[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{\underline{v}olume varies inversely with \underline{p}ressure}}{V=\cfrac{k}{p}}~\hfill[/tex]
Peter and his four brothers combined all of their money to buy a video game. If 20% of the total money is Peter's, and $4.00 of the total money is Peter's, how much do all five brothers have combined?
Given that Peter contributes 20% of the total money and his part is $4.00, it is deduced that the total combined amount the five brothers have is $20.00.
To solve this, we can set up a simple proportion where 20% (or 0.20 in decimal form) of the total amount is equal to $4.00.
Step-by-Step Solution:
Let x represent the total combined amount of money that Peter and his brothers have.
Since Peter contributes 20% of the total, we can express this as 0.20 imes x = $4.00.
To find x, we divide both sides of the equation by 0.20, giving us x = $4.00 / 0.20.
By performing the division, we find that x = $20.00.
Therefore, the total combined amount Peter and his brothers have is $20.00.
How many different strings can be formed by rearranging the letters in the word troposphere?
Step-by-step explanation:
The letters of the word troposphere can be sorted to be:
ee h oo pp rr s t
with 7 distinct letters of which 4 are in pairs for a total of 11 letters.
The number of words that can be formed from n distinct letters
= n!/(1!1!1!....1!) [n times in the denominator]
The number of words that can be formed from n letters of which 2 are duplicated and the rest distinct is
= n!/(2!1!1!....1!) [n-1 times 1!]
Similarly, the number of words that can be formed from 11 letters, of which there are 4 pairs of duplicated letters is
N=11! / (2!2!2!2!1!1!1!)
= 39916800 / (2*2*2*2*1*1*1)
= 2494800
For a limited time, Sammy’s gas station is offering a discount on the cost of gasoline when amounts greater than 5 gallons are purchased. The table below shows the cost for different amounts of gasoline.
Which of these could be used to determine c, the cost for purchasing g gallons of gasoline with the discount?
A: C=2.65g
B: C=2.65g-12
Answer:
C = 26.5g - 2
Step-by-step explanation:
We can plug in our given numbers for g and see if the C corresponds.
g = 7, C = 16.55
A) C = 2.65*7 --> C = 18.55
We know that C ≠ 18.55, so it should be B (I think you typed that one wrong, it is C = 2.65g - 2)
The equation C=2.65g could be used to determine the cost for purchasing g gallons of gasoline with the discount.
Explanation:To determine the cost for purchasing g gallons of gasoline with the discount, we need to examine the given options. Option A states that the cost, C, equals 2.65g, which means the cost is directly proportional to the number of gallons. This could be a valid equation for determining the cost with the discount. However, option B states that the cost, C, equals 2.65g-12. This equation subtracts a constant value of 12, which is not mentioned in the problem, so it is not a valid way to determine the cost with the discount. Therefore, option A could be used to determine the cost for purchasing g gallons of gasoline with the discount.
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What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4
Answer:
Required logarithmic function is :
[tex]f\left(x\right)=\log_3\left(x\right)[/tex]
Step-by-step explanation:
We have been fiven that table for the logarithmic function is:
x f(x)
9 2
27 3
81 4
which can be rewritten as:
x f(x)
3^2 2
3^3 3
3^4 4
Which are basically powers of 3
So we can use logarithmic function as
[tex]\log_3\left(9\right)=\log_3\left(3^2\right)=2\log_3\left(3\right)=2(1)=2[/tex]
Hence required logarithmic function is :
[tex]f\left(x\right)=\log_3\left(x\right)[/tex]
The amount of time it takes Joel to check e-mail is directly proportional to the number of messages he has. If it takes him t minutes when there are n new e-mail messages, then how long does it take him (in terms of t and n) if there are 50 new messages?
A) 50tn
B) 50n t
C) 50t n
D) t n
Answer:
50t/n minutes.
Step-by-step explanation:
The equation of proportionality is t = kn where k is a constant.
So k = t/n.
So for 50 new message the time = 50k = 50 * t/n
= 50t/n minutes.
A hypothetical population includes 1 million men and 1 million women. Suppose that a sample of this population of 100 included 20 men and 80 women. Identify the misuse of statistical data.
A) Sample bias
B) Loaded questions
C) Data manipulation
D) Overgeneralization
Answer:
A) Sample bias
Step-by-step explanation:
If a sample of 100 participants includes 20 men and 80 women, then the sample is biased. Women account for;
(80/100)*100 = 80% of the total participants while men only for 20%.
The sample does not represent the entire population in fair proportions hence the sample is biased
What is the scale factor ABC to XYZ???
Answer:
A) 6
Step-by-step explanation:
This would be your best answer.
Given four functions, which one will have the highest y-intercept?
f(x) g(x) h(x) j(x)
Blake is tracking his
savings account with
an interest rate of 5%
and a original deposit
of $15.
x g(x)
1 6
2 8
3 12
the function h of x equals 4 to the x power, plus 3 j(x) = 10(2)x
f(x)
g(x)
h(x)
j(x)
Answer:
f(x)
Step-by-step explanation:
f(x) apparently has an initial value of 15.
g(x) apparently will have an initial value of 6 or less, since g(1) = 6 and it has increasing slope.
h(0) = 4^0 +3 = 3
j(0) = 10·2^0 = 10
The largest initial value among the initial values {15, <6, 3, 10} is 15.
f(x) has the largest y-intercept
_____
The graph shows two ways g(x) can be modeled. One is exponential with an initial value of 4; the other is quadratic with an initial value of 6.
Final answer:
Among the functions provided, j(x) = 10(2)^x has the highest y-intercept, which is 10, found by evaluating the function at x equals 0.
Explanation:
To determine which function has the highest y-intercept, we need to examine each function and look for the point where the graph crosses the y-axis (when x is 0). Unfortunately, the only function provided with enough information to determine the y-intercept directly is h(x) = 4^x + 3. Evaluating h at x equals 0 gives us h(0) = 4^0 + 3, which simplifies to 1 + 3, yielding a y-intercept of 4. The function j(x) = 10(2)^x would have a y-intercept of 10 when x is 0. However, without the specifics of f(x) and not enough points to determine a pattern in g(x), it is not possible to accurately determine their y-intercepts. Thus, between h(x) and j(x), j(x) has the highest y-intercept at 10.
For the function given below, find a formula for the riemann sum obtained by dividing the interval [a,b] into n equal subintervals and using the right-hand endpoint for each c subscript k. then take a limit of this sum as n right arrow infinity to calculate the area under the curve over [a,b]. f(x)equals2x over the interval [2,4].
The Riemann sum for f(x) = 2x on [2,4] is evaluated as n approaches infinity to give the integral from 2 to 4 of 2x dx, resulting in an area of 12 square units under the curve.
Explanation:To find the Riemann sum for the function f(x) = 2x over the interval [2, 4], we start by dividing the interval into n equal subintervals, with each subinterval of width ∆x = (b - a) / n. For the right-hand endpoint, the kth point c at which f(x) is evaluated is given by c_k = a + k*∆x. Therefore, the Riemann sum is:
∑_{k=1}^{n}f(c_k)*∆x = ∑_{k=1}^{n}2(a + k*∆x)*∆x.
As n → ∞, the Riemann sum approaches the definite integral of the function. For the given function, the integral can be calculated directly, and the limit of the Riemann sum as n approaches infinity gives us the area under the curve, which in this case is equivalent to the area of a right triangle with base 2 and height 4.
Thus, we find that the area under the curve on the interval [2, 4] for f(x) = 2x is simply integral from 2 to 4 of 2x dx, which evaluates to 4^2 - 2^2, or 12 square units.
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Help asap
What is the approximate area of a sector given Θ≈212 with a radius of 45 m?
Question 1 options:
2613.59 m²
3744.45 m²
3371.26 m²
2928.36 m
Answer:
[tex]3,744.45\ m^{2}[/tex]
Step-by-step explanation:
we know that
The area of a sector is equal to
[tex]A=\frac{\theta}{360\°}\pi r^{2}[/tex]
where
[tex]\theta[/tex] ------> is the angle in degrees
r is the radius of the circle
In this problem we have
[tex]r=45\ m[/tex]
[tex]\theta=212\°[/tex]
assume
[tex]\pi =3.14[/tex]
substitute the values
[tex]A=\frac{212\°}{360\°}(3.14)(45)^{2}[/tex]
[tex]A=3,744.45\ m^{2}[/tex]
HELP PLEASE! I’m having a hard time answering this.
Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70*. Will the ladder be safe at this height? Show work.
The question is asking to solve a problem that'll "add up", or in other words, makes sense; through the use of Trigonometric functions. The leaning ladder is the hypotenuse of 17ft, adjacent to that is a wall that measures 16.5ft above the ground. The angle both sides make must be <=70°. The function here is Opposite over Hypotenuse i.e 16.5/17 . We use the inverse operation of Sin which is Sin^(-1) to find if the angle is < or = to 70°. Using a calculator, we find the angle to be 76.06°, which is > more than, 70°.
Thus, the ladder will not be safe for its height and therefore won't make sense.
12 - 6x - 5 = -23 *
6
5
-5
-6
2x - 4 - 4x = 8 *
16
6
2
-6
4x + 4 - 8x = 16 *
1 point
5
3
-3
-5
-6 + 3x - 5x = 24 *
24
15
-6
-15
3x + 10 + 5x = 50 *
12
5
-5
-12
Answer:
1.) 5
2.) -6
3.) -3
4.) -15
5.) 5
Find the solution set of this inequality. Select
the correct graph.
18x + 161 > 16
Click on the correct answer.
Answer:
"first number line shown in the diagram"
Step-by-step explanation:
Whenever we have inequality of the form
| x + a | > b
we can write
1. x+a > b, and
2. -(x+a) > b
and solve both.
So we can write
1. 8x + 16 > 16
2. -(8x+16) > 16
Solving 1:
8x > 16 - 16
8x > 0
x > 0
Solving 2:
-(8x+16) > 16
-8x - 16 > 16
-16 -16 > 8x
-32 > 8x
-32/8 > x
-4 > x
Putting these together, we can say x is greater than 0 & x is less than -4
The first number line is right.
The answer is:
The first option.
[tex]-4>x>0[/tex]
Why?To solve absolute values inequalities, we need to remember that absolute value functions have a positive and a negative solution.
For example, we have that:
[tex]|x|>1[/tex]
The solution will be
[tex]-1>x>1[/tex]
So, we are given the inequality:
[tex]|8x+16|>16[/tex]
Isolating "x", we have:
[tex]-16>8x+16>16[/tex]
[tex]-16-16>8x+16-16>16-16[/tex]
[tex]-32>8x>0[/tex]
[tex]\frac{-32}{8}>\frac{8x}{32}>\frac{0}{32}\\\\-4>x>0[/tex]
Hence, we have that the correct option is the first option.
The solution is:
[tex]-4>x>0[/tex]
or
(-∞,-4)U(0,∞)
Have a nice day!
5^12 ÷ 5^4 = _____
A) 5^3
B)5^8
C) 5^16
The answer is:
The correct option is:
B) [tex]5^{12}\div5^{4}=5^{8}[/tex]
Why?To solve the problem, we need to remember the quotient of power property, it's defined by the following relation:
[tex]\frac{a^{m} }{a^{n} }=a^{m-n}[/tex]
If we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.
So, we are given the expression:
[tex]5^{12}\div5^{4}[/tex]
Which is equal to write:
[tex]\frac{5^{12} }{5^{4}}[/tex]
Then, calculating we have:
[tex]\frac{5^{12} }{5^{4}}=5^{12-4}=5^{8}[/tex]
Hence, the answer is:
B) [tex]\frac{5^{12} }{5^{4}}=5^{8}[/tex]
or
[tex]5^{12}\div5^{4}=5^{8}[/tex]
Have a nice day!
Answer:
The correct answer is option B. 5^8
Step-by-step explanation:
Points to remember
Identities
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾
x⁻ᵃ = 1/xᵃ
To find the correct option
It is given an expression, 5^12 ÷ 5^4
⇒ 5¹²/5⁴
By using identities we can write,
5¹²/5⁴ = 5⁽¹² ⁻ ⁴⁾
= 5⁸
Therefore the correct answer is option B. 5^8
Each of
6
students reported the number of movies they saw in the past year. This is what they reported:
6, 8, 16, 7, 19, 20
Find the mean and median number of movies that the students saw.
The median is 12.
The arithmetic mean is 12.7
The geometric mean is 11.3
A cake has circumference of 25 1/7 inches. What is the area of the cake? Use 22/7 to approximate π. Round to the nearest hundredth. Enter your answer in the box.
Answer:
50.29 in^2
Step-by-step explanation:
From the circumference we need to find the radius.
Since C = 2*pi*r, r = C / (2*pi).
Here, with C = 25 1/7 in, r = (25 1/7 in) / [ 2(22/7) ], or r = 4 in
The area of the cake is A = pi*r^2, or (here) A = (22/7)(4 in)^2 = 50.29 in^2
Check math problem?
a vector has both a magnitude and a
Direction?
Scalar?
Reverse?
number?
I choose Direction, but not sure.
Answer:
Step-by-step explanation:
What sets a vector apart from a scalar is that the vector has both magnitude (length) and direction, whereas a scalar has only magnitude, no direction.
Answer:
Direction is correct
Step-by-step explanation:
A scalar quantity has magnitude but no direction while
a vector has both magnitude and direction
Padma also pays for a subscription to a sports channel.Yhe channel cost $132 for a year.How much does Padma pay for the sports channel per month? How much does Padma pay each month for the sports channel and the magazine combined?
Answer:
Padma pays $11 dollars a month for the sports channel. I do not see the question for the magazine:(
Step-by-step explanation:
Identify the volume and surface area of the hemisphere in terms of π. HELP ASAP!!
Answer:
D
Step-by-step explanation:
Use the formula for the SA of a hemisphere.
[tex]SA=2\pi r^2[/tex]
Now we can find the radius of the hemisphere, which is 15.
Then, we can square that and multiply it by 2 to get 450.
Now, let's use the formula for the Volume of a hemisphere.
[tex]V=\frac{2\pi r^3}{3}[/tex]
Now we can cube 15 and multiply it by 2 to get 6750.
Then we can divide this number by 3.
2250.
So the answer is D.
CAN SOMEONE HELP ME WITH NUMBER 7??
I WILL GIVE BRAINLIEST!
Answer:
tanx-(\sqrt(11))/(5)cosx>0
Step-by-step explanation:
Because to do this kind of trig you first have to know how to do basic trg
Angles that have a common vertex and side is called ______
ANSWER
Adjacent Angles
EXPLANATION
Angles that have a common vertex and side are called adjacent angles.
The vertex is the point of intersection of the arms of an angle.
A vertex can be formed by two more rays.
From the diagram, angle x and y and adjacent angles.
The common vertex is V.
The common side is VZ
Angles m and n are not adjacent angles because they do not have the same vertex.
Given a polynomial f(x), if (x − 2) is a factor, what else must be true?
A. f(0) = 2
B. f(0) = −2
C. f(−2) = 0
D. f(2) = 0
Answer:
D. f(2) = 0
Step-by-step explanation:
If x-2 is a factor of a function, then f(2) must be zero
f(x) = p(x) * (x-2) since (x-2) is a factor of f(x)
Substitute in x=2
f(2) = p(2) (2-2)
f(2) = p(2) *(0)
Anything times 0 = 0
f(2) = 0
(1.) Solve for x. Show ALL work: -2x + 5 = 4x - 7
(2.) Solve for y. Show ALL work: 12y + 4 = 8y - 12
(3.) Solve for z. Show ALL work: 7z - 18 = -2z + 18
(4.) Solve for x. Show ALL work: 10x + 15 = 5x - 10
The answers are:
1
[tex]x=2[/tex]
2
[tex]y=-4[/tex]
3
[tex]z=4[/tex]
4
[tex]x=-5[/tex]
Why?Solving for each of the given equations and variable, we have:
1[tex]-2x + 5 = 4x - 7[/tex]
Solving for "x", we have:
[tex]-2x + 5 = 4x - 7\\\\-2x-4x=-7-5\\\\-6x=-12\\\\x=\frac{-12}{-6}=2[/tex]
So, we have that:
[tex]x=2[/tex]
2[tex]12y+4=8y-12[/tex]
Solving for "y", we have:
[tex]12y+4=8y-12\\\\12y-8y=-12-4\\\\4y=-16\\\\y=\frac{-16}{4}=-4[/tex]
So, we have that:
[tex]y=-4[/tex]
3[tex]7z-18 =-2z+18[/tex]
Solving for "z", we have:
[tex]7z-18 =-2z+18\\\\7z+2z=18+18\\\\9z=36\\\\z=\frac{36}{9}=4[/tex]
So, we have that:
[tex]z=4[/tex]
4[tex]10x+15 =5x-10[/tex]
Solving for "x", we have:
[tex]10x+15 =5x-10\\\\10x-5x=-10-15\\\\5x=-25\\\\x=\frac{-25}{5}=-5[/tex]
So, we have that:
[tex]x=-5[/tex]
Hence, the answers are:
1
[tex]x=2[/tex]
2
[tex]y=-4[/tex]
3
[tex]z=4[/tex]
4
[tex]x=-5[/tex]
Have a nice day!
Find the product. 3(x + 4) (x - 5) A. 3x2 ? 20x B. 3x2 ? 11x ? 20 C. 3x2 ? 3x ? 60 D. 3x2 ? x ? 20
For this case we must find the product of the following expression:[tex]3 (x + 4) (x-5)[/tex]
We must apply distributive property to the terms of the first parenthesis:
[tex](3x + 12) (x-5) =[/tex]
Again we apply the distributive property:
[tex]3x ^ 2-15x + 12x-60 =\\3x ^ 2-3x-60[/tex]
ANswer:
[tex]3x ^ 2-3x-60[/tex]
Step 1: Distribute the 3 to x and 4
(3x + 12)(x - 5)
Step 2: FOIL (First, Outside, Inside, Last)
Multiply the first of the values in the parentheses together
(3x + 12) (x - 5)
[tex]3x^{2}[/tex]
Multiply the outside values in the parentheses together
(3x + 12)(x - 5)
-15x
Multiply the inside values of the parentheses together
(3x + 12)(x - 5)
12x
Multiply the last values of the parentheses together
(3x + 12)(x - 5)
-60
Step 3: Add all the FOIL values together
3[tex]x^{2}[/tex] + (-15x) + 12x + (-60)
Step 4: Combine like terms
3[tex]x^{2}[/tex] + (-15x) + 12x + (-60)
3[tex]x^{2}[/tex] - 3x - 60
Hope this helped!
Jared has some quarters and dimes that total $5.50. If he has 8 more quarters that dimes, how much dimes does Jared have?
Final answer:
To determine the number of dimes Jared has, we set up an equation based on the total value of dimes and quarters equaling $5.50. After solving the equation, we find that Jared has 10 dimes.
Explanation:
The student's question asks how many dimes Jared has if he has a total of $5.50 consisting of quarters and dimes, with 8 more quarters than dimes. Let 'd' represent the number of dimes. Since a dime is worth $0.10, the total value of the dimes is 0.10d dollars. Jared has 8 more quarters than dimes, so he has 'd+8' quarters. A quarter is worth $0.25, so the total value of the quarters is 0.25(d+8). The sum of the values of the dimes and quarters is $5.50, so we can set up the equation 0.10d + 0.25(d+8) = 5.50.
Now, solving for d:
0.10d + 0.25(d+8) = 5.50
0.10d + 0.25d + 2 = 5.50
0.35d + 2 = 5.50
0.35d = 5.50 - 2
0.35d = 3.50
d = 3.50 / 0.35
d = 10
Jared has 10 dimes.
What statement represents the reasonable time when the basketball is in the air
The ball hits the ground at 2.5sec
The answers aren’t all showing but neither of the top two showing are correct. Pick the answer that fits with the ball being in the air for 2.5sec.
What is the coordinates of T' if T(-4,2) after a rotation of the triangle 180°about the origin?
Answer:
T'(4, -2)
Step-by-step explanation:
Rotation 180° about the origin (same as reflection across the origin) negates both coordinates:
T' = -T = -(-4, 2)
T' = (4, -2)
What is the value of θ for the acute angle in a right triangle?
sin(θ)=cos(48°)
Enter your answer in the box.
θ=
°
Answer:
Step-by-step explanation:
cosΘ=sin(90-Θ)
cos(48)=sin(90-48)
cos(48)=sin(42)
Answer:
cosine (48) = 0.66913
The arc sine of (.66913) = 42 degrees
Step-by-step explanation:
A sporting goods store received an order of 80 baseball caps, of which 12 were green. If 1 of the 80 caps is selected at random, what is the probability it will NOT be green?
15%
68%
85%
88%
Answer:
85%
Step-by-step explanation:
If the sporting goods store received a lot of 80 baseball caps... and 12 of them were green that means that 68 (80-12) were NOT green.
Thus, the probably to randomly pick up a cap that is NOT green is 68 out of 80...
68/80 = 17/20 = 85%
A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred years. What is the population of the village today?
This is an example of exponential growth. The population of this village triples every hundred years. Given the village was founded 400 years ago by 20 people, the current population would be 1620 people.
Explanation:The given situation is an example of exponential growth, which can be found in various scenarios such as population growth. From the information provided, the population of the village triples every hundred years. Since the village was founded four hundred years ago and initially had 20 people, we can calculate the population today using the following steps:
The population after 100 years is 20 (initial population) x 3 (tripling) = 60.The population after the next 100 years is 60 (population after the first hundred years) x 3 (tripling) = 180.The population after three hundred years is 180 (population after two hundred years) x 3 (tripling) = 540.Finally, the population after the fourth hundred years, which is now, is 540 (population after three hundred years) x 3 (tripling) = 1620.So, the population of the village today would be 1620 people.
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The population of the village today is 720 people.
Explanation:To find the population of the village today, we need to calculate the number of population doublings that have occurred over the four hundred year period.
Since the population triples every one hundred years, it doubles twice in that time frame.
Doubling a number is the same as multiplying it by 2.
So, the population at the start was 20, then it doubled to 40 after one hundred years, and doubled again to 80 after two hundred years.
Finally, it tripled to 240 after three hundred years, and tripled again to 720 after four hundred years.
Therefore, the population of the village today is 720 people.
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