1. Let S represent the cost of the sofa and C represent the cost of the chair.
If the sofa costs $50 less than three times the cost of the chair, then effectively we can write this as:
S = 3C - 50
If the sofa and chair together cost $650, we can write this as:
S + C = 650
2. Now, we can find out how much the sofa and chair cost by solving the two equations we obtained above for C, and substituting S = 3C - 50 into S + C = 650. Thus, we get:
S + C = 650
if S = 3C - 50, then:
3C - 50 + C = 650
4C - 50 = 650 (Add C and 3C)
4C = 700 (Add 50 to both sides)
C = 175 (Divide both sides by 4)
Thus, the cost of the chair is $175. Now, to find the cost of the sofa we need to simply substitute C = 175 into our first equation, S = 3C - 50:
S = 3(175) - 50
S = 525 - 50
S = 475
Thus, the sofa costs $475.
3. Now that we know that the sofa costs $475 and the chair costs $175, all we need to do is to subtract the cost of the chair from the cost of the sofa to find the difference in price:
475 - 175 = 300
Therefor, the sofa costs $300 more than the chair (answer C).
A pizza store offers three different party packages of pizza. The packages and price are listed below. If pizza cost the same individually or in a package, what is the cost of a large pizza
Answer:
it doesnt say the prices on here
Step-by-step explanation:
Stuck on a math: Fraction exponent factoring and simplifying.
Step-by-step explanation:
(x+2)^(-1/5) - (x+2)^(-6/5)
Factor out (x+2)^(-1/5):
(x+2)^(-1/5) [ 1 - (x+2)^(-5/5) ]
(x+2)^(-1/5) [ 1 - (x+2)^-1 ]
(x+2)^(-1/5) [ 1 - 1/(x+2) ]
Common denominator:
(x+2)^(-1/5) [ (x+2)/(x+2) - 1/(x+2) ]
(x+2)^(-1/5) [ (x+2-1)/(x+2) ]
(x+2)^(-1/5) [ (x+1)/(x+2) ]
[tex](x+2)^{-\frac{1}{5}}-(x+2)^{-\frac{6}{5}}[/tex]
[tex]\dfrac{1}{(x+2)^{\frac{1}{5}}}-\dfrac{1}{(x+2)^{\frac{6}{5}}}[/tex]
[tex]\dfrac{1}{\sqrt[5]{x+2}}-\dfrac{1}{(x+2)\sqrt[5]{x+2}}[/tex]
[tex]\boxed{\dfrac{x+1}{\sqrt[5]{x+2}\cdot(x+2)}}[/tex]
Hope this helps.
r3t40
One hundred thirty people were asked to determine how many cups of fruit and water they consumed per day. The results are shown in the frequency table. Identify the conditional relative frequency by row. Round to the nearest percent. The conditional relative frequency that someone ate more than 2 cups of fruit, given the person drank less than or equal to 4 cups of water is approximately . The conditional relative frequency that someone ate less than or equal to 2 cups of fruit, given the person drank more than 4 cups of water is approximately .
Answer:
1. 24%
2.38%
Step-by-step explanation:
Answer:
The first one is 24% and the second one is 38%
Step-by-step explanation:
i did it on egdenuity
The length of a rectangle is 5 cm less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?
Plz help ASAP!! help a girl out
width = w
length = 2w - 5
Perimeter = 26
The formula for perimeter is:
P = l + l + w + w
Plug in corresponding values into this equation...
26 = (2w - 5) + (2w - 5) + w + w
Now you must solve for w
26 = 2w - 5 + 2w - 5 + w + w
Combine like terms
26 = 2w - 5 + 2w - 5 + w + w
26 = 6w - 5 - 5
26 = 6w - 10
Bring -10 to the other side by adding it to both sides
26 + 10 = 6w + (-10 + 10)
36 = 6w + 0
36 = 6w
Isolate w by dividing 6 to both sides
36/6 = 6w/6
6 = w
Width is 6 cm
To find length plug 6 in for w in the equation 2w - 5
2(6) - 5
12 - 5
7
Length is 7 cm
Hope this helped!
~Just a girl in love with Shawn Mendes
Question 24 (1 point)
Leanne has a gas card that has $150 on it. She spends $25 a week on gas. Write a recursive
rule that represents the amount of money she has on her gas card after the first week.
Answer:
[tex]A_{(x)}[/tex] = 150 - 25x
Step-by-step explanation:
Let Leanne uses gas for x weeks.
Since expenditure on gas for one week = $25.00
Therefore, Leanne will spend on gas for x weeks = $25x
It is given in the question that she has total amount = $150.00
So the amount Leanne is left with after x weeks = 150 - 25x
If we represent amount left, by [tex]A_{(x)}[/tex]
so the recursive formula will be
[tex]A_{(x)}[/tex] = 150 - 25x
Now for x = 1 week
[tex]A_{(1)}[/tex] = 150 - 25 = $125
Therefore, Leanne will have $125 in her gas card after the first week.
A stereo system is being installed in a room with a rectangular floor measuring 16 feet by 12 feet and an 8-foot ceiling. The stereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. You must run a wire from the amplifier to the speaker, and the wire must run along the floor or walls (not through the air). What is the shortest length of wire you can use for the connection?
Answer:
4√41 ≈ 25.61 feet
Step-by-step explanation:
The shortest route is the one that crosses the longest edge between room surfaces. In this case, that is the 16-foot edge between the floor and wall opposite the amplifier, or the 16-foot edge between the ceiling and the wall adjacent to the amplifier.
The length of the required wire is ...
√((8+12)² +16²) = √656 = 4√41 ≈ 25.61 . . . feet
Answer:
√((8+12)² +16²) = √656 = 4√41 ≈ 25.61 feet
Step-by-step explanation:
Please help me! Will mark brainliest!
Answer:
2 root 21
Step-by-step explanation:
14 + 6 equals 20
Add x is 21
2 root21
Answer:
B. 2sqrt(30)
Step-by-step explanation:
The three right triangles are similar.
In the left right triangle, the short leg measures 6, and the hypotenuse measures x.
In the large triangle, the short leg measures x, and the hypotenuse measures 6 + 14 = 20.
Since all three triangles are similar, the ratios of the lengths of corresponding sides are equal.
6/x = x/20
x^2 = 6 * 20
x^2 = 120
x = sqrt(120)
x = sqrt(4 * 30)
x = 2sqrt(30)
Answer: B. 2sqrt(30)
Will markk the brainliest
1. If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f-1(x)?
2. If the graph of a function f(x) includes the point (3, 0), what point must the graph of f-1(x) include? Explain.
3.The first term in an arithmetic sequence is 2. The twelfth term is 211. Find the value of n so that an = 135.
Answer:
1. the range of f^-1(x) is {10, 20, 30}.
2. the graph of f^-1(x) will include the point (0, 3)
3. n = 8
Step-by-step explanation:
1. The domain of a function is the range of its inverse, and vice versa. The range of f^-1(x) is {10, 20, 30}.
__
2. See above. The domain and range are swapped between a function and its inverse. That means function point (3, 0) will correspond to inverse function point (0, 3).
__
3. The n-th term of an arithmetic sequence is given by ...
an = a1 +d(n -1)
You are given a1 = 2, a12 = 211, so ...
211 = 2 + d(12 -1)
209/11 = d = 19 . . . . . solve the above equation for the common difference
Now, we can use the same equation to find n for an = 135.
135 = 2 + 19(n -1)
133/19 = n -1 . . . . . . . subtract 2, divide by 19
7 +1 = n = 8 . . . . . . . . add 1
135 is the 8th term of the sequence.
SAFF (Students against Fatty Food) is a group of students who are protesting the food in high school cafeterias. At a recent rally, the students covered the first 40 yards by 40 yards of the football field. There were 24 students in each 8 feet by 8 feet square. What steps would you take to determine how many students were present at the rally?
Convert yards to feet, then divide by feet square and multiply by the number of students.
Multiply the feet by the number of students.
Multiply yards by feet and divide by the number of students
Multiply the number of students by the yards of the football field.
Answer:
The total area covered by students is 40 yd x 40 yd = 1600 yd^2
24 students covered 8 ft x 8ft or (8 ft x 1 yd/3 ft)^2 = [(8/3) yard]^2 = (64/9) yd^2
Therefore, you need the amount of students per yard or 24 students/(64/9) yd^2
and multiply (students/yd^2) x (area covered by students) = number of total students present
Therefore: number of students present = 24 students/(64/9) yd^2 x 1600 yd^2 = 5400 students
Step-by-step explanation:
Please mark brainliest and have a great day!
Is the work shown in the simplification below correct? explain. csc(t) sec(t) = 1 cos(t) ÷ 1 sin(t) = 1 cos(t) • sin(t) 1 = 1 sin(t) = tan(t)?
Answer:
The work shown in the simplification below is incorrect.
Step-by-step explanation:
To start; we have to know what csc(t) and sec(t) is.
csc(t) = 1/sin(t) and sec(t)= 1/cos(t)
So in the above simplification it was all mixed up, csc(t) was substituted with 1/cos(t) instead of 1/sin(t) and sec(t) was substituted with 1/sin(t) instead of 1/cos(t).
So, we are going to solve it the right way;
csc(t) sec(t) = [tex]\frac{1}{sin(t)}[/tex] ÷ [tex]\frac{1}{cos(t)}[/tex]
= [tex]\frac{1}{sin(t)}[/tex] × [tex]\frac{cos(t)}{1}[/tex]
=[tex]\frac{cos(t)}{sin(t)}[/tex]
= cot(t)
Therefore csc(t) sec(t) = cot(t) and not tan(t).
The simplification shown is not correct because the steps used are incorrect and the resulting expression is not equivalent to the original. The correct simplification is csc(t) sec(t) = 1/(sin(t) * cos(t)).
Explanation:The simplification shown is not correct. Let's break it down step by step:
csc(t) sec(t) = 1/sin(t) * 1/cos(t) = (1/cos(t)) * (1/sin(t)).Using the commutative property of multiplication, we can switch the order: (1/sin(t)) * (1/cos(t)) = (1/cos(t)) * (1/sin(t)).Multiplying the fractions together, we get 1/(cos(t) * sin(t)).However, 1/(cos(t) * sin(t)) is not equal to 1/sin(t). Therefore, the simplification is incorrect.To simplify the expression correctly, we can use the reciprocal identities: csc(t) = 1/sin(t) and sec(t) = 1/cos(t). When multiplying these together, we get:
csc(t) * sec(t) = (1/sin(t)) * (1/cos(t)) = 1/(sin(t) * cos(t)).
So, the correct simplification is csc(t) sec(t) = 1/(sin(t) * cos(t)).
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Please explain how to get the answer, with step by step explination. I would like to know, so I can do it by my self in the future.
Answer:
(-8, 135°)
Step-by-step explanation:
(8, -45°) has magnitude 8 and direction -45°.
If we add 180° to the direction and change the sign of the magnitude, we'll have the same point.
(-8, -45° + 180°) = (-8, 135°)
A cube with a volume of 64 cubic meters is scaled by a factor of 5. What is the volume of the modified cube in meters
[tex]\bf \textit{volume of a cube}\\ V=s^3~~ \begin{cases} s=&side's\\ &length\\ \cline{1-2} V=&64 \end{cases}\implies 64=s^3\implies \sqrt[3]{64}=s\implies \boxed{4=s} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{scaling all sides by a factor of 5}}{V=s^3\implies V=(4\cdot 5)^3}\implies V=20^3\implies V=8000[/tex]
Answer:
8,000
Step-by-step explanation:
When the sides of the cube are scaled by a factor of k, the volume increases by a factor of k3. Here, the new volume is 64 cubic meters × 53 = 8,000 cubic meters.
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
A. $3.63
Step-by-step explanation:
You can choose the correct answer simply by estimating.
The almonds are about $5.50 for each of the 2 kg, so will total about $11. Since the total amount paid is just over $25, the amount paid for cashews is about $25 -11 = $14.
That amount pays for 4 kg of cashews, so 1 kg will be half of half that amount, or about $3.50 -- certainly, less than $7.26.
_____
If you want to write an equation, you can write ...
2(5.49) +4(c) = 25.50
4c = 14.52 . . . . . . . . . . . . subtract 10.98
14.52/4 = c = 3.63 . . . . . divide by the coefficient of c
1 kg of cashews has a price of $3.63.
Order the polynomial in descending powers of r. Do not repeat terms.
Answer:
[tex]-4r^3-3r^2+2rs-5[/tex]
Step-by-step explanation:
The terms have powers of r that are 2, 0, 1, and 3 (in the order shown here). You want to rearrange those terms so the powers have order 3, 2, 1, 0. The above answer shows that arrangement.
Ordering a polynomial in descending powers of r involves arranging the terms from the highest to the lowest exponent of r. When squaring exponentials, square the digit and double the exponent. For large r compared to d, d can be disregarded.
Explanation:Ordering a polynomial in descending powers of r involves organizing the terms from highest to lowest exponent of the variable r. For example, for a polynomial of r as 6r^4 - 2r + 7r^2 - 3, we would arrange it as 6r^4 + 7r^2 - 2r - 3. Note that the polynomial starts with the term with the highest power of r (r^4), followed by the term with the next highest power (r^2). The process continues down to the term with the lowest power of r (r), and lastly, the constant term (-3). Remember to retain the corresponding coefficients while reordering terms.
When dealing with terms involving the squaring of exponentials, remember to square the digit as usual and double the exponent. For instance, (r^3)^2 would be r^6.
Also, comparisons of terms such as r » d (meaning r is much larger than d), we disregard d as its contribution to the final polynomial will be negligible.
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Chuck is making a salad to go with his soup. The recipe calls for 2.1 cups of lettuce per person and 0.56 ounces of salad dressing per cup of lettuce. If 11 dinner guests want salad, how many ounces of dressing will be necessary? Round the answer to the nearest whole ounce. 1 ounce 2 ounces 6 ounces 13 ounces
The answer is:
There will be necessary 13 ounces of salad dressing.
Why?
Since we already know that there will be needed 0.56 ounces of salad dressing per cup, and the recipe calls 2.1 cups of lettuce per person, we need to calculate the total ounces of salad dressing per each person, and then, calculate it for 11 persons.
So, calculating we have:
[tex]SaladDressingPerPerson=Cups*SaladDressing=2.1*0.56oz\\\\SaladDressingPerPerson=1.176oz[/tex]
Therefore, we know that there will be needed 1.176 ounces of salad dressing per person.
Then, calculating the ounces of dressing for 11 dinner guests, we have:
[tex]TotalOunces=SaladDressingPerPerson*NumberOfPersons\\\\TotalOunces=1.176ounces*11=12.94ounces=13ounces[/tex]
Hence, we have that there will be necessary 13 ounces of salad dressing.
Have a nice day!
Answer:
the answer is D
Step-by-step explanation:
which of the following sets are discrete? check all that apply.
A. {1,3,5,7,...}
B. (-10,20)
C. {5,8}
D. (1,99)
E. {-3,6,9,17,24}
Answer:
All are discrete sets
Step-by-step explanation:
Any set for which you can list the elements is a discrete set, even if that list has "..." (continues in like fashion). Sets that are not discrete are those that are continuous, such as "all real numbers" or "the numbers between 0 and 1".
The discrete sets from the options given are A. {1,3,5,7,...}, C. {5,8}, and E. {-3,6,9,17,24}.
A discrete set is one where the elements are separate and distinct, often meaning each member can be counted and there is no continuous spectrum of values between any two elements.
A. {1,3,5,7,...} - This set represents odd numbers which is discrete because we can identify each individual element.
B. (-10,20) - This is not a set but an interval representing a continuous range of real numbers; therefore, it is not discrete.
C. {5,8} - This set has only two elements, each distinct and countable, making it discrete.
D. (1,99) - Similar to B, this is an interval showing a continuous range of real numbers, and thus not discrete.
E. {-3,6,9,17,24} - This set includes separate, identifiable numbers and is therefore discrete.
Base your answer to the following question on the diagram shown and the given information
In the diagram shown, /ll m, m_1 = 3x + 25 and m28 = 4x - 17
Find the measure of 2.
29
49
131
151
Answer:
29°
Step-by-step explanation:
∠1 ≅ ∠8
3x+25 = 4x -17
42 = x . . . . . . . . . . add 17-3x
Now, we can find the measure of ∠1:
m∠1 = 3(42) +25 = 151
Angle 2 is the supplement to this, so has measure ...
m∠2 = 180° -151° = 29°
A triangle has two sides of lengths 5 and 13. What value could the length of the
third side be? Check all that apply.
A. 8
B. 5
D.2
-
E
19
-
F. 24
Answer:
A. 8
Step-by-step explanation:
The length of the remaining side will be between the sum and difference of the given sides:
5 + 13 = 18 . . . . upper limit of 3rd side length
13 - 5 = 8 . . . . . lower limit of 3rd side length
The only answer choice in this range is 8.
_____
Comment on question and answers
Please note that this would not be an allowed answer for some triangle inequality questions. Some authors insist that the sum of the two shortest sides be greater than the longest side, so the triangle has non-zero area. Other authors allow the sum to be greater than or equal to the longest side. The only viable answer choice here is one that makes use of the "or equal to" condition. The 5-8-13 triangle will look like a line segment of length 13. It will have no area.
Answer:
THE CORRECT ANSWER IS 10, PLEASE DO NOT CHOOSE 8, IT WAS WRONG FOR ME SO THE CORRECT ANSWER IS 10
Step-by-step explanation:
NEED HELP WITH A MATH QUESTION
Answer:
Step-by-step explanation:
The total number of orders for large is 27
the probability of ordering something hot is 22/27=0.8148
to convert to percentage, multiply by 100: 0.8148*100=81.48%. rounded = 81%
There are 27 people total who are buying large drinks. 22 of those large drinks are hot drinks.
To figure out what percentage 22 is of 27, divide 22 by 27.
22/27= .814... or 81% or 80%.
81% of large drinks bought are hot.
Hope this helps!
The Anza-Borrego Desert State Park is one of the best places in the United States for viewing stars. During one 50-day period, cloud cover obstructed nighttime views just 6% of the time. Based on that sample, how many days a year would you predict that clouds there will interfere with stargazing? Complete the explanation.
The clouds wlll interfere for 21 ⁹/₁₀ days in a year
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here one 50-day period, cloud cover obstructed nighttime views just 6% or for the 50 day period the cloud obstructed t = 6% of 50
= 3 days
the number of 50 days period in a year = 365/50
= 350/50 + 15/50
= 7 + 15/50
Therefore the number of days the cloud will obstruct is = (7 + 15/50)×3
= 21⁹/₁₀
Hence the clouds will obstruct 21⁹/₁₀ days in a year.
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Final answer:
Based on a 50-day sample with 6% cloud coverage, one would predict that at Anza-Borrego Desert State Park, clouds will interfere with stargazing for approximately 22 days out of the year.
Explanation:
The Anza-Borrego Desert State Park had cloud coverage that obstructed nighttime views 6% of the time during a 50-day period. To predict how many days a year clouds would interfere with stargazing, you would use this percentage. The calculation is as follows:
Find the total number of days in a year, which is 365.
Calculate 6% of 365 days to find the number of days with cloud coverage. This is done by multiplying 365 by 0.06.
The result gives you the predicted number of days with cloud coverage obstructing stargazing. In numbers: 365 days/year × 0.06 (6%) = 21.9 days/year.
Therefore, based on the given sample, you would predict that clouds will interfere with stargazing at Anza-Borrego Desert State Park for approximately 22 days each year (rounding 21.9 up to the nearest whole number).
Select the values for p, q, and r that will make the following equation true.
px2 + qx + r = (3x + 1)(x - 5)
A. p = 3
B. p = 4
C. q = -16
D. 9 = -14
E. r = -5
F. r = -4
Answer:
P= 3
Q= -14
R= -5
Step-by-step explanation:
Just solve the equation on the right side, you'll get:
=3x^2 -15x +x -5
=3x^2 -14x -5
Now compare it to the equation on the left side,
The coefficient of x^2 on the left is "p", on the right that we just solved is 3.
Same for "q" which is the coefficient on the left, on the right it's -14.
And for "r" it's -5 from the equation on the right.
Expanding the right side of the equation (3x + 1)(x - 5), we get 3x^2 - 14x - 5. Matching coefficients, we find that p = 3, q = -14, and r = -5.
Explanation:To solve for the values of p, q, and r that will make the equation px2 + qx + r = (3x + 1)(x - 5) true, we need to expand the right side and then compare coefficients. Expanding the right side, we have:
3x2 - 15x + x - 5
This simplifies to:
3x2 - 14x - 5
Now, we match the coefficients from the expanded form to the left side of the equation:
p must match the coefficient of x2, which is 3.
q must match the coefficient of x, which is -14.
r must match the constant term, which is -5.
Therefore, the correct values are:
A. p = 3
D. q = -14
E. r = -5
Rewrite the following linear equation in slope-intercept form. Write your
answer with no spaces
Answer: Y = 4x - 14
Step-by-step explanation:
See paper attached. (:
Jan takes a sales job that pays 4.15% commission. He typically sells $48,500 worth of merchandise per month. What is his gross annual income?
Answer:
$24,153
Step-by-step explanation:
Jan's monthly income from commissions is ...
4.15% × $48,500 = $2012.75
Multiplied by 12 months in the year, that is ...
$2012.75 × 12 = $24,153 . . . . gross annual income from commissions
y-9/5 = 3 solve for y
a. 24
b. 6
c. -6
d. -24
Answer:
[tex]\large\boxed{a.\ y=24}[/tex]
Step-by-step explanation:
[tex]\dfrac{y-9}{5}=3\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{y-9}{5\!\!\!\!\diagup_1}=5\cdot3\\\\y-9=15\qquad\text{add 9 to both sides}\\\\y-9+9=15+9\\\\y=24[/tex]
Which item is considered to be a negative in Penny's creditworthiness?
This profile belongs to Penny:
A. Owns her own house
B. Pays her bills on time
C. Has held several jobs in the last three years
D. Has one credit card and pays off the balance each month
Answer:
C. Has held several jobs in the last three years
Step-by-step explanation:
Stable employment is a positive with respect to creditworthiness. Changing jobs frequently is considered a negative.
__
The lack of credit history other than one credit card can also detract from Penny's creditworthiness. Lenders like to see that a few other lenders have extended you credit, and that all your payments have been "as agreed."
This question is called "Create equations to solve for missing angles"
Help me!! Its very confusing.
Answer:
A
But it needs explanation.
Step-by-step explanation:
The first one hides the fact, but it is indeed the answer.
6x + 12x = 90 degrees is the way the equation should actually be set up.
A does that by adding 90 to both sides to start with.
6x + 12x + 90 = 90 + 90
The reason it does this is to show that the three angles (6x 12x and 90 make up the entire straight angle shown in the diagram.
The answer is going to be the same.
18x = 90 Combine like terms on the left
18x /18 = 90 / 18 Divide by 18
x = 5
Answer:
A
Step-by-step explanation:
The 3 given angles form a straight angle and sum to 180°, hence
6x + 12x + 90 = 180 ← is the required equation
PLEASE HELP ME WITH THIS MATH PROBLEM
Answer:
A'(-1, -1)
Step-by-step explanation:
Dilation about the origin multiplies each individual coordinate value by the dilation factor.
A' = (1/3)A = (1/3)(-3, -3) = (-1, -1)
Answer:
(-1, -1)
Step-by-step explanation:
When you figure scale factor, it's always a number that's multiplied into the coordinates of the pre-image. The coordinates of A are (-3, -3), so multiplying in the scale factor of 1/3 divides each of those coordinates by 3. -3/3 = -1
A car with 24 in tires in diameter travels at a speed of 60 mph. What is the angular speed of the tires? Express your answer in degrees per second and round to the nearest degree per second
The tire has a circumference [tex]24\pi[/tex] inches, or [tex]2\pi[/tex] feet. It has a linear speed of 60 mph, or 88 feet/second. This means that any point on the rim of the tire will have traveled 88 feet in 1 second. We have
[tex]\dfrac{88}{2\pi}=\dfrac{44}\pi\approx14.006[/tex]
which means the tire completes a little over 14 revolutions in 1 second. One complete revolution corresponds to a rotation of 360º. Then its angular speed in degrees per second is
[tex]\left(\dfrac{44}\pi\dfrac{\rm rev}{\rm s}\right)\dfrac{360\,\rm deg}{1\,\rm rev}}=5042\dfrac{\rm deg}{\rm s}[/tex]
Given the car's speed of 60 mph and the tires' diameter of 24 inches, we can convert them to more standard units of meters and seconds. Using the physical concept that the angular speed equals the rate of change of angular displacement, we calculate the angular speed of the tires in radians per second. The result is then converted back to the desired unit of degrees per second, yielding an approximate angular speed of 5041 deg/sec.
Explanation:To determine the angular speed of the tires, we need to understand some basic physics. First, we should calculate the linear velocity in more standard units. As we know 1 mile is approximately 1609.34 meters, and 1 hour is 3600 seconds, thus we can convert 60 mph into approximately 26.82 meter per second.
Next, the diameter of the tire is given as 24 inches, which is approximately 0.61 meters (as 1 inch = 0.0254 meters), so the radius r of the tire will be half of that, which is about 0.305 meters. The linear speed v of the edge of the tire is equal to the speed of the car, v = 26.82 meter per second.
The angular velocity w is defined as the rate of change of angular displacement with respect to time, which can also be expressed in terms of linear velocity and radius of the circular path as w = v/r. Plugging in our values, we can calculate w to be approximately 87.9 rad/sec.
Now, to convert to degrees per second, we should know that 1 radian is equal to approximately 57.2958 degrees. Therefore, the angular speed of the tire in degree per second is approximately 5041 degrees per second, or rounded to the nearest degree per second, it's approximately 5041 deg/sec.
Learn more about Angular Speed here:https://brainly.com/question/14663644
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Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
The answer is C.
Step-By-Step Explanation:
Once you combine the like terms of 5x^2-8x-7 and 2x^2-3x-7 you get 7^2-11x-5. Then you need to subtract x^2-9x-4 from 7^2-11-5x. Then you will get the answer which is C.
Answer:
C. 6x² -2x -1
Step-by-step explanation:
You want the sum of ...
(5x² -8x +2) + (2x² -3x -7) - (x² -9x -4)
Eliminating parentheses gives ...
5x² -8x +2 +2x² -3x -7 -x² +9x +4
Grouping like terms, we have ...
(5x² +2x² -x²) + (-8x -3x +9x) + (2 -7 +4)
Then combining like terms gives ...
6x² -2x -1 . . . . matches choice C
Need help with math
Answer:
45
Step-by-step explanation:
So more than 3 people.
Families with 4 =245
Families with 5=125
Families with 6=66
Families with 7=10
Families with 8=4
Add up (this will be our numerator)
Add up all the frequency numbers to get your denominator.
So the answer is =450/1000=45/100=45%