By solving a system of equations we will see that the two-digit number is 84.
Which expression best represents the word problem?
"The tens digit of a number is twice the ones digit"
"The sum of the digits is 12".
A two-digit number can be written as:
a*10 + b
Where a is the tens digit and b is the ones digit.
The word problem can then be written as:
a = 2*b
a + b = 12
So we have a system of equations.
To find the number we need to solve these, if we replace the first equation into the second one:
a + b = 12
(2b) + b = 12
3b = 12
b = 12/3 = 4
Then:
a = 2b = 2*4 = 8
So the two-digit number is 84.
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A tennis ball can in the shape of a right circular cylinder holds four tennis balls snugly. If the radius of a tennis ball is 3.5 cm, what percentage of the can is not occupied by tennis balls?
Answer:
about 33.3%
Step-by-step explanation:
The fraction of space not occupied will be the same as the unoccupied fraction of a cylinder of the same height and diameter as a sphere.
Volume of a cylinderThe volume of a cylinder of diameter d and height d will be ...
V = πr²h = π(d/2)²(d) = (π/4)d³
Volume of a sphereThe volume of a sphere of diameter d is ...
V = 4/3πr³ = 4/3π(d/2)³ = (π/6)d³
Unoccupied spaceThe fraction of space that is occupied is ...
occupied space = (sphere volume)/(cylinder volume)
occupied space = ((π/6)d³) / ((π/4)d³) = 4/6 = 2/3
The fraction of unoccupied space is ...
unoccupied fraction = 1 -2/3 = 1/3
unoccupied fraction ≈ 33.3%
Answer:
Putangina okay
Step-by-step explanation:
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What are the solutions of the equation x4 + 3x² + 2 = 0? Use u substitution to solve.
O x=+√√√2 and x = +1
Ox=ti√√2 and x = ti
Ox=± √√2 and x = ti
Ox=+√√2 and x = +1
Answer:
[tex]\pm i\sqrt{2}\text{ and } \pm i[/tex]
Step-by-step explanation:
[tex]\text{let u = } x^2[/tex] so then [tex]u^2=x^4[/tex].
This gives you the equation: [tex]u^2+3u+2=0[/tex].
Now factor the equation by looking for factors of 2 that add up to 3, which is just 2 and 1. Use these to rewrite the equation: [tex](u+2)(u+1)[/tex]. So now just set each factor equal to 0:
[tex]u+2=0\\u=-2[/tex]
Now substitute x^2 back in as u
[tex]x^2=-2[/tex]
Take the square root of both sides
[tex]x=\pm \sqrt{-2}[/tex]
Separate the radical into sqrt(-1) * sqrt(2)
[tex]x=\pm \sqrt{-1}*\sqrt{2}[/tex]
Rewrite using i
[tex]x=\pm i\sqrt{2}[/tex]
Now set the other factor equal to 0
[tex]u+1=0\\u=-1[/tex]
substitute x^2 back in as u
[tex]x^2=-1[/tex]
Take the square root of both sides
[tex]x=\pm\sqrt{-1}[/tex]
rewrite using i
[tex]x=\pm i[/tex]
Find f(x-4) if f(x)=-x+2. f(x-4)
Answer:
= -x+6
Step-by-step explanation:
we can simply substitute (x-4) in x place because when we say function of x , we are basically saying when we substitute a given value in the place of x we will find a given y.so for example if we have a question f(4), we can simply plug 4 to -x +2 so we will find y or f(x) = -2.
so the answer for the above question will be f(x)= -x +6.
What is the radius of a sphere that has a surface area of 2903.33 in²?
Answer:
15.2 in
Step-by-step explanation:
The surface area of a sphere is given by the formula below:
Surface area of sphere= 4πr², where r is the radius
Given that the surface area is 2903.33 in²,
2903.33= 4πr²
Divide both sides by 4π:
[tex] {r}^{2} = \frac{2903.33}{4\pi} [/tex]
Square root both sides:
[tex]r = \sqrt{ \frac{2903.33}{4\pi} } [/tex]
r= 15.2 in (3 s.f.)
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Answer:
Move all the points on the graph two points to the right
Step-by-step explanation:
f(x-2) is just a translation to the right by 2. The whole formula is typically y = a f(b(x + c)) + d. In this case, the C value is the one being changed and that indicates a translation left or right. -2 indicates 2 to the right.
Answer:
The Slope: 0
The y-intercept: (0,0_
x y
0 0
1 0 (there is supposed to be a line between the x and y that goes down all the way down the numbers but i cannot type that)
Step-by-step explanation:
A town has population of 5000 and grows at 3.5% every year. To the nearest tenth
of a year, how long will it be until the population will reach 7300?
It would take approximately 11 years for this population to reach 7300.
How to calculate the time?Based on the information provided, the future size of the population can be modelled by using an exponential function:
F = Pe^rt
Substituting the given parameters into the formula, we have;
7300 = 5000e^{0.035 × t}
7300/5000 = e^{0.035t}
1.46 = e^{0.035t}
Taking the ln of both sides, we have:
ln(1.46) = ln(e^{0.035t})
0.378 = 0.035t
t = 0.378/0.035
Time, t = 10.8 ≈ 11 years.
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............help ?????????????
Step-by-step explanation:
Solution.x+40°+35°=180°(straight line)x+75°=180°x=180°-75°x=105hope it helps!!
Answer:
x = 75°
Step-by-step explanation:
∠ p = 40° [alternate interior angles]
∠ q = 35° [alternate interior angles]
x = ∠ p + ∠ q
x = 40° + 35°
x = 75°
What is the simplified value of the exponential expression
the simplified value of the exponential expression is 1/9
What’s one of the goals set out by the Healthy People 2010 program?:
a)
Ensuring that complaints against unfair billing are addressed
b)
Ensuring that private hospitals accept payment from any health insurance company
c)
Encouraging all employers to provide health insurance to their employees
d)
Eliminating the difference between the healthcare available to low and high income persons
Answer:
d i did the thing
Step-by-step explanation:
To raise funds for a new fire truck, a fire department is conducting a raffle. Residents can purchase a raffle ticket for $10.00 each. After writing his/her name on the ticket, the resident will place it in a container. Later on, a fire department official will randomly select one ticket from the container. The resident who purchased the selected ticket will win a prize of $2,000.00.
a. Suppose at the time of the drawing there are a total of 1000 purchased raffle tickets in the container. If a particular resident has purchased 10 tickets, what is his/her probability of winning the prize?
b. Compute the expected profit (winnings − cost) for a particular resident who purchased 10 raffle tickets.
c. After paying out the $2,000.00 prize, how much money has the fire department raised for its new fire truck? Other than the prize, ignore any other raffle costs incurred by the fire department.
a. The probability of winning the prize by the resident who purchased 10 tickets is 1% (10/1,000).
b. The expected profit (winnings - cost) for the resident who purchased 10 raffle tickets is $1,900 ($2,000 - $100).
c. The amount raised by the fire department after paying out the $2,000 prize (ignoring other raffle costs) is $8,000 ($10,000 - $2,000).
What is a raffle?A raffle is a gambling competition or lottery organized to raise money for a purpose.
A raffle involves the sale of tickets which are drawn randomly to select some winners.
Data and Calculations:Price of a raffle ticket = $10
Prize = $2,000
Cost of purchasing 10 tickets = $100 ($10 x 10)
Number of raffle tickets sold = 1,000
Total revenue realized = $10,000 ($10 x 1,000)
Thus, if a resident purchases 10 tickets, the chance of winning the raffle is 1%.
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Parentheses three times to parentheses divided by parentheses 5×4 parentheses
find the values of m&n if x
2
−2
[tex]f(x) = mx ^{4} + 2x ^{3} - 3x ^{2} + nx - 4[/tex]
The values of m and n from the given equation are 1/4 and -2
Polynomial functionsGiven the polynomial function below
f(x) = mx^4+2x^3-3x^2+nx-4
If the zeros are 2 and -2, hence;
0 = 16m+16-12+2n-4
0 = 16m-16+12-2n-4
_______________
16m+2n = 0
16m - 2n = 8
Subtract
2n+2n = -8
4n = -8
n = -2
Substitute for "m'
16m + 2(-2) = 0
16m = 4
m = 1/4
Hence the values of m and n from the given equation are 1/4 and -2
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Can someone please help me
Answer:
Number 4
Standard form - Not sure if right
y = − 0.2734375x^2 − 1.09375x +11.40625
Factored form - Not sure if right
y= 0.0390625 (−7x^2 −28x+292)
Number 5
Either form of the equation other than standard form
Vertex form : y = −(x +3)^2 + 25
Vertex of the parabola
(-3,25)
X and Y intercepts
x-intercept(s): (2,0) ,(−8,0)
y-intercept(s): (0,16)
If the cost of milk is $3 per gallon, what is the amount of money a farmer can make by selling the milk produced by the cow in the month of April?
The amount of money a farmer can make by selling the milk produced by the cow in the month of April is $90
How to determine the amountFrom the equation given, we have that
$3 = I gallon
Let's take it that the farmer sells one gallon by per day
We know that the month of April has 30 days
So if he makes $3 in 1 day
He would make x in 30 days
Collect like terms
$30 × 30 days = amount
Multiply through
Amount = $90
Thus, the amount of money a farmer can make by selling the milk produced by the cow in the month of April is $90
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If n + 2, 5, and 9 represent the lengths of the sides of a triangle then < n
Answer:
n>2 (see below)
Step-by-step explanation:
Triangle side rule says n+2 + 5 must be greater than 9
n+2 +5 > 9
n > 2
(but it must be less than 12 o/w 5 + 9 will not be greater than n+2)
Please help! Consider the following subset of the real number line. How can this set be expressed using inequalities?
Answer:
-2 ≤ x ≤10
Step-by-step explanation:
Notice that x can never be less than -2 and can never exceed.
-2 and 10 are all inclusive thus the last answer is not correct as it tries to leave them out
I need help with this question please!!
Answer:
31465
Step-by-step explanation:
n!/((n-r)! r!)
= 31!/(31-4)! 4!
= 31!/ 27! 4!
= 31465
Given the function defined by g(x)=x²+4x-3, find g (s).
Answer:
[tex]g(s)=s^{2} +4s-3[/tex]
Step-by-step explanation:
If we have a function f(x) and want to find f(a) , just substitute by x=a in the Equation of f(x) , the Result will be f(a)So for our Question , we have [tex]g(x)=x^{2} +4x-3[/tex]
and we want to find g(s) , so just substitute by x = s in the Equation of g(x)
[tex]g(s)=s^{2} +4s-3[/tex]
Which of the following are geometric sequences?
Check all that apply.
A. 5, 10, 15, 20, 25
B. 10, 5, 2.5, 1.25, 0.625, 0.3125
C. 1, 1, 2, 3, 5, 8, 13
D. -9, -3, -1, -1/3, -1/9, -1/27
Answer: B and D
Step-by-step explanation:
A is not, it's an arithmetic sequence where each term is +5 greater than the previous
B is because each term is 1/2 the previous term (common ratio of 1/2) thus making it a geometric sequence
C is not, it's the Fibonnaci sequence which is neither an arithmetic or geometric sequence
D is because each term is 1/3 the previous term (common ratio of 1/3) thus making it a geometric sequence
Write this in logarithm form √x = y
The logarithmic form of √x = y is ㏒ₓy = 1/2
How to determine the logarithmic formWe have, logarithmic form as;
㏒ₓ n = bⁿGiven √x = y
Convert the square root to power of 1/2 as that is what it represents, we get
x^1/2 = y
Then compare with the universal logarithmic form, we have
㏒ₓy = 1/2
Thus, the logarithmic form of √x = y is ㏒ₓy = 1/2
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Dante has scored 30, 18, and 28 points in his three basketball games so far. How many points does he need to score in his next game so that his average (mean) is 26 points per game
Answer:
He needs to score 28 points.
Step-by-step explanation:
[tex]1^{st}\,\,score: 30\,\,points;\\\\2^{nd}\,\,score: 18\,\,points;\\\\3^{rd}\,\,score: 28\,\,points;\\\\4^{th}\,\,score: \,\,?[/tex]
Let's calculate Dante's 4th score, given that the average is 26 points:
[tex]\frac{S1 + S2 + S3 + S4}{4} = 26\\\\\frac{30 + 18 + 28 + S4}{4} = 26\\\\76 + S4 = 104\\\\S4 = 28\,\,points.[/tex]
Work out the reciprocal of 0.0005. Give your answer in standard form. 7 Work out the reciprocal of 0.0005 . Give your answer in standard form .
Answer:
that's all I could do. hope it helps.
good day.
What will sue pay for 18 oranges if the cost 0.49 for 6 show the process
Answer:
[tex]\huge\boxed{\sf \$ \ 1.47}[/tex]
Step-by-step explanation:
Given that,6 oranges = $0.49
Multiply 3 to both sides
6×3 oranges = $0.49 × 3
18 oranges = $1.47
[tex]\rule[226]{225}{2}[/tex]
The graph is of a function in the form p(t) = a*b^t. What is the function?
Answer:
p(t) = 5*2^t
Step-by-step explanation:
We can solve for 'a' and 'b' using the point coordinates shown on the graph.
SetupSubstituting for (t, p(t)), the two equations we can make from the given points are ...
p(t) = a*b^t
5 = a*b^0 . . . . . . . (t, p(t)) = (0, 5)
10 = a*b^1 . . . . . . . (t, p(t)) = (1, 10)
SolutionThe first equation tells you ...
5 = a
The second equation tells you ...
10 = 5*b
2 = b
EquationThe function is ...
p(t) = a*b^t
p(t) = 5*2^t
Maria spends $19 on lottery tickets every week and spends $122 per month on food.On an annual basis, the money spent on lottery tickets is ______% of the money spent to buy food.
The money spent on lottery tickets is 15.6% of the money spent to buy food.
How to determine the proportion?The given parameters are:
Food = $122
Lottery = $19
The proportion of the lottery tickets is:
Proportion = Lottery/Food * 100%
This gives
Proportion = 19/122* 100%
Evaluate
Proportion = 15.6%
Hence, the money spent on lottery tickets is 15.6% of the money spent to buy food.
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They work-infested $18,000 into accounts, one yielding 4% interest and the other yielding 12%. If he received a total of $1,280 and interest at the end of the year, how much did he invest at 4%?
Answer:
$11,000
Step-by-step explanation:
Let amount invested for 12% yield be p . Amount for 4% yield is therefore (18000-p)
Interest for 12%: 12% of p=0.12p
Interest for 4%: 4% of (18000-p)=0.04(18000-p)=720-0.04p
Total interest:
=0.12p + (720-0.04p)
=0.12p-0.04p+720
=0.08p+720
But we already know the total interest is 1280
Therefore: 0.08p+720=1280
0.08p=1280-720
0.08p=560
p=560÷0.08
p=7000
Therefore at 4% the person invested:
(18000-p)
18000-7000
$11,000
Use the spinner to identify the probability to the nearest hundredth of the pointer landing on a non-shaded area
Here are the shopping times (in minutes) of ten shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 5 .)
The frequency which is to filled in the table is 3,1,2,4.
Given shopping time of ten shopkeeper: 36,20,32,18,20,33,28,34,37,23.
We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.
Shopping time is given as 36,20,32,18,20,33,28,34,37,23.
Intervals for which frequency is given is 18 to 22, 23 to 27, 28 to 32, 33 to 37.
Numbers in the range 18 to 22=18,20,23 therefore 3
Numbers in the range 23 to 27=23 therefore 1
Numbers in the range 28 to 32=32 , 28 therefore 2
Numbers in the range 33 to 37=36, 33, 37, 34 therefore 4.
Hence the frequency which is to filled are 3,1,2,4.
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can you please help me with this question? thanks!
Answer:
Step 2
Step-by-step explanation:
In step 1, Gary had the right idea of multiplying both sides by 4 to eliminate the denominator, but in step 2, Gary makes a mistake since e should equal 10 not 8. 2.5 * 4 = 10 not 8
Answer:
B) Step 2
Step-by-step explanation:
Gary's mistake occurs in Step 2. He was right to multiply both sides of the equation by 4 to find e, but his error is in the multiplication of 2.5*4. 2.5*4 = 10, not 8.
Choose the lowest common denominator.
03 04 05 06 08 010 012
Find the sum:
Alw
The sum is
and
colch
The expression written in equivalent form with a
common denominator is
Done
1) 8
2) [tex]-\frac{3}{4}=-\frac{6}{8}[/tex], so it is equal to [tex]-\frac{6}{8}+\frac{5}{8}[/tex]
3) 1/8