nºg)(x) = AX-
The solution is, the value of (f• Hºg)(x) = 4x+2.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
f(x) = x-4
g(x) = x+ 2,
and h(x) = 4x+1
now, (f• Hºg)(x)
= (f•(4(x+2)+1)(x)
=((4x+6)-4)
=4x+2
Hence, The solution is, the value of (f• Hºg)(x) = 4x+2.
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10x³•2 √5x4 I need help
Answer:
20√5x7
Step-by-step explanation:
You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating. How much interest is accrued after the first month?
Answer:
$90.12
Step-by-step explanation:
The principal amount of the loan is ...
(sale price)(1 + sales tax rate) - (down payment)
= $19,725×1.0475 -2175 = $18,486.94
For a secured loan, the APR charged for an average credit rating appears to be 5.85%, so the interest for the first month is
i = Prt = ($18,486.94)(0.0585)(1/12)
i = $90.12
Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of Planes are Green?
There are 29% of the Planes are Green.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of green vehicles = 870
The percent of green planes = (number of green planes/number of total green vehicles) x 100
The percent of green planes = (250/870) x 100
The percent of green planes = 0.2873 x 100
The percent of green planes = 28.73
Round to the nearest percent, and we get
The percent of green planes = 29%
Thus, 29% of Planes are Green.
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what is the length of (3,5),(7,3)
Answer:
Step-by-step explanation:
The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:
d = √((7 - 3)^2 + (3 - 5)^2)
d = √((4^2) + (2^2))
d = √(16 + 4)
d = √20
So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.
Solve for x
2,4, and 6 i need help with
Answer:
2. 56°
4. 56°
For number 6, it is not shown on the photo, sorry!
Step-by-step explanation:
2. The square at the corner means that it is 90°, so 90 - 34 = 56
4. The line is straight, so it means that it is 180°, so 180 - 124 = 56
ax+bx=c make x subject
Answer:
x=c/(a+b)
Step-by-step explanation:
ax+bx=c
x(a+b)=c
x(a+b)/(a+b)=c/(a+b)
x=c/(a+b)
Answer:
[tex]x=\dfrac{c}{a+b}[/tex]
Step-by-step explanation:
To make x the subject of the equation ax + bx = c, rearrange the equation using algebraic operations to isolate a single x-variable.
Given equation:
[tex]ax + bx = c[/tex]
Factor out x from the left side of the equation:
[tex]x(a+b)=c[/tex]
Divide both sides of the equation by (a + b):
[tex]\dfrac{x(a+b)}{(a+b)}=\dfrac{c}{(a+b)}[/tex]
Simplify:
[tex]x=\dfrac{c}{a+b}[/tex]
What are the answers to these?
The values of the vacant spaces are $3.75, 4 oranges, 10 oranges, $15 and 20 percent of 160 is 32
What are the values?The table can be completed using the following values
If 8 oranges cost $10,
Then 1 orange will cost 10/8 = $1.25
This means that 3 oranges will cost 1.25*3 = $3.75
$5 can buy 8/10*5 = 40/10 = 4 oranges
In the same way, $12.50 will buy 8/10 * 12.50 = 10 Oranges
In the same manner, 12 oranges will cost 1.25*12 = $15
20% of 160 can be calculated as follows
Recall that percentage is a proportion of 100
This implies that 20/100 * 160 = 3200/100 = 32
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Need help solving three questions on algebra homework
The values of the composite functions are (f + h)(5) = 7, (h - f)(2) = 0, (fh)(3) = 0 and (h/f)(0) = 3/5
How to evaluate the composite functionsFrom the question, we have the following parameters that can be used in our computation:
The graphs
Using the graphs as a guide, we have the following:
(f + h)(5) = f(5) + h(5)
(f + h)(5) = 3 + 4
(f + h)(5) = 7
(h - f)(2) = h(2) - f(2)
(h - f)(2) = 1 - 1
(h - f)(2) = 0
(fh)(3) = f(3) * h(3)
(fh)(3) = 4 * 0
(fh)(3) = 0
(h/f)(0) = h(0)/f(0)
(h/f)(0) = 3/5
Hence, the value of the function (h/f)(0) is 3/5
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A magician has a magic trick that uses an 18" length of string that is cut into two pieces. One piece is two inches longer that the other. Find the length of each piece. Use algebraic equations.
The length of each piece is 10 in and 8 in.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total length of the string = 18 in
One piece = x + 2
Another piece = x
Now,
Solve for x.
x + 2 + x = 18
2x + 2 = 18
2x = 18 - 2
2x = 16
x = 8
Now,
One piece = 8 + 2 = 10 in
Another piece = 8 in
Thus,
The length of each piece is 10 in and 8 in.
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The perimeter is 30cm.
Work out the lengths of all the sides.
3x + 2
X
4x - 6
Answer: To solve for the length of all sides, we need to set the perimeter equal to the sum of the lengths of the three sides:
30 cm = 3x + 2 + x + 4x - 6
30 cm = 8x + 2
Now we can solve for x:
30 cm = 8x + 2
28 cm = 8x
x = 28/8
x = 3.5
So each of the sides is 3.5 cm long, and the lengths of the three sides are:
3x + 2 = 3 * 3.5 + 2 = 11.5 cm
x = 3.5 cm
4x - 6 = 4 * 3.5 - 6 = 11.5 cm
Therefore, the lengths of the sides are 11.5 cm, 3.5 cm, and 11.5 cm.
Step-by-step explanation:
Answer:
(3x+2+4x-6)2=30
7x-4=30
7x=34
x=34/7
To find the side lengths of the rectangle;
3x+2=116/7. and. 4x-6=94/7
Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11
Answer:do homework
Step-by-step explanation:
Please hurry!! Write one complete sentence to interpret the solution of the graph below.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The coordinates of points where the two lines intersect, is the solution of the equations/lines, that is (6, 64)
A cell phone plan charges $47.35 per month plus $13.94 in taxes, plus $0.60 per minute for calls beyond the 400-minute monthly limit. Write a piecewise-
defined function to model the monthly cost C(x) (in S) as a function of the number of minutes used for the month.
C(x).
18
for (Choose one) Y
for (Choose one) ▼
X
!!
The two pieces relate to the number of minutes used, since there's the 400-minute limit.
Piece #1: When you use less than or equal to 400 minutes:
Cost calculation: $47.35 + $13.94 = $61.29
Piece #2: When you use more than 400 minutes:
Cost calculation: $47.35 + $13.94 + $0.60(x-400)
The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge
Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71
Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.
[tex]C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.[/tex]
Your system might not require the "0≤x", but it technically should be there.
Martin gives 40% of £75 to his sister. How much money does Martin give to his sister?
Answer:
Step-by-step explanation:
75 x 0.40= £30
1: Amelia is organising a game for a charity fête.
She has put 1 orange, 1 pink, 1 green and 2 yellow counters into a bag.
To play, each person will pay £1 and take out a counter at random.
They will then replace the counter and then take a second counter at random.
The person will win £2.50 if both counters are the same colour.
autet
Amelia expects 200 people to play the game.
How much money would Amelia expect to raise for charity?
The amount of money that Amelia is expected to raise is given as follows:
£78.13.
How to obtain the expected amount?The outcomes of a person winning, and their probabilities, as given as follows:
Two orange: 1/4 x 1/4 = 1/16.Two pink: 1/4 x 1/4 = 1/16.Two yellow: 2/4 x 2/4 = 4/16.Hence the probabilities of winning and losing are given as follows:
Winning: 6/16.Losing: 10/16.Then the distribution of earnings for each person is given as follows:
P(X = -1) = 10/16. -> Lose.P(X = 2.5) = 6/16 -> wins.Hence, considering 250 people, the expected amount raised is given as follows:
E(X) = 250/16 x (2.5 x 6 - 1 x 10)
E(X) = £78.13.
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Refrigerator a uses 500 watts per hour when the motor is operating. The motor needs to run an average of 12 hours per day, every day, to stay at a constant, cold temperature. This model of refrigerator lasts an average of 20 years before it needs to be replaced and costs $1,000. Each kwh of electricity costs $0. 12.
To determine the total energy consumption of refrigerator A in a day, we need to first convert the power usage from watts to kilowatts.
500 watts/hour * 1 kilowatt/1000 watts = 0.5 kilowatts/hour
Next, we can calculate the energy consumption in kilowatt-hours (kWh) per day:
0.5 kilowatts/hour * 12 hours/day = 6 kilowatt-hours/day
To find the daily cost of running the refrigerator, we can multiply the energy consumption by the cost per kWh:
6 kWh/day * $0.12/kWh = $0.72/day
To calculate the yearly cost of running the refrigerator, we can multiply the daily cost by 365 days:
$0.72/day * 365 days = $262.80/year
To calculate the total cost of running the refrigerator for 20 years, we can multiply the yearly cost by 20:
$262.80/year * 20 years = $5,256.00
In addition to the cost of running the refrigerator, there is also the cost of purchasing the unit itself. In this case, the cost is $1,000.
Therefore, the total cost of owning and operating Refrigerator A for 20 years is:
$5,256.00 (operating cost) + $1,000.00 (purchase cost) = $6,256.00
It's worth noting that this calculation assumes that the cost of electricity remains constant over the 20-year lifespan of the refrigerator. In reality, the cost of electricity may increase over time, which would increase the overall cost of running the refrigerator.
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