A package of 3 pairs of insulated socks costs $25.17. What is the unit price of the pairs of socks?
Molly had 1/8 of a bag of birdseed. She separated it equally into 2 bird feeders. What part of a bag did each feeder get?
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325. Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points) Part B: Write the equation obtained in Part A using function notation. (2 points) Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. at t = 0, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 8 gal/min. find the amount of salt in the tank when the tank contains exactly 40 gal of solution.
To find the amount of salt when the tank contains exactly 40 gallons, create and solve differential equations for salt concentration and tank size over time. We find the tank size is 40 at 10 minutes, at which point there is approximately 14.2 lbs of salt.
Explanation:To solve this, you need to understand that the total amount of salt at any time t is equal to the amount of salt coming in minus the amount of salt going out.
To begin with, the tank has 80 gal x 1/8 lb/gal = 10 lbs of salt.
The amount of salt coming in is 4 gal/min * 1 lb/gal = 4 lbs/min
The amount of salt going out depends on the concentration of the salt in the tank at that time. This is (4-8)(total salt/liters in tank at time t).
Setting up a differential equation and solving gives us an equation for salt concentration and volume at time t:
The equation for the tank size(in gallons) at time t (in minutes) is: tank size = 80 - 4t
The equation for the salt in tank at time t (in minutes) is: salt = 10 - 4t + 80e^-2t
When the tank size is exactly 40 gallons, tank size = 40 = 80 - 4t so t = 10 minutes
Plugging t = 10 into our equation for salt gives us: salt = 10 - 4*10 + 80e^-20 = approximately 14.2 lbs.
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A circle with a radius of 1/2 ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all that apply.
A.The length of the new radius will be 4 feet.
B. The length of the new radius will be 32 feet.
C.The new circumference will be 8 times the original circumference.
D.The new circumference will be 64 times the original circumference.
E.The new area will be 8 times the original area.
F.The new area will be 64 times the original area.
G.The new circumference will 8PI be
H.The new area will be 16PI square feet.
Answer:
The statements A,C,F,G and H are true.
Step-by-step explanation:
It is given that the radius of circle before dilation is [tex]\frac{1}{2}ft[/tex] and the scale factor is 8.
The circumference of original circle is,
[tex]S_1=2\pi r[/tex]
[tex]S_1=2\pi \times \frac{1}{2}=\pi[/tex]
The area of original circle is,
[tex]A_1=\pi r^2[/tex]
[tex]A_1=\pi (\frac{1}{2})^2[/tex]
[tex]A_1=\frac{\pi}{4}[/tex]
The dilation by scale factor 8 means the radius of new circle is 8 times of the original circle.
[tex]r=8\times \frac{1}{2}[/tex]
Therefore the radius of new circle is 4 ft and the statement A is true.
The circumference of original circle is,
[tex]S_2=2\pi r[/tex]
[tex]S_2=2\pi \times 4=8\pi[/tex]
[tex]\frac{S_2}{S_1}=\frac{8\pi}{\pi} =8[/tex]
The new circumference will be 8 times the original circumference. The statement C is true.
The area of original circle is,
[tex]A_2=\pi r^2[/tex]
[tex]A_2=\pi (4)^2[/tex]
[tex]A_2=16\pi[/tex]
[tex]\frac{A_2}{A_1}=\frac{16\pi}{\frac{\pi}{4}}=64[/tex]
The new area will be 64 times the original area. Therefore statement F is true.
The new circumference will [tex]8\pi[/tex],The new area will be [tex]16\pi[/tex] square feet.
Calculate the slope m, if defined, of the straight line through the given pair of points. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.) (6, 5) and (7, 2)
The slope m of the straight line through the points (6, 5) and (7, 2) is -3.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
The slope of the line is defined as the ratio of the rise to the run.
To find the slope, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (6, 5) and (x₂, y₂) = (7, 2).
Substituting these values, we get:
m = (2 - 5) / (7 - 6) = -3 / 1 = -3
Therefore, the slope of the straight line through the given pair of points is -3.
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In a right triangle, angle C measures 40°. The hypotenuse of the triangle is 10 inches long. What is the approximate length of the side adjacent to angle C?
6.4 inches
7.7 inches
8.4 inches
13.1 inches
Answer
Find out the what is the approximate length of the side adjacent to angle C .
To prove
As given
In a right triangle, angle C measures 40°.
The hypotenuse of the triangle is 10 inches long.
Than by using the trignometric identity
[tex]cos\angle C= \frac{Base}{Hypotenuse}\\cos\angle C= \frac{BC}{AC}[/tex]
As shown the diagram is given below
AC= 10 inches , ∠C = 40 °
cos 40 = 0.766 (approx)
Put in the above formula
0.766 × 10 = BC
7.66 = BC
7.7 inches (approx) = BC
Option (b) is correct .
The correct option is Option C [tex]\boxed{{\mathbf{7}}{\mathbf{.66 inches}}}[/tex] .
Further explanation:
The cosine ratio can be represented as,
[tex]\cos \theta = \frac{{{\text{base}}}}{{{\text{hypotenuse}}}}[/tex]
Here, base is the length of the side adjacent to angle [tex]\theta[/tex] and hypotenuse is the longest side of the right angle triangle.
The length of side opposite to angle [tex]\theta[/tex] is perpendicular that is used for the sine ratio.
Step by step explanation:
Step 1:
From the given information, the observed right angle is attached.
First find the hypotenuse and the base of the right angle triangle.
It can be seen from the attached figure that the side [tex]BC[/tex] is adjacent to angle [tex]C[/tex] and the side [tex]AC[/tex] is the hypotenuse of triangle.
Thus, the [tex]{\text{base}}=BC[/tex] and [tex]{\text{hypotenuse}}=10[/tex] .
Step 2:
We know that the cosine ratio is [tex]\cos \theta =\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}[/tex] .
Therefore, it can be written as,
[tex]\cos \theta=\frac{{BC}}{{AC}}[/tex]
Now substitute the value [tex]BC=x[/tex] and [tex]{\text{AC}}=10[/tex] in the cosine ratio.
[tex]\begin{aligned}\cos C&=\frac{x}{{10}}\\{\text{co}}s40&=\frac{x}{{10}}\\0.766&=\frac{x}{{10}}\\x&=7.66\\\end{aligned}[/tex]
Therefore, the approximate length of the side adjacent to angle [tex]C[/tex] is [tex]7.7{\text{ inches}}[/tex] .
Thus, option C is correct.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Trigonometry
Keywords: Distance, Pythagoras theorem, base, perpendicular, hypotenuse, right angle triangle, units, squares, sum, cosine ratio, adjacent side to angle, opposite side to angle.
Write the equation 6x − 3y = −12 in the form y = mx + b.
How many possible hands of 3 cards can be obtained from a deck of cards? what are the odds of dealing three eights in a row from the deck?
There are 22,100 possible hands of 3 cards from a 52-card deck using combinations. The probability of dealing three eights in a row from the deck is approximately 0.000181.
This question involves calculating probabilities and combinations related to card hands from a deck of 52 cards.
Possible Hands of 3 Cards:
To determine the number of possible hands of 3 cards from a 52-card deck, we use the combination formula: C(n, k) = n! / [k! * (n - k)!], where n is the total number of cards and k is the number of cards to choose.
C(52, 3) = 52! / [3! * (52 - 3)!] = 52! / (3! * 49!) = (52 × 51 × 50) / (3 × 2 × 1) = 22100. Therefore, there are 22,100 possible hands of 3 cards.
Probability of Dealing Three Eights:
The probability of dealing three eights in a row can be determined as follows:
There are 4 eights in the deck.The probability of drawing the first eight: 4/52.The probability of drawing the second eight: 3/51.The probability of drawing the third eight: 2/50.Therefore, the probability of dealing three eights is: (4/52) × (3/51) × (2/50) = 24 / 132600 = 1 / 5525 ≈ 0.000181.
This detailed explanation helps in understanding how combinations and probabilities in card games are calculated.
latoya drove 864 miles in 12 hours. at the same rate, how long would it take her to drive 576 miles?
Answer:
8 Hours!!
Step-by-step explanation:
What is the rate of growth as a percent for 23(1.0032)
The area of a rectangular wall of a barn is 168 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.
The following table shows the probability distribution for a discrete random variable.
X 13| 16 |17| 21| 23| 25 |26 |31
P(X) 0.07 |0.21| 0.17| 0.25| 0.05| 0.04| 0.13| 0.08
What is the mean of this discrete random variable. That is, what is E(X), the expected value of X?
Answer: APEX- 20.42
Step-by-step explanation: Multiply 13 by 0.07, multiply 16 by 0.21, and so on. then add up all of the decimals and that is your answer
The dimension of a rectangular pool are 24.5 feet by 13 feet. The depth of the water is 4 feet. Each cubic foot contains 7.48 gallons of water. How many gallons of water to the nearest tenth, are needed to fill the pool to 80% capacity
Answer:
Pool needed to be filled = 7623.62 gallons
Step-by-step explanation:
Length of rectangular pool = 24.5 feet
Width of rectangular pool = 13 feet
Depth of rectangular pool = 4 feet
Now, Volume of the pool = Length × Width × Depth
= 24.5 × 13 × 4
= 1274 cubic feet
Now, 1 cubic feet = 7.48 gallons
⇒ 1274 cubic feet = 7.48 × 1274
= 9529.52 gallons
So, Volume of the pool = 9529.52 gallons
Now, the pool is to be filled 80%
So, Pool needed to be filled = 9529.52 × 0.80
= 7623.62 gallons
The number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.
Number of gallons of waterFirst step:
Volume of the pool=Length × Width × Depth
Volume of the pool= 24.5 ft × 13ft × 4ft
Volume of the pool=1274 cubic feet
Second step:
Number of gallons=(7.48 × 1274)×80%
Number of gallons=9529.5 gallons×80%
Number of gallons=7623.6 gallons
Inconclusion the number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.
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Sam is 5 years old. His older brother, Tom, is three times as old as Sam. When Sam is 20, how old will Tom be?
The two lines, X and Y, are graphed below:
Line X is drawn by joining ordered pairs negative 3,12 and 7,negative 16. Line Y is drawn by joining ordered pairs 0, negative 14 and 11, 8
Determine the solution and the reasoning that justifies the solution to the systems of equations.
(2, 7), because this point is true for both the equations
(4, −6), because this point lies only on one of the two lines
(4, −6), because this point makes both the equations true
(2, 7), because the lines intersect the x-axis at these points
Answer:c
Step-by-step explanation:
(4,-6), because this point makes both the equations true.
what is an infinite set in geometry please help asap
A mule deer can run 1/4 of a mile in 25 seconds. At this rate which expression can be used to determine how fast a mule deer runs in miles per hour
A certain solution has a hydrogen ion concentration of 3.54 x 10−5 moles per liter. Write this number in standard notation.
A man invests
$3700
in three accounts that pay
5%,
6%
, and
7%
in annual interest, respectively. He has
3
times as much invested at
7%
than he does at
5%
. If his total interest for the year is
$234
, how much is invested at each rate?
Which equation represents the line that passes through the points (3, 7) and ( - 1, - 1)?
if a number is a whole number then it cannot be.......
a...an irrational number
b...a natural number
c...an integer
d...a rational number
Using number sets, it is found that a whole number cannot be irrational, hence option a is correct.
What are rational and irrational numbers?All numbers that can be represented by fractions are rational.Numbers that cannot be represented by fractions, such as non-repeating decimals and the square roots of numbers that are not perfect squares are irrational.In this problem, any whole number can be represented by a fraction, hence it cannot be irrational and option a is correct.
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Answer:
A. An Irrational Number
Step-by-step explanation:
Irrational numbers are numbers like pi or angles with degrees, while whole numbers are numbers from 0+
Hope it helped!
The height of a right cylinder is 3 times the radius of e base. The volume of the cylinder is 24π cubic units. What is the height of the cylinder?
A. 2 units
B.4 units
C.6 units
D. 8 units
Volume = pi * r^2 * h
h = 3r
pi * r^2 * (3r) = 24 pi
3r^3 = 24
r^3 = 8
r = 2
Height = 3*2 = 6 units
evaluate the surface integral:S
(x^2z + y^2z) dS
S is the hemisphere
x2 + y2 + z2 = 9, z ≥ 0
53 ℃ below zero degrees
solve for a in terms of F and m: F=ma
To find acceleration 'a' in the equation F = ma, divide both sides by mass 'm', resulting in the formula [tex]a =\frac{f}{m}[/tex]
To solve for a in terms of F and m from the equation F = ma,
where F represents force,
m represents mass,
and a represents acceleration,
we need to isolate the variable a.[tex]f= m*a\\a =\frac{f}{m}[/tex]
This gives us the formula:
[tex]a =\frac{f}{m}[/tex]
This formula tells us that the acceleration of an object is equal to the force applied to it divided by its mass.
We did not find results for: A measure of malnutrition, called the pelidisi, varies directly as the cube root of a person's weight in grams and inversely as the person's sitting height in centimeters. A person with a pelidisi below 100 is considered to be undernourished, while a pelidisi greater than 100 indicates overfeeding. A person who weighs 48,820 g with a sitting height of 78.7 cm has a pelidisi of 100. Find the pelidisi (to the nearest whole number) of a person whose weight is 54,688 g and whose sitting height is 72.6 cm. Is this individual undernourished or overfed?The pelidsi is _____Round to the nearest integer as needed..
Since a pelidisi below ( 100 ) is considered undernourished and a pelidisi greater than ( 100 ) indicates overfeeding, with a pelidisi of ( 114 ), this individual is considered to be overfed.
Let's denote the pelidisi as ( P ), the weight in grams as ( W ), and the sitting height in centimeters as ( H). According to the given information, the pelidisi varies directly as the cube root of the person's weight and inversely as the person's sitting height. This relationship can be expressed mathematically as:
[tex]\[ P = k \times \frac{\sqrt[3]{W}}{H} \][/tex]
where ( k ) is the constant of variation.
We are given that a person with a weight of ( 48,820 ) g and a sitting height of ( 78.7 ) cm has a pelidisi of ( 100 ). We can use this information to find the value of ( k ):
[tex]\[ 100 = k \times \frac{\sqrt[3]{48820}}{78.7} \][/tex]
Solving for \( k \):
[tex]\[ k = \frac{100 \times 78.7}{\sqrt[3]{48820}} \]\[ k \approx \frac{7870}{36} \approx 218.611 \][/tex]
Now that we have the value of \( k \), we can find the pelidisi for a person with a weight of \( 54,688 \) g and a sitting height of \( 72.6 \) cm:
[tex]\[ P = 218.611 \times \frac{\sqrt[3]{54688}}{72.6} \][/tex]
Calculating \( P \):
[tex]\[ P \approx 218.611 \times \frac{38}{72.6} \]\[ P \approx 218.611 \times 0.522 \]\[ P \approx 114.14 \][/tex]
Rounded to the nearest whole number, the pelidisi of a person with a weight of ( 54,688 ) g and a sitting height of ( 72.6 ) cm is ( 114 ).
Since a pelidisi below ( 100 ) is considered undernourished and a pelidisi greater than ( 100 ) indicates overfeeding, with a pelidisi of ( 114 ), this individual is considered to be overfed.
find the sum of the first 10 terms. 0.5,0.9,1.3,1.7.....
The sum of the first 10 terms of the series is 23.
What is an arithmetic progression?An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.
For the given situation,
The series is 0.5,0.9,1.3,1.7.....
Here the first term, a = 0.5,
The common difference, d = [tex]0.9-0.5[/tex]
⇒ [tex]d=0.4[/tex]
Number of terms, n = 10
The formula of sum of n terms is
[tex]S_{n}=\frac{n}{2} [2a+(n-1)d][/tex]
On substituting the above values,
⇒ [tex]S_{10}=\frac{10}{2} [2(0.5)+(10-1)(0.4)][/tex]
⇒ [tex]S_{10}=5 [1+9(0.4)][/tex]
⇒ [tex]S_{10}=5 [1+3.6][/tex]
⇒ [tex]S_{10}=5 [4.6][/tex]
⇒ [tex]S_{10}=23[/tex]
Hence we can conclude that the sum of the first 10 terms of the series is 23.
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imagine you live only one mile from work and you decide to walk if you walk 4 miles per hour how long will it take you to walk one mile
It will take you 15 minutes to walk one mile at a speed of 4 miles per hour.
To determine how long it will take you to walk one mile, we can use the formula:
Time = Distance / Speed
Let's plug in the values:
Distance = 1 mile
Speed = 4 miles per hour
Time = 1 mile / 4 miles per hour
Time = 0.25 hours
Since there are 60 minutes in an hour, we can convert the time to minutes:
Time = 0.25 hours × 60 minutes per hour
Time = 15 minutes
Therefore, it will take you 15 minutes to walk one mile at a speed of 4 miles per hour.
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The prize of bronze has increased by 10% per year from 2000. In the year 2000, Harry bought a bronze medal for $120. Which of the following functions f(x) can be used to represent the price of the medal x years after 2000?
The function that should be used to represent the price of the medal x years after 2000 is [tex]f(x) = 120 (1.10)^x[/tex]
Given that,
The prize of bronze has increased by 10% per year from 2000. In the year 2000, Harry bought a bronze medal for $120.Based on the above information, the calculation is as follows:
[tex]f(x) = P(1 + rate)^t[/tex]
Here P means $120
rate is 10%
T = x
So, it should be
[tex]f(x) = 120 (1.10)^x[/tex]
Therefore we can conclude that The function that should be used to represent the price of the medal x years after 2000 is [tex]f(x) = 120 (1.10)^x[/tex]
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