Based on the calculations, the age of this person is equal to 25 years.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to solve this word problem, we would assign a variable to the age of this person and then translate the word problem into algebraic equation as follows:
Let x represent the age.
Translating the word problem into an algebraic equation, we have;
x + 65 = 6(x - 10)
Opening the bracket, we have:
x + 65 = 6x - 60
Re-arranging the equation, we have:
6x - x = 60 + 65
5x = 125
Dividing both sides by 5, we have:
x = 125/5
x = 25 years.
In conclusion, we can reasonably infer and logically state that this person's age was 25 years ten (10) years ago.
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Complete Question:
In 65 years I will be 6 times as old as I was 10 years ago. How old am I?
Check the attachment
Answer:
[tex]a\:\dfrac{\sqrt{a^3}}{a^4} =\dfrac{\sqrt{a}}{a^2}[/tex]
Step-by-step explanation:
I believe this question is wrongly or part of it has been truncated in the screenshot
I have simplified the original expression and checked my answer.
[tex]\mathrm Simplify \;\;a\dfrac{\sqrt{a^3}}{a^4}\\\\\sqrt{a^3} = a^{\dfrac{3}{2}} = a^{(1 + \frac{1}{2})} = a \cdot a^\frac{1}{2} = a \sqrt{a} \\\\a\dfrac{\sqrt{a^3}}{a^4}\\\\ = \dfrac{a\cdot a\cdot \sqrt{a}}{a^4}\\\\= \dfrac{a^2\sqrt{a}}{a^4}\\\\= \dfrac{\sqrt{a}}{a^{(4-2)}}\\\\\\=\dfrac{\sqrt{a}}{a^2}[/tex]
if r and s are integers and an expression of the form (x − r)(x − s) is multiplied out, a quadratic polynomial with integer coefficients is obtained. for instance, (x − 2)(x − 7)
The quadratic expression when ( x - 2) ( x - 7 ) is multiplied is x² - 9x + 14.
A polynomial of degree two or a quadratic polynomial that has two as the highest exponent of the variable. A quadratic polynomial will typically have the following form: p(x): ax² + bx + c, a ≠ 0.
A coefficient is a multiplicative factor in a polynomial term, a series term, or an expression; it often has the form of a number but can also take the form of any expression.
When an expression ( x - r )( x - s ) is multiplied, where r and s are integers, we obtain a quadratic polynomial.
Therefore, when ( x - 2 )( x - 7 ) is multiplied we get:
( x - 2 )( x - 7 ) = x( x - 7 ) - 2( x - 7 )
( x - 2 )( x - 7 ) = x² - 7x - 2x + 14
( x - 2 )( x - 7 ) = x² - 9x + 14
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Which of the following represents the prime factorization of 72? (need answer asap please)
2^3 x 3^2 x 4
2^3 x 3 ^2
2 x 3^2 x 4^2
2^2 x 3^3
Answer:
I believe the answer is 2^3x3^2
A radioactive sample has a half-life of 12 hours. after hours, 4 milligrams of the sample remain. what is the initial amount of the radio-active substance?
After 18 hours the remaining quantity of the radioactive sample will be (A) 4.68 grams.
What are mathematical operations?An operation, also known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied.So, original radioactive substance = 3000 grams.
Half-life = 3 hoursSo, a number of half-lives in 18 hours:
18/3 = 6Then, after 18 hours:
1/(2)⁶ ⇒ 1/64 × 300 = 4.6875 gramsTherefore, after 18 hours the remaining quantity of the radioactive sample will be (A) 4.68 grams.
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The correct question is given below:
300 grams of a radioactive sample has a half-life of 3 hours. After 18 hours, the remaining quantity will be:
(A) 4.68 gm
(B) 2.34 gm
(C) 3.34 gm
(D) 9.37 gm
A mutual fund starts the day at a price of $100 1/2 and then loses 1/10 of its value n one day. Identify the daily change.
Answer:
one tenth of 100.5 is 10.05 so 10.05$
Step-by-step explanation:
First take 100.5 multiply by one tenth=10.05$ or ten dollars and 5 cents
An 8 1/4 candle burnt down in 11 hours how far has it burn after 4 1/2 hours
Answer:
27/8 or 3⅜
Step-by-step explanation:
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The silo shown has a volume of 14,250 cubic feet. The top of the silo
is a hemisphere. And has a radius of 9. Find the height of the silo
Answer:
Step-by-step explanation:
Part A. The figure at the right is of 2 grain, storage silos. The diameter of each measures 24 feet and the height of the cylinder measures 51 feet. The height ...
i need help please thanks
Answer:
8, B
Step-by-step explanation:
[tex]-6(3-r)=30 \\ \\ -18+6r=30 \\ \\ 6r=48 \\ \\ r=8[/tex]
You have $60 in your bank account each week you plan to deposit $7 from your allowance and $25 from your paycheck the equation b = (60 + (25+7)w gives the amount b in your account after w weeks how many weeks from now will you have $280 in your bank account
After completing 6 week and 8 days, the amount in the bank account will be $280.
What is defined as the equation?In its most basic form, an equation is an algebraic statement that shows that 2 mathematical expressions were indeed equal. In mathematics, the most basic as well as simple algebraic equations comprise of one or more variables.The initial balance in the bank account = $60.
Allowance deposit per week = $7.
Paycheck deposit per week = $25.
Let 'w' be the number of week.
Th equation of the total amount 'b' after 'w' week becomes;
b = 60 + (25+7)w
As, the total amount becomes $280, after the week .
Put b = 280 in equation and find w.
280 = 60 + (25+7)w
Simplifying;
220 = 32w
w = 6.875
Thus, after completing 6 week and 8 days, the amount in the bank account will be $280.
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If x [tex]\neq[/tex] 0, what is the value of (5x)^0?
Answer:
1
Step-by-step explanation:
from the rule of exponents
• [tex]a^{0}[/tex] = 1 , then
[tex](5x)^{0}[/tex] = 1
From a hot-air balloon, Nayeli measures a 35^{\circ} ∘ angle of depression to a landmark that’s 905 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
The balloon's vertical distance above the ground is equal to 633.7 feet
What is angle of depression?
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.
Given data ,
we have Angle of depression = 35°
Base distance D = 905 ft
Let the vertical distance be H
To calculate the vertical distance H of the balloon above the ground , we use the angle of depression and the base distance.
Therefore , using the trigonometric identities ,
sin = Opposite / Hypotenuse
cos = Adjacent / Hypotenuse
tan = Opposite / Adjacent
So , tan Ф = tan 35°
= H / D
tan 35°= H / 905
H = tan 35° x 905 ft
H = 0.7002075 x 905
H = 633.7 ft
Hence , vertical distance is equal to 633.7 ft
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Solve for n.
solve for n.
−2(n − 4.5) > 11
n > 1
n < 1
n > −1
n < −1
Answer:
n < - 1
Step-by-step explanation:
- 2(n - 4.5) > 11 ← distribute parenthesis on left side
- 2n + 9 > 11 ( subtract 9 from both sides )
- 2n > 2
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
n < - 1
Answer:
n < -1
Step-by-step explanation:
-2(n -4.5) > 11 (multiply the contents within the bracket by -2.)
-2n + 9 > 11 (- × - = +)
-2n > 11 - 9 [ like terms have to be with each other (transposing); and when u transpose a number it changes signs.]
-2n > 2 (divide both sides by negative 2)
n < -1 (sign changes as a reslut of the negative division)
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the product. Write your answer as a mixed number in simplest form.
5 × 2 =
=
Answer:
667/45 or 14 37/45
Step-by-step explanation:
you have to convert 5 4/5 x 2 5/9 then you multiply those numbers but simply them which would be 29/5 x 23/9 then you get 667/45 or 14 37/45 as an alternative form
hope this helps
Admission to a movie theater is $7 for children and $12 for adults. on a certain day, 67 people bought tickets at the theater and $704 was collected. how many children's tickets were sold and how many adult's tickets were sold?
Answer: 20 children’s tickets and 47 adult’s tickets
20 children's tickets were sold and 47 adult tickets were sold.
People bought tickets at the theater and $704 was collected.
charge - $7 for children and $12 for adults.
let, x number of children and y number of an adult take admission,
then, according to question ->
7*x+12*y=704; said eq. 1
and, given 67 people bought tickets at the theater.
x + y=67; said eq. 2
now, on solving these equations,
we get,
multiply eq.2 by 7 then subtract with eq. 1
then we get, y=47 then put the value of y in eq. 2 we get x=20;
so,
20 children's tickets were sold and 47 adult tickets were sold.
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Bottled Drinking Water Americans drank an average of 23.2 gallons of bottled water per capita in 2004. If the standard deviation is 2.7 gallonvariable is normally distributed, find the following probabilities. Use a graphing calculator and round the answers to four decimal places.More than 25 gallons of bottled water.P (more than 25 gallons of botted water)
They tell us that it is distributed in a normal way, which means that the distribution has the following characteristics:
If teh standart deviation is 2.7 gallon and the avriabe is normal distributed we need to know the probability highlighted in the image above, when replacing in the formula with x greater than 25 we obtain:
[tex]P(x>25)=0.2525[/tex]Model Real Life The Elephant
Building is 335 feet high. A real
Asian elephant is 12 feet tall. If
29 real elephants could stand on
top of each other, would they reach
the top of the building?
Answer:
Yes
Step-by-step explanation:
The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?
They are asking if 29 12' elephants are as tall as as a 335' building:
29 × 12' = 348' elephant stack
because 348' is taller than 335' building then yes, 29 staked elephant would reach and pass the top of a 335' building.
help me please I really need it
Answer:
15
Step-by-step explanation:
Divide it into triangles, then solve for area.
A class contains 12 students who study Geography(G), 11 students who study History(H) and 10 students who study Economics(E). If no student studies more than one of these subjects, what is the probability that three students chosen at random all study History? Give your answer as a decimal correct to three significant figures.
Is the answer 3/33 or 1/3 * 1/3 *1/3 (11/33 = 1/3)
0.030 is the probability that three students chosen at random all study History.
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty. Mathematics' discipline of probability investigates potential outcomes of events as well as their relative likelihoods and distributions.
Given Data
12 students who study Geography(G),
11 students who study History(H)
10 students who study Economics(E)
Probability that three students chosen at random all study History
[tex]\frac{11}{3}[/tex] ÷ [tex]\frac{33}{3}[/tex]
[tex]\frac{11}{3}[/tex] ×[tex]\frac{3}{33}[/tex]
0.030
0.030 is the probability that three students chosen at random all study History.
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Which equation represents the same proportional relationship as the graph? On a coordinate plane, a line goes through points (0, 0), (5, 3), (10, 6). Group of answer choices y = five-thirds x x y = three-fifths y = three-fifths x x y = five-thirds
Based on the line and the points that it goes through, the equation with the same proportional relationship as the graph is y = three-fifths x.
How to find the relationship of the graph?To find the relationship of the points on the line in the coordinate plane, you need to find the slope of the line. The slope can be found by the formula:
= Change in y / Change in x
Solving for the slope gives:
= (3 - 0) / (5 - 0)
= 3 / 5
For equations to be proportional, they need to have the same slope. With the slope of the line being 3/5, the equation that would have the same proportional relationship is:
y = 3/5x
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You use the equation M/5 - 26 = 2L- 1/2g to calculate the amount of money M in your account at the end of the month, where L is the number of lawns mowed and g is the number of gallons of gas used.
a. Solve the equation for M
Based on the given equation, the change of subject of the equation to M is given by M = 10L - 5/2g + 130
How to make M the subject of the formulaChanging the subject of formula of an equation is the working out of a particular variable from the list of variables in the formula. The variable is either denoted with letter or symbol.
M/5 - 26 = 2L- 1/2g
Where,
M = the amount of money in your account at the end of the monthL = number of lawns mowedg = number of gallons of gas used.M/5 - 26 = 2L- 1/2g
Add 26 to both sidesM/5 = 2L - 1/2g + 26
Cross productM = 5(2L - 1/2g + 26)
M = 10L - 5/2g + 130
Therefore, the solving for M in the equation will give M = 10L - 5/2g + 130
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can someone help with the last problem
Answer:
Bro x =21
Step-by-step explanation:
X=21 and AM=14
As all the lines are same so all will be 7 and x will be 3 times 7 which is 21 and in the AM case there 7 is 2 times thus multiply 7 by 2 for 14
please help asap due monday
[tex]\frac{x^{2} - 9}{3x^{2} + 8x - 3 } : \frac{x - 3}{x + 2} =\frac{(x^2 - 9)(x + 2)}{(3x^2 +8x - 3)(x - 3)} =\frac{x^3 + 2x^2 - 9x - 18}{3x^3 - 9x^2 + 8x^2 - 24x - 3x + 9} =\frac{ x^3 + 2x^2 - 9x - 18}{3x^3 - x^2 - 27x + 9} = \frac{0}{3 - 3x} = 0[/tex]
Answer:
0
Step-by-step explanation:
when you multiply, and add and subtract it all up, you eventually get 0 over 3-3x. what is 0 divided by 3-3x? 0
A tennis ball machine fires balls a distance that is approximately normally distributed. The mean distance, μ, is unknown and the standard deviation is 1.2 feet. If 5% of balls go farther than 70 feet, find μ. (Round to 3 decimal places.)
The mean distance, μ, If 5% of balls go farther than 70 feet is; μ = 68.032
How to calculate the population mean?We know that the formula to find the z-score is;
z = (x' - μ)/σ
where;
z is z-score
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
σ = standard deviation = 1.2
x' = sample mean = 70 ft
Now, the z-score that produces a p-value of 0.05 or 5% is; z = 1.64
Thus;
1.64 = (70 - μ)/1.2
μ = 70 - (1.64 * 1.2)
μ = 68.032
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Paul is a carpenter and earns $21.50 per hour. Last week Paul worked 40 hours, what is
Paul's gross pay?
Answer: $860 this week.
Step-by-step explanation:
Paul worked 40 hours this week, and makes 21.50 dollars an hour. Gross pay means the amount of money paid before taxes.
So we don't need to calculate any taxes, which means all we need to do is multiply 21.50 by 40 hours, since he makes 21.50 an hour, and he worked 40 hours.
in a school board election between two candidates, 539 votes were cast. George received 23 more votes than abe. How many votes did each receive
A = votes to Abe
G = votes to George
we know that all votes together were 539, so A + G = 539, we also know that George got 23 more than Abe, so "G = A + 23"
[tex]\stackrel{Abe's}{A}~~ + ~~\stackrel{George's}{(A+23)}~~ = ~~\stackrel{total}{539}\implies 2A+23=539\implies 2A=516 \\\\\\ A=\cfrac{516}{2}\implies \boxed{\stackrel{Abe}{A=258}}\hspace{12em}\boxed{\underset{George}{\stackrel{258~~ + ~~23}{281}}}[/tex]
Which of the following has eight faces?ООO A. octahedronO B. tetrahedronO C. icosahedronO D. dodecahedron
Given:
The number of faces =8.
Required:
We need to find the polyhedron with 8 faces.
Explanation:
Recall that the tetrahedron is a polyhedron composed of four triangular faces
The number of faces in tetrahedron =4.
Recall that the octahedron is a polyhedron with 8 faces.
The number of faces in the octahedron= 8.
Recall that the dodecahedron is a polyhedron with 12 faces.
The number of faces in the dodecahedron = 12.
Recall that the icosahedron is a polyhedron with 20 faces.
The number of faces in icosahedron =20.
Final answer:
octahedron
IF ANYONE ANSWERS THIS CORRECTLY, I WILL GIVE YOU BRAINLIEST!
The value of x in this geometric sequence is equal to √2.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ is the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.For this exercise, we would formulate an equation from the common ratio of this geometric sequence as follows:
r = a₂/a₁ = a₃/a₁
Substituting the given parameters into the common ratio formula, we have;
1/√X + 1 = √x - 1/1
Next, we would take the square of both sides, we have:
1/x + 1 = x - 1/1
Cross-multiplying, we have:
(x + 1)(x - 1) = 1
x² - x + x - 1 = 1
x² - 1 = 1
Adding 1 to both sides, we have:
x² - 1 + 1 = 1 + 1
x² = 1 + 1
x² = 2
x = √2
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What does the standard deviation measure?
Answer:
Standard deviation measures the dispersion of a dataset relative to its mean
Step-by-step explanation:
Nicole went for a drive in her new car. She drove for 169.6 miles at a speed of 53 miles per hour. For how many hours did she drive?
169.6/53 = 3.2
about 3.2 hours
Answer:
3.2 hours
Step-by-step explanation:
169.6 ÷ 53 = 3.2
so, she drove 3.2 hours
What is the inverse of the function f(x) = 1/9x + 2?
Answer:
h(x) = 9x-18 is the correct inverse function
Step-by-step explanation:
f(x) -> y (first we need to rewrite the equation with y)
y= 1/9x+2 (next we need to solve for x)
y=1/9x
-2 -2 (subtract 2 from both sides)
y-2= 1/9x (multiply 9 on both sides
9y-18= x (and lastly switch back x and y)
y = 9x - 18 (if a real equation than write h(x) or [tex]f(x)^{-1}[/tex], if not real equation keep it in y)
h(x) = 9x-18
Hope this helps!
Answer:
9x–18
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