Answer: T⊂U⊂W are subspaces of V
Step-by-step explanation:
Proof: This is the easier direction.
If T⊂U⊂W or W⊂U⊂T then we have U⊂T⊂W = T or T⊂U⊂W = U
orT⊂U⊂W=W respectively.
SoT⊂U⊂W is a subspace as T, U and W are subspaces.
1st case :T⊂U⊂W is true Then the disjunction W⊂U⊂T or U⊂T⊂W is trivially true.
Let x∈W1 and y∈W2−W1.
By the definition of the union, we have x∈W∪T∪C and y∈T⊂U⊂W
As T∪U∪W is a subspace, x+y∈T∪C∪W which, again by the definition of the union, means that x+y∈W∪T∪C
V∈W∪T∪C
As V was arbitrary, as desired.
Final answer:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one.
Explanation:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one. We can prove this by contradiction. Assume that none of the subspaces is contained in the other. This means that there is an element in T that is not in U ∪ W, an element in U that is not in T ∪ W, and an element in W that is not in T ∪ U. If we take any two of these elements, one from each subspace, and add them together, the result will not be in T ∪ U ∪ W, which contradicts the assumption.
Therefore, two of the subspaces must be contained in the other one.
Biologists tagged 103 fish in a lake january 1. On feburary 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged. How many fish does the lake have
Answer:
206
Step-by-step explanation:
We have been given that Biologists tagged 103 fish in a lake January 1. On February 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged.
To find the number of fish in the lake, we will use proportions because ratio of tagged fish and collected fish on February 1 will be equal to ratio of tagged fish and total fish on January 1.
[tex]\frac{\text{Tagged fish}}{\text{Collected fish}}=\frac{12}{24}[/tex]
Upon substituting the number of tagged fish in our proportion, we will get:
[tex]\frac{103}{\text{Total fish}}=\frac{12}{24}\\\\\frac{103}{\text{Total fish}}=\frac{1}{2}[/tex]
Cross multiply:
[tex]1\cdot \text{Total fish}=103\cdot 2\\\\\text{Total fish}=206[/tex]
Therefore, there are approximately 206 fishes in the lake.
Chris is purchasing a house and needs to finance a $150,000 mortgage from the bank with an annual percentage rate (APR) of 3.8%
He is financing it over 30 years and making monthly payments. What is the total amount Chris will pay back to the bank?
Group of answer choices
$501,796
$299,998
$251,618
$150,001
Answer:
$251,618 is the answer
Step-by-step explanation:
From the previous question, we know he pays $698.94 monthly.
He has to make 360 payments. $698.94 * 360 = $251,618
In the year 2011, Ryan's boat had a value of $23,000. When he bought the boat in 2004 he paid $26,500. If the value of the boat depreciated linearly, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.
The constant amount of depreciation in the value of boat per year is $ 500
Solution:
When he bought the boat in 2004 he paid $26,500
Therefore,
Initial value in 2004 = $ 26500
In the year 2011, Ryan's boat had a value of $23,000
Value in 2011 = $ 23000
The value of the boat depreciated linearly
If the boat depreciation is linear, then the amount by which the value of boat depreciates must be constant.
Let x be the constant depreciation in the value of boat per year
Then we can say,
Value in 2011 = Initial value in 2004 - nx
Here, "n" is the number of years
2011 - 2004 = 7 years
Therefore,
23000 = 26500 - 7x
7x = 26500 - 23000
7x = 3500
Divide both sides by 7
x = 500
Thus the rate of depreciation per year is $ 500
The annual rate of change of the boat's value is approximately -71.43 dollars.
Explanation:The annual rate of change of the boat's value can be calculated using the formula for slope of a line. We subtract the initial value from the final value and divide it by the number of years the boat has depreciated. In this case, the initial value is $26,500 and the final value is $23,000. The number of years is 7 (2011 - 2004). So the annual rate of change is ($23,000 - $26,500)/7 = -$500/7 = -71.43. Therefore, the annual rate of change of the boat's value is approximately -71.43 dollars.
The student is asking about the annual rate of change in the value of a boat, which is a problem related to linear depreciation. To solve this, we need to calculate the total amount the boat depreciated over a certain period and then divide by the number of years to get the annual rate.
Ryan's boat was worth $23,000 in 2011 and was purchased for $26,500 in 2004. The total depreciation over these 7 years is $26,500 - $23,000 = $3,500. To find the annual depreciation rate, we divide the total depreciation by the number of years: $3,500 ÷ 7 years = $500 per year.
Therefore, the annual rate of change of the boat's value is $500 per year, which means the boat's value decreased by $500 every year on average.
A machinist produced 22 items during a shift. Three of the 22 items were defective and the rest were not defective. In how many different orders can the 22 items be arranged if all the defective items are considered identical and all the nondefective items are identical of a different class?
Answer: There are 1540 different orders.
Step-by-step explanation:
The number of ways to arrange n things where 'a' things are alike and 'b' things are a like and so on...[tex]\dfrac{n!}{a!\ b!\ ....}[/tex]
Given : Total items = 22
Defective items = 3
Not defective items = 22-3 = 19
Then, the number of different orders can the 22 items be arranged if all the defective items are considered identical and all the non-defective items are identical of a different class :
[tex]\dfrac{22!}{3!\times19!}\\\\=\dfrac{22\times21\times20\times19!}{6\times19!}=1540[/tex]
Hence, there are 1540 different orders.
To rental car companies are running specials this month at Joseph rentals customers will pay $47 to rent a midsize car for the first day plus Two dollars for each additional day affair Fox rental the price for a midsize car is $36 for the first day and $13 for every additional day beyond that at some point renting from either one of these companies would cost to customer the same amount how many additional days would it take? How much with the customer pay?
Answer: it will take 2 days and the customer will pay $49
Step-by-step explanation:
Let x represent the number of days for which the cost would be the same.
At Joseph rentals, customers will pay $47 to rent a midsize car for the first day plus two dollars for each additional day. This means that the total cost of using Joseph rental for x days would be
47 + 2(x - 1) = 47 + 2x - 2
= 45 + 2x
At Fox rental, the price for a midsize car is $36 for the first day and $13 for every additional day beyond that. This means that the total cost of using Fox rental for x days would be
36 + 13(x - 1) = 36 + 13x - 13
= 23 + 13x
At the point where renting at either companies will cost the customer the same amount, then
45 + 2x = 23 + 13x
13x - 2x = 45 - 23
11x = 22
x = 22/11 = 2
The amount that the customer will psy is
23 + 13 × 2 = 49
Which relation is a function?
PLEASE GIVE ME ANSWER! I NEED AN ANSWER RIGHT NOW BEFORE MY SCHOOL ENDS..
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle,
AC represents the hypotenuse of the right angle triangle.
With m∠A as the reference angle,
AB represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine m∠A, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos A = 13/15 = 0.8667
A = Cos^-1(0.8667)
A = 29.92
Which expression is equivalent to 30 (one-half x minus 2) + 40 (three-fourths y minus 4)? 45 x y minus 220 15 x minus 30 y minus 220 15 x + 30 y minus 220 15 x + 30 y minus 64
Answer:
The third option is correct i.e. 15 x + 30 y minus 220.
Step-by-step explanation:
We have to choose expression from the option that is equivalent to
[tex]30(\frac{1}{2}x - 2) + 40(\frac{3}{4}y - 4)[/tex]
Now, [tex]30(\frac{1}{2}x - 2) + 40(\frac{3}{4}y - 4)[/tex]
= 15x - 60 + 30y - 160
= 15x + 30y - 220
Therefore, the third option is correct i.e. 15 x + 30 y minus 220. (Answer)
Step-by-step explanation: C.
22 POINTS!!!! The polygons below are similar. Find the value of x.
4.5
7.5
12
16
Answer:
The answer is 16. 8 divided 6 is 1.333. When 1.333 is multipled by 12 you get 15.9.
Answer:
x = 16, y = 4.5, z = 7.5
Step-by-step explanation:
Similar figures have the sides in the same ratio
Ratio = BC/FG = 8/6 = 4/3
AD/EH = 4/3
x/12 = 4/3
x = 16
AB/EF = 4/3
6/y = 4/3
y = 6×3÷4
y = 4.5
DC/HG = 4/3
10/z = 4/3
z = 10×3÷4
z = 7.5
The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees , will the outside temperature be represented by a positive integer or negative integer?Explain your reasoning
Answer:
The temperature would be -5 degrees Fahrenheit
Step-by-step explanation: It's represented by a negative integer because 15 - 20 = -5. This means the temperature outside would be -5 degrees Fahrenheit.
Hope this helps! (:
The temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees,
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.
It is given that:
The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees
=15 - 20
= -5.
A negative sign means the temperature outside would be -5 degrees Fahrenheit.
Thus, the temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit. If the temperature drops 20 degrees,
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Isaac is painting a wall that is 9 feet by 18 feet.So far he has painted a part of the wall that is a 4feet by 7feet rectangle.How much of the wall does Isaac have left to paint?
Final answer:
Isaac has 134 square feet of the wall left to paint after subtracting the area he has already painted (28 square feet) from the total area of the wall (162 square feet).
Explanation:
The student's question is regarding an area calculation problem. Isaac is painting a wall with dimensions of 9 feet by 18 feet and has painted a 4 feet by 7 feet section so far. To find the area left to paint, we need to calculate the total area of the wall and subtract the area that's already been painted.
Step 1: Calculate the total area of the wall
The total area of the wall is:
(Length of the wall) × (Width of the wall) = 9 ft × 18 ft = 162 square feet.
Step 2: Calculate the area that has been painted
The area that Isaac has painted is:
(Length of painted section) × (Width of painted section) = 4 ft × 7 ft = 28 square feet.
Step 3: Calculate the area left to paint
To find the remaining area to paint:
(Total area of the wall) - (Area painted) = 162 sq ft - 28 sq ft = 134 square feet.
So, Isaac has 134 square feet of the wall left to paint.
Need help doing this
Answer:
A. -2
B. -10
Step-by-step explanation:
The slope of a perpendicular line will be the negative reciprocal of the slope of the given line:
-1/(1/2) = -2 . . . . slope of the perpendicular line
__
The y-intercept will let the given point satisfy the equation ...
y = -2x +b
2 = -2(-6) +b
-10 = b . . . . . . . subtract 12. This is the y-intercept.
_____
The graph shows the two lines and the points they go through.
In each diagram below, determine whether the triangles are congruent, similar, but not congruent, or not similar. If you claim that the triangles are similar or congruent, make a flowchart justifying your answer.
Part a
Angle ABC = angle CDA (given by the angle markers)
Angle BAC = angle DCA (alternate interior angles)
Segment AC = segment AC (reflexive property)
Through AAS (angle angle side) we can prove the two triangles are congruent. We have a pair of congruent angles, and we have a pair of congruent sides that are not between the previously mentioned angles.
If two triangles are congruent, they are always similar as well (scale factor = 1).
The same cannot be said the other way around. Not all similar triangles are congruent.
Answer: Congruent======================================================
Part b
Angle FGH = angle JIH (both shown to be 50 degrees)
Angle FHG = angle JHI (vertical angles)
We have enough information to prove the triangles to be similar triangles. This is through the AA (angle angle) similarity rule. Since FG and JI are different lengths, this means the triangles are not congruent.
Answer: Similar but not congruent======================================================
Part c
For each right triangle shown, divide the longer leg over the shorter leg
larger triangle: (long leg)/(short leg) = 6/3 = 2
smaller triangle: (long leg)/(short leg) = 3/2 = 1.5
The two results are different, so the sides are not in proportion to one another, therefore the triangles are not similar.
Any triangles that are not similar will also never be congruent.
Answer: Not similar======================================================
Part d
Use the pythagorean theorem to find that PQ = 5 and KL = 12
We have two triangles with corresponding sides that are the same length
So we use the SSS (side side side) triangle congruence theorem to prove the triangles congruent. The triangles are also similar triangles (scale factor = 1)
Answer: Congruent======================================================
Summary of the answers:a. Congruentb. Similar but not congruentc. Not similard. CongruentIn Mathematics, triangles can be congruent, similar, or neither. Congruency means the triangles have the same three sides and angles. Similarity means the triangles have the same shape but not necessarily the same size.
Explanation:In Mathematics, particularly in Geometry, determining whether two triangles are congruent, similar, or neither is a pivotal concept. Triangles are congruent when they have exactly the same three sides and exactly the same three angles. On the other hand, triangles are similar when they have the same shape but not necessarily the same size.
To determine if triangles are congruent, you can use several postulates, including the Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA) postulates. For triangle similarity, the Angle-Angle (AA) postulate is often used. In the absence of sufficient information, the triangles cannot be declared similar or congruent.
A flowchart to justify the congruence or similarity would begin by assessing if all corresponding angles and sides match. If so, the triangles are congruent. If only the angles match and the sides are proportional, then the triangles are similar. In the absence of either, the triangles are neither similar nor congruent.
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Solve for x. −6≥10−8x Enter your answer as an inequality in the box.
The solution of the expression of the inequality - 6 ≥ 10 - 8x for x
would be;
⇒ x ≥ 2
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The expression of the inequality is;
⇒ - 6 ≥ 10 - 8x
Now,
Solve the inequality for x as;
The inequality is;
⇒ - 6 ≥ 10 - 8x
Add 8x both side, we get;
⇒ - 6 + 8x ≥ 10 - 8x + 8x
⇒ - 6 + 8x ≥ 10
Add 6 both side, we get;
⇒ - 6 + 8x + 6 ≥ 10 + 6
⇒ 8x ≥ 16
Divide by 8 both side, we get;
⇒ x ≥ 16/8
⇒ x ≥ 2
Hence, - 6 ≥ 10 - 8x ⇒ x ≥ 2
Thus, The solution of the expression of the inequality - 6 ≥ 10 - 8x, for x will be;
⇒ x ≥ 2
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Function A and Function B are linear functions. Compare the two functions and choose all that are correct.
1. The slope of Function A is greater than the slope of Function B.
2 .The slope of Function A is less than the slope of Function B.
3. The y-intercept of Function A is greater than the y-intercept of Function B.
4 .The y-intercept of Function A is less than the y-intercept of Function B.
Answer:
2 .The slope of Function A is less than the slope of Function B
Step-by-step explanation:
A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)
The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)
_____
More detailed working
The slope of Function A can be figured easily between the points with x-values that differ by 1:
m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.
The slope of Function B is the coefficient of x in the equation: 3.
__
The y-intercept of Function A can be found starting with point-slope form:
y -22 = 2(x -9)
y = 2x -18 +22
y = 2x +4 . . . . . . . slope-intercept form
The intercept of +4 is the same as that of Function B.
what does 124.06=2.35h+72.36
a.16
b.22
c.2.2
d.none of these
Answer:
B. 22
Step-by-step explanation:
124.06 = 2.35h + 72.36
124.06 - 72.36 = 2.35h
51.7 = 2.35h
51.7/2.35 = h
22 = h
Brian has an unlimited number of cents (pennies), nickels, and dimes. in how many different ways can he pay 1414cents¢ for a chocolate mint?
Answer:
The answer is 470 191 764
Step-by-step explanation:
Let's see how we got the figure. First, we need to check our data, or the information supplied.
Data:
There are unlimited pennies, nickels, and dimes. Therefore, it means that Brian can use any one of those to buy his chocolate. Second, there is 1414 coins. These coins come in three different forms mentioned in the first point: pennies, nickels, and dimes.Thus, we have 3 types of coins.We need to use a number of combinations so that none of the combinations is repeated. A formula for n distinct objects taken at different times will be: nCr = C(n,r) = n!/r!(n-r)!n = 1414 coins, r is the types of coins = 3Therefore, the formula will be:nCr = 1414!/ 3! (1414-3)!
= 470 191 764
It therefore means that Brian can combine all the 1414 coins in 470 191 764 ways. This makes sense as reflected by the large number of coins he has.
Having trouble with this and 3 others
Answer:
View Image
Step-by-step explanation:
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Riley needs to rent a car while on vacation. The rental company charges $18.95, plus 16 cents for each mile driven. If Riley only has $50 to spend on the car rental, what is the maximum number of miles she can drive
Answer:
Step-by-step explanation:
Let x represent the maximum number of miles that she can drive.
Riley needs to rent a car while on vacation. The rental company charges $18.95, plus 16 cents for each mile driven. Converting 16 cents to dollars, it becomes 16/100 = $0.16
Assuming Riley drives the car for x miles, the total charge would be
0.16x + 18.95
If Riley only has $50 to spend on the car rental, it means that
0.16x + 18.95 = 50
0.16x = 50 - 18.95
0.16x = 31.05
x = 31.05/0.16 = 194.0625
The maximum number of miles that
she can drive is 194 miles.
A bacteria culture initially contains cells and grows at a rate proportional to its size. After an hour the population has increased to . (a) Find an expression for the number of bacteria after
hours.(b) Find the number of bacteria after 3 hours.(c) Find the rate of growth after 3 hours.(d) When will the population reach 10,000?
Answer:
Step-by-step explanation:
given that a bacteria culture initially contains cells and grows at a rate proportional to its size.
If P be the size then growth rate
[tex]P'=kP[/tex] where k is constant of proportionality
separate the variables as
[tex]\frac{dP}{P} =kdt\\ln P =kt+C\\P = Ae^{kt}[/tex]
If after 1 hour population is B (say)
[tex]B=Ae^{k} \\\\k = ln B - ln A[/tex]
then k = ln B - ln A
Using this
P(t) = [tex]Ae^{(lnB-lnA)t}[/tex]
b) P(e) = [tex]Ae^{(lnB-lnA)3}[/tex]
c) Rate of growth = [tex](ln B- ln A)Ae^{(lnB-lnA)3}[/tex]
Unless you give B value, d cannot be solved
PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTUR
Answer:
[tex] \frac{24}{26} = \frac{12}{13} \\ [/tex]
Answer:
A
Step-by-step explanation:
Sin(C) = opposite/hypotenuse
Hypotenuse is the length opposite to the right angle, AC for this triangle
Opposite is the length opposite to the angle, AB in this case
Sin(C) = AB/AC
= 24/26 = 12/13
What is the surface area of the figure?
144π cm²
12π cm²
36π cm²
24π cm²
Answer:
36π cm^2.
Step-by-step explanation:
This is a sphere . Surface area = 4πr^2.
This sphere has surface area = 4π3^2
= 36π.
The surface area of the sphere would be = 36πcm². That is option C.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
to calculate the surface area of a sphere:
The surface area of a sphere can be calculated through the use of the formula = 4πr²
Where,
radius (r) = 3 cm
surface area
=4πr²
= 4π × 3²
= 36π cm² ( in the terms of π)
Hence, The surface area of the sphere would be = 36πcm². That is option C.
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A swimming pool has to be drained for maintenance. The pool is shaped like a cylinder with a diameter of 5 m and a depth of 1.7 m. Suppose water is pumped out of the pool at a rate of 12 m3 per hour. If the pool starts completely full, how many hours will it take to empty the pool?
Answer:
2.78hrs
Step-by-step explanation:
Volume of water in the pool =πr2h
V = 3.142 * 2.5² *1.7
V = 33.38m³
Emptying the pool out at 12m³ per hour
= 33.38/12
= 2.78hrs
Which statement best describes how to determine whether f(x) = 9 – 4x2 is an odd function?
A. Determine whether 9 – 4(–x)2 is equivalent to 9 – 4x2.
B. Determine whether 9 – 4(–x2) is equivalent to 9 + 4x2.
C. Determine whether 9 – 4(–x)2 is equivalent to –(9 – 4x2).
D. Determine whether 9 – 4(–x2) is equivalent to –(9 + 4x2).
Answer:
Option C - determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.
Step-by-step explanation:
To find : Which statement best describes how to determine whether [tex]f(x) = 9-4x^2[/tex] is an odd function?
Solution :
We have a property for odd functions,
Let f(x) be an odd function then it must satisfy
[tex]f(-x)= -f(x)[/tex]
Now, we have been given the function [tex]f(x) = 9-4x^2[/tex]
For this function to be odd, it must satisfy the above property.
Replace x with -x,
[tex]f(-x)=9-4(-x)^2[/tex]
and
[tex]-f(x)=-(9-4x^2)[/tex]
Hence, in order to the given function to be an odd function, we must determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.
Therefore, C is the correct option.
Peter takes16 minutes longer to mow the lawn by himself than Charles . Together they can mow the lawn in 18 minutes. How long will it take Charles to do it alone?
Answer:
about 29.7 minutes
Step-by-step explanation:
If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:
1/c + 1/(c+16) = 1/18
Multiplying by 18c(c+16), we get ...
18(c +16) + 18(c) = c(c+16)/18
36c +288 = c^2 +16c
c^2 -20c = 288 . . . . . subtract 36c
c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square
(c -10)^2 = 388
c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root
It takes Charles about 29.7 minutes to mow the lawn by himself.
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
Answer:
[tex]m\angle R=69.4^o[/tex]
Step-by-step explanation:
we know that
In the right triangle PQR
[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(R)=\frac{8}{3}[/tex]
using a calculator
[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]
PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTURE !!!
Answer:option D is the correct answer
Step-by-step explanation:
The given triangle is a right angle triangle.
From the given right angle triangle,
The hypotenuse of the right angle triangle is 8
With m∠60 as the reference angle,
The adjacent side of the right angle triangle is 4
The opposite side of the right angle triangle is 4√3
To determine Cos 60, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 60 = 4/8 = 1/2
To determine Tan 60, we would apply the Tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan 60 = 4√3/4
Tan 60 = √3
One night a theater sold 548 movie tickets. An adult's costs $6.50 an child's cost $3.50. In all, $2,881 was takin in. How many of each kind of tickets were sold?
Answer:
321 adult227 childStep-by-step explanation:
The fraction of tickets that are adult tickets is ...
((average price per ticket) - (child's ticket cost)) / (difference in ticket costs)
so the fraction of adult tickets is ...
((2881/548) -3.50)/(6.50 -3.50) = 321/548
Then the number of adult tickets is ...
(321/548)·548 = 321
and the number of child tickets is ...
548 -321 = 227
321 adult and 227 child tickets were sold that night.
_____
If you want to write an equation, you can let "a" represent the number of adult tickets sold. Total revenue is ...
6.50a +3.50(548 -a) = 2881
3.00a +1918 = 2881 . . . . . . eliminate parentheses
3a = 963 . . . . . . . . . . . . . . . subtract 1918
a = 321 . . . . . . . . . . . . . . . . . divide by 3
The number of child tickets is ...
548 -a = 548 -321 = 227
Jamaica is considering buying either a car which goes 25 miles on 1 gallon of gas, or a truck that goes 10 miles on a gallon of gas. If gasoline costs $2.50 per gallon and Jamaica drives 1000 miles per month, how much less would it cost to drive the car each month than it would to drive the truck?
Answer: if he drives the car each month, he would spend $150 lesser than when he drives the truck.
Step-by-step explanation:
The car goes 25 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is
1000/25 = 40 gallons of gas
If gasoline costs $2.50 per gallon and Jamaica chooses to buy a car, the cost of gas per month would be
2.5 × 40 = $100
The truck goes 10 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is
1000/10 = 100 gallons of gas
If gasoline costs $2.50 per gallon and Jamaica chooses to buy a truck, the cost of gas per month would be
2.5 × 100 = $250
The difference between both costs is
250 - 100 = $150
Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister's house partway between their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen's average speed was 10 miles per hour faster than Anne's. Find Helen's average speed and Anne's average speed.
Answer:
Helen: 60mph and Anne: 50mph
Step-by-step explanation:
3.2r+2.8(r-10)=332 is the equation that we use, given the information we have.
We distribute and combine like terms and add 28 to both sides and divide by 6.
3.2r+2.8(r-10)=332
3.2r+2.8r-28=332
6r=360
6r/6=360/6
r=60 So, Helen's speed is 60mph.
Next, we'll solve Anne's speed.
r-10=50
60-10=50 So, Anne's speed is 50mph.
Anne's average speed was approximately 45 mph, and Helen's average speed was approximately 55 mph.
Let's denote Helen's average speed as "H" and Anne's average speed as "A." We are given that Helen drove for 3.2 hours, and Anne drove for 2.8 hours. We also know that Helen's average speed was 10 miles per hour faster than Anne's, so we can write this relationship as:
H = A + 10
Now, using the formula Speed = Distance / Time, we can express the distances traveled by Helen and Anne:
Distance covered by Helen = H * 3.2
Distance covered by Anne = A * 2.8
Given that the sum of their distances equals the distance between their homes (332 miles):
H * 3.2 + A * 2.8 = 332
Substituting the relationship H = A + 10, we get:
(A + 10) * 3.2 + A * 2.8 = 332
Solving this equation will provide us with Anne's average speed (A), and subsequently, we can find Helen's average speed (H) using the relationship H = A + 10.
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