Answer:
B = 53°
C = 74°
The correct option for Suppose that we know that a=5cm, b=5cm, and angle A=53o in a certain triangle. According to the Law of Sines D. There is exactly one triangle that meets the criteria.
Given:
a = 5, b = 5, A = 53°
⇒ a/sin A = b/sin B ⇒ Sin B = Sin A
⇒ B = A (or) 180-A
⇒ B = 53° (or) 127°
B = 53°:
C = 180-A-B = 0 (not possible)
⇒ B = 53°, C = 74° ⇒ C = (Sin C) (b/sin B) ≅ 6.02 cm
In which cases, can we use the law of sines?
Generally, the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.
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Consider the functions.
f(x)=4x^2
g(x)=15/4x^2
h(x)=4/15x^2
Answer:
see the explanation
Step-by-step explanation:
we know that
As the leading coefficient of the quadratic equation gets larger the parabola gets steeper and "narrower"
we have
[tex]f(x)=4x^{2}[/tex]
[tex]g(x)=\frac{15}{4}x^{2}[/tex]
[tex]h(x)=\frac{4}{15}x^{2}[/tex]
Compare the leading coefficients
The leading coefficient of f(x) is 4
The leading coefficient of g(x) is 15/4=3.75
The leading coefficient of h(x) is 4/15=0.27
so
4> 3.75> 0.27
therefore
f(x) is steeper than g(x) and h(x)
g(x) is steeper than h(x)
Verify each statement
1) f(x) is steeper than h(x)
The statement is true
2) h(x) is steeper than g(x)
The statement is false
3) g(x) is steeper than f(x)
The statement is false
What is the value of \dfrac{d}{dx}\left(\dfrac{2x+3}{3x^2-4}\right) dx d ( 3x 2 −4 2x+3 )start fraction, d, divided by, d, x, end fraction, (, start fraction, 2, x, plus, 3, divided by, 3, x, squared, minus, 4, end fraction, )at x=-1x=−1x, equals, minus, 1 ?
The question asks for the derivative of the function (2x+3)/(3x^2-4) at x=-1. Using the quotient rule, we find the derivative and then substitute x=-1 into it to get the required value.
Explanation:The question aims to find the derivative of the function f(x) = (2x + 3) / (3x^2 - 4) and then find its value at x = -1. To do this, we need to use the Quotient Rule which is (f(x)/g(x))' = (g(x)*f'(x) - f(x)*g'(x))/(g(x))^2.
Here f(x) = 2x + 3 and g(x) = 3x^2 - 4. So, the derivative of the function becomes f'(x) = ( (3x^2 - 4)*2 - (2x + 3)*6x ) / (3x^2 - 4)^2 which simplifies to (6x^2 - 8 - 12x^2 - 18x) / ( 9x^4 - 24x^2 + 16). Now, substitute x = -1 into f'(x) to get the desired value.
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The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?
Answer:
[tex]2\sqrt{2}\ ft\ longer[/tex]
Step-by-step explanation:
Area Of A Cube
Suppose a cube with side length s, the area of one side is
[tex]A_s=s^2[/tex]
Since the cube has 6 sides, the total area is
[tex]A=6A_s=6s^2[/tex]
But if we have the area, we can solve the above formula for s to get
[tex]A=6s^2[/tex]
[tex]\displaystyle s=\sqrt{\frac{A}{6}}[/tex]
We have two different cubes with areas 1,200 square inches and 768 square inches. Let's compute their side lengths
[tex]\displaystyle s_1=\sqrt{\frac{1,200}{6}}=\sqrt{200}[/tex]
[tex]\displaystyle s_1=10\sqrt{2}\ ft[/tex]
[tex]\displaystyle s_2=\sqrt{\frac{768}{6}}=\sqrt{128}[/tex]
[tex]\displaystyle s_2=8\sqrt{2} ft[/tex]
The difference between them is
[tex]10\sqrt{2}\ ft-8\sqrt{2}\ ft=2\sqrt{2}\ ft\approx 2.83\ ft[/tex]
The side of the cube with area 1,200 square inches is [tex]2\sqrt{2}\ ft[/tex] longer then the side of the cube with area 768 square inches
Answer:
Its B
Step-by-step explanation:
Edge 2021
Find the LCM of 2, 10 and 6
Answer:
30
Plz click the thxs button or mark brainliest!
Yours Truly.
Answer:
30
Step-by-step explanation:
2 2 10 6
3 1 5 3
5 1 5 1
1 1 1
2*3*5 30
A rug has an area of x2+x−20 square feet. Which expression represents the dimensions of the rug? A (x+4)(x−5) B (x+2)(x−10) C (x−4)(x+5) D (x−2)(x+10)
Answer: the correct option is
C (x−4)(x+5)
Step-by-step explanation:
The area of the rug in square feet is expressed as
x^2+x−20
The given equation is a quadratic equation and the roots of the equation represents the dimensions of the rug. To simplify the equation, we would apply the factorization method.
We will get two numbers such that, their difference will be x and their sum will be -20x^2. The numbers are 5x and 4x. Therefore
x^2+ 5x - 4x −20 = 0
x(x + 5) - 4(x +5)
The roots are (x - 4)(x + 5)
The area of the rug is represented by the quadratic expression[tex]x^2 + x - 20,[/tex] which factors to (x + 4)(x - 5). This matches option A, verifying that these are the dimensions of the rug.
The student has a quadratic expression representing the area of a rug, which is[tex]x^2 + x - 20[/tex] square feet. To find the dimensions of the rug, we need to factor this expression. Factoring quadratic expressions involves finding two binomials that multiply to give the original quadratic expression. In this case, the correct factorization is (x + 4)(x - 5).
We can verify this by using the FOIL method (First, Outer, Inner, Last) to expand the binomials: (x + 4)(x - 5) = [tex]x^2 - 5x + 4x - 20 = x^2 - x - 20[/tex], which matches our original expression.
Thus, option A is the correct choice.
5+3r=5r-19(if there is no solution,type in ''no solution'')r= Answer
Answer: 12 = r
Step-by-step explanation: When we have this kind of a setup, we want to put our variables together on one side of the equation and our numbers together on the other side of the equation.
First, let's put our variables on the right side by subtracting 3r from both sides of the equation. That gives us 5 = 2r - 19.
Now we can move our numbers to the left by adding 19 to both sides of the equation and we get 24 = 2r.
Divide both sides by 2 and 12 = r
Note:
Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper or digitally. It will really pay off for you down the line.
For the given pentagon ABCDE the diagonal
EC
∥
AB
. I, G, F, H are midpoints of
BC
,
CD
,
DE
,
EA
respectively. The length of
FG
is 50% more than the length of AB. Find the area of the quadrilateral HFGI, if A△ADB = 16sq. in.
Answer:
28 in²
Step-by-step explanation:
Without constraining the problem unduly, we can make the assumption that AB = 2 inches. Then the altitude from AB to D is h in ...
Area ABD = (1/2)(AB)h
16 in² = (1/2)(2 in)(h)
16 in = h . . . . . . . . . . . divide by 1 in
__
The altitude D to AB is the sum of the heights from D to EC (h1) and from AB to EC (h2). That is ...
16 = h1 + h2
We also know that the height from FG to EC is 1/2 the height from D to EC, hence (1/2)h1. Likewise, the height to midsegment HI from either EC or AB is half the height from EC to AB, hence (1/2)h2. This means the total height of the quadrilateral HFGI is (1/2)h1 + (1/2)h2 = (1/2)(h1 +h2) = 8.
__
We are given that FG is 50% longer than AB, so its length will be ...
FG = AB×(1 + .5) = (2 in)(1.5) = 3 in
Since FG is the mid-segment of triangle CDE, base EC is twice its length, or ...
EC = 2×FG = 2(3 in) = 6 in
__
Mid-segment HI is the average of the base lengths of trapezoid ABCE, so is ...
HI = (EC +AB)/2 = (6 + 2)/2 = 4
__
Now, we know the height and base lengths of trapezoid HFGI, so we can find its area as ...
A = (1/2)(b1 +b2)h = (1/2)(3 in + 4 in)(8 in) = 28 in²
The area of quadrilateral HFGI is 28 square inches.
_____
You can make any assumption you like about the dimension of AB, and the rest of the dimensions scale accordingly. The result is still the same.
30% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
Answer:
30% companies will offer both wireless internet and free on-board snacks.
Step-by-step explanation:
Percentage of major companies who equip their planes with wireless internet access = 30%
Percentage of major airlines who offer passengers free on-board snacks = 70%
Therefore, from the given information, the maximum percentage of the companies who offer both wireless internet facility as well as on-board snacks may be 30% only.
Solve for x. The triangles in each pair are similar.
Answer:
Step-by-step explanation:
Triangle TML is similar to triangle TVU. Side TV measures 36 and side TM meaures 9; side TV is 4 times longer than side TM. Same with sides VU and ML. VU is 4 times longer than ML. That means that side TU is 4 times longer than side TL. Side TL measures x - 4; side TU measures 24 + x - 4 which is x + 20. That means that x + 20 = 4(x - 4) and x + 20 = 4x - 16 and
3x = 36 so
x = 12
The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min. t (min) 0 0.5 1 1.5 2 2.5 3 r (l/min) 44 40 37 34 30 27 23
Answer:
100.75 liters
Step-by-step explanation:
Data provided in the question:
t (min) 0 0.5 1 1.5 2 2.5 3
r (l/min) 44 40 37 34 30 27 23
Now,
left endpoint approximation
= 0.5 × ( 44 + 40 + 37 + 34 + 30 + 27 )
= 0.5 × 212
= 106
Right endpoint approximation
= 0.5 × ( 40 + 37 + 34 + 30 + 27 + 23 )
= 0.5 × 191
= 95.5
Therefore,
the average of the left- and right-endpoint approximations
= [ 106 + 95.5 ] ÷ 2
= 100.75 liters
The total amount of water drained during the first 3 min is: 100.75 liters/min.
Total amount of waterLeft endpoint approximation
r = 1/2 ( 44 + 40 + 37 + 34 + 30 + 27 )
r= 1/2 × 212
r= 106 L/m
Right endpoint approximation
r= 1/2 × ( 40 + 37 + 34 + 30 + 27 + 23 )
r= 1/2 × 191
r= 95.5 L/min
Average of the left- and right-endpoint approximations
Average= [ 106 + 95.5 ] ÷ 2
Average=201.5÷2
Average= 100.75 liters/min
Inconclusion the total amount of water drained during the first 3 min is: 100.75 liters/min.
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Ben drinks tea at an incredible rate. He drinks 3\dfrac123 2 1 3, start fraction, 1, divided by, 2, end fraction liters of tea every \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction of an hour. Ben drinks tea at a constant rate.
Answer:
[tex]5\frac{1}{4}[/tex] liters per hour.
Step-by-step explanation:
Consider the question: Ben drinks tea at an incredible rate. He drinks [tex]3\frac{1}{2}[/tex] liters of tea every [tex]\frac{2}{3}[/tex] of an hour. Ben drinks tea at a constant rate. How many liters of tea does he drink in one hour?
To find the liters of tea drank by Ben in one hour, we will divide amount of tea drank by time taken as:
[tex]3\frac{1}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]
Convert mixed fraction into improper fraction:
[tex]\frac{7}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]
Convert division problem into multiplication problem by flipping the 2nd fraction:
[tex]\frac{7}{2}\text{ Liters}\times \frac{3}{2}\text{ hour}[/tex]
[tex]\frac{21}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]
[tex]5\frac{1}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]
Therefore, Ben drinks [tex]5\frac{1}{4}[/tex] liters per hour.
Answer:
He drinks 21/4, or 5 1/4, liters of tea in 1 hour
Step-by-step explanation:
The following question is missing: How much does he drink in one hour?
Given that he drinks 3 1/2 (= 7/2) liters of tea every 2/3 of an hour, and we want to know how much he drink in 1 hour, then the following proportion must be satisfied:
7/2 liters / x liters = 2/3 hour / 1 hour
x = (7/2)/(2/3) = 7/2 * 3/2
x = 21/4 = 5 1/4 liters
Let R and S be partial orders on a nonempty set A prove that T = R intersection S is also a partial order on A.
Answer:
See proof below
Step-by-step explanation:
We denote (x,y)∈R as xRy, and we also use the similar notation xSy for (x,y)∈S. Remember that R and S are reflexive, antisymmetric and transitive relations (the definition of partial order).
To prove that R∩S⊆A is a partial order, we will prove that R∩S is reflexive, antisymmetric and transitive.
Reflexive: Let a∈A. R is reflexive thus aRa. S is also reflexive, then aSa. Then (a,a)∈R and (a,a)∈S which implies that (a,a)∈R∩S, that is, a(R∩S)a for all a∈A.Antisymmetric: Let a,b∈A and suppose that a(R∩S)b and b(R∩S)a hold. In particular, aRb and bRa. Since R is antisymmetric, a=b.Transitive: Let a,b,c∈A and suppose that a(R∩S)b and b(R∩S)c hold. Then aRb, bRc, aSb and bSc are true. The first two statements imply by the transitivity of R that aRc. Similarly, from the last two we have that aSc. Thus a(R∩S)c as we wanted to prove.A cylinder has radius r and height h how many times greater is the surface area of a cylinder when both dimensions are multiplied by a factor of 2?3?5?10?
Answer:
Correct answer: 4, 9, 25, 100
Step-by-step explanation:
Surface area of cylinder A = 2r²π + 2rπ h = 2rπ (r+h)
r₁ = 2r and h₁ = 2h => A₁ = 2 (2r) π (2r+2h) = 2 2rπ 2(r+h) = 4 2rπ (r+h)
A₁ = 4 A
r₁ = 3r and h₁ = 3h => A₁ = 2 (3r) π (3r+3h) = 3 2rπ 3(r+h) = 9 2rπ (r+h)
A₁ = 9 A and so on......
God is with you!!!
Ray hired sun and peter to help him move .Sun charged a $20 flat fee and $30 per hour.Peter charged $25 per hour. Write an expression for ray's total cost if sun and peter each work h hours.
Answer:
Step-by-step explanation:
Ray hired sun and peter to help him move.
Let h represent the number of hours that each of them worked.
Let y represent Ray's total cost for hiring Sun and Peter for h hours.
Sun charged a $20 flat fee and $30 per hour. The total amount that Sun charges would be
20 + 30h
Peter charged $25 per hour. The total amount that Peter charges would be
25h
An expression for Ray's total cost if Sun and Peter each work h hours would be
y = 20 + 30h + 25h
y = 20 + 55h
Answer:
[20+(30+25)]h or (20+55)h
Step-by-step explanation:
20 will not be changed.
Total cost per hour is 55
add $20
Hope this helps
If 10 50-74 is written as an integer in base decimal notation, what is the sum of the digits in that integer?
Answer:
The required sum of the digits in that integer is 440.
Step-by-step explanation:
Consider the provided expression.
[tex]10^{50}-74[/tex]
We need to find the sum of the digits in that integer.
For [tex]10^2[/tex] = 100 (3 digits)
Now subtract 74 from it.
100-74=26
For [tex]10^3[/tex] = 1000 (4 digits)
Now subtract 74 from it.
1000-74=926
For [tex]10^4[/tex] = 100000 (5 digits)
Now subtract 74 from it.
10000-74=9926
Similarly,
[tex]10^50[/tex] = 1000....[51 digits]
Now subtract 74 from it.
[tex]10^50-74=99999....26[/tex]
The number of 9 after subtracting 74 is 3 less than the number of digits.
Therefore, the number of 9 after subtracting 74 from [tex]10^50[/tex] must be: 51-3=48
The sum of the digits is = 9×48 + 2 + 6 = 432 + 2 + 6 = 440.
Hence, the required sum of the digits in that integer is 440.
Final answer:
The sum of the digits in the integer 10⁵⁴ - 74 is 476, which is calculated by adding the contribution of the 52 nines and the digits in '26'.
Explanation:
To determine the sum of the digits of the integer written in base decimal notation for 10⁵⁴ - 74, we first need to understand what 10⁵⁴ represents. This value is a 1 followed by 54 zeros in decimal form. When we subtract 74 from this value, we alter only the last two non-zero digits. This results in a number that looks like 999...9926, where the '9's continue until the last two digits, which are '26'.
To find the sum of the digits, we simply add up the '9's and '26'. Since there are 52 nines (54 digits minus the last two which are '26'), and each nine contributes nine to the sum, we can calculate this part of the sum as 52 multiplied by 9. Then we also add the sum of the digits in '26'.
Therefore, the sum of digits in 10⁵⁴ - 74 is (52 × 9) + 2 + 6 = 468 + 8 = 476.
There are three grades in the school. One grade has 1/3 of the students, one grade has 1/4 of the students. What fraction of students is in the remaining grade?
Answer:
Step-by-step explanation:
Let x represent the total number of stdents that has all grades in the school.
There are three grades in the school. One grade has 1/3 of the students, this means that number of students that belongs tho this grade is 1/3 × x = x/3
One grade has 1/4 of the students, this means that number of students that belongs to this grade is 1/4 × x = x/4
Total number of students in both grades would be x/3 +/x/4 = 7x/12
The number of students in the remaining grade would be
x - 7x/12 = 5x/12
fraction of students in the remaining grade would be
(5x/12)/x = 5/12
Answer:
2/4
Step-by-step explanation:
i dont want to think
Howdy! Id love to have these questions answered asap! Thank you for the help!
1) Which angle is not coterminal to 120 degrees?
A. 840
B. -180
C. 480
2) Use the unit circle and the reference angle to determine which of the following trigonometric values is correct when theta = -90
A. Cos theta = undefined
B. Sin theta = -1
C. Tan = 0
1) Which angle is not coterminal to 120 degrees?
A. 840
B. -180
C. 480
Answer:From given options, -180 is not a coterminal angle of 120 degrees
Solution:Coterminal Angles are angles who share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians
Coterminal angles of 120 degrees are:
120 degrees + 360 degrees = 480 degrees
120 degrees - 360 degrees = 240 degrees
720 degrees + 120 degrees = 840 degrees
120 degrees - 720 degrees = -600 degrees
Therefore:
Positive Angle 1 (Degrees) 480
Positive Angle 2 (Degrees) 840
Negative Angle 1 (Degrees) -240
Negative Angle 2 (Degrees) -600
Therefore from given options, -180 is not a coterminal angle of 120 degrees
2) Use the unit circle and the reference angle to determine which of the following trigonometric values is correct when theta = -90A. Cos theta = undefined
B. Sin theta = -1
C. Tan theta = 0
Answer:Sin theta = -1 is correct
Solution:given angle is -90
Find the reference angle for -90
Reference angle = 360 - 90 = 270 degrees
Unit circle diagram is attached below
And from the unit circle, we know the coordinates for 270 degrees are (0, -1)
Our angle - 90 degrees lies in (0, -1)
Unit circle coordinates are given by [tex](cos \theta , sin \theta )[/tex]
This means,
cos (-90 ) = 0 and sin(-90) = -1
We know that,
[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]
[tex]tan \theta = \frac{-1}{0}[/tex] = undefined
Therefore from options, sin theta = -1 is correct
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
If it's 4 o'clock, the hour hand will be on the 4 and the minute hand will be on the 12.
This takes 4 partitions/pieces of the clock, and there are 12 different partitions. That's 4/12, or 1/3 of the entire clock.
The total clock is a 360 degree angle.
360 * (1/3) = 120
1/3 of 360 degrees is 120 degrees.
Since the angle between the minute and hour hand takes up 1/3 of the clock, the angle is 120 degrees.
Let me know if you need any clarifications, thanks!
A group of 444 friends is playing cards. The deck has 707070 cards. To start the game, the dealer makes a pile of 151515 cards in the center. Then she deals the remaining cards one at a time to each player until all the cards are gone. What is the greatest number of cards any player will have after all the cards are dealt?
Answer:
The correct answer is 14 not 17 or 7
Step-by-step explanation:
Martina will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $54 and costs an additional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?
Answer:
100 miles
Step-by-step explanation:
Let
x ----> the number of miles driven
y ---> the total cost
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value
In this problem we have
First Plan
The slope is equal to [tex]m=\$0.15\ per\ mile[/tex]
The y-intercept is [tex]b=\$54[/tex]
so
The linear equation is
[tex]y=0.15x+54[/tex] -----> equation A
Second Plan
The slope is equal to [tex]m=\$0.10\ per\ mile[/tex]
The y-intercept is [tex]b=\$59[/tex]
so
The linear equation is
[tex]y=0.10x+59[/tex] -----> equation B
To find out for what amount of driving do the two plans cost the same, equate equation A and equation B
[tex]0.15x+54=0.10x+59[/tex]
solve for x
[tex]0.15x-0.10x=59-54[/tex]
[tex]0.05x=5[/tex]
[tex]x=100\ miles[/tex]
Find the cost
for x=100 miles
substitute in equation A or equation B (the cost is the same)
[tex]y=0.15(100)+54=\$69[/tex]
Final answer:
The two car rental plans cost the same for 100 miles driven. To find this, the total cost equations for both plans are set equal to each other, and the resulting equation is solved for the number of miles.
Explanation:
To determine when the two car rental plans cost the same, we need to set up and solve an equation where the total costs of both plans are equal. We will let x represent the number of miles driven.
Cost Equations for Two Plans:
Plan 1: $54 + $0.15x
Plan 2: $59 + $0.10x
To find where they cost the same, we set the cost equations equal to each other:
54 + 0.15x = 59 + 0.10x
We then solve for x by first subtracting $0.10x from both sides:
54 + 0.05x = 59
Next, we subtract $54 from both sides:
0.05x = 5
Finally, we divide both sides by 0.05:
x = 100
Therefore, the two plans cost the same when Martina drives 100 miles.
Laneka owns a cake shop.She is currently preparing cakes for two anniversary parties. The first cake has 3 small tiers and 1 medium tier and will serve a total of 100 guests. The second one has 3 small tiers and 2 medium tiers and will serve a total of 140 guests represent the situation with a system of equations
Answer:
The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].
Step-by-step explanation:
Let 's' represents the number of guest small tier can serve.
Let 'm' represents the number of guest medium tier can serve.
Now Given:
For First cake:
Number of small tiers = 3
Number of medium tier = 1
Total serving guest = 100
Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.
Framing in equation form we get;
[tex]3s+m=100[/tex]
For Second cake:
Number of small tiers = 3
Number of medium tier = 2
Total serving guest = 140
Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.
Framing in equation form we get;
[tex]3s+2m=140[/tex]
Hence The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].
Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest. If that interest was approximately 6.5 percent of the bond's selling price, approximately what was the bond's selling price?A. $4,063
B. $5,325
C. $5,351
D. $6,000
E. $6,154
Answer:
E. $6,154
Step-by-step explanation:
Let x represent selling price of the bond.
We have been given that last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest.
Let us calculate 8% of $5,000 to find amount of interest as:
[tex]\text{Amount of interest }=\$5,000\times \frac{8}{100}[/tex]
[tex]\text{Amount of interest }=\$50\times 8[/tex]
[tex]\text{Amount of interest }=\$400[/tex]
We are also told that the amount of interest was approximately 6.5 percent of the bond's selling price. 6.5 percent of the bond's selling price would be [tex]\frac{6.5}{100}x[/tex].
We can represent our given information in an equation as:
[tex]\frac{6.5}{100}x=\$400[/tex]
[tex]100*\frac{6.5}{100}x=\$400*100[/tex]
[tex]6.5x=\$40,000[/tex]
[tex]\frac{6.5x}{6.5}=\frac{\$40,000}{6.5}[/tex]
[tex]x=\$6,153.846153846[/tex]
[tex]x\approx \$6,154[/tex]
Therefore, the selling price of the bond was approximately $6,154 and option E is the correct choice.
Which system of linear inequalities is represented by the graph?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]x+5y\geq 5[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the solid line [tex]x+5y=5[/tex]
The slope of the solid line is negative
The y-intercept of the solid line is (0,1)
The x-intercept of the solid line is (5,0)
[tex]y\leq 2x+4[/tex] ----> inequality B
The solution of the inequality B is the shaded area below the solid line [tex]y= 2x+4[/tex]
The slope of the solid line is positive
The y-intercept of the solid line is (0,4)
The x-intercept of the solid line is (-2,0)
therefore
The graph in the attached figure
two jets leave an air base at the same time and travel in opposite directions. one jet travels 71 mih slower than the other. if the two jets are 5764 miles apart after 4 hours, what is the rate of each jet?
Answer:
Speed of Faster jet is 756 miles/hr and speed of slower jet is 685 miles/hr.
Step-by-step explanation:
Let the speed of faster jet be represent as 's'
Now Given:
one jet travels 71 mih slower than the other.
Hence Speed of slower jet will be = [tex]s-71[/tex]
Distance = 5764 miles
Time = 4 hrs
Now we know that;
Distance is equal to product of speed and time.
Framing in equation for we get;
Distance = (Speed of Faster Jet + Speed of Slower jet) × Time.
Substituting the given values we get;
[tex]5764=(s+s-71)\times 4\\\\5764= (2s-71)\times 4\\\\\frac{5764}{4} = 2s-71\\\\1441=2s-71\\\\2s=1441+71\\\\2s =1512\\\\s =\frac{1512}{2} = 756\ mi/h[/tex]
Speed of faster jet = 756 miles/hr
Speed of slower jet = [tex]s-71 =756-71 = 685\ mi/hr[/tex]
Hence Speed of Faster jet is 756 miles/hr and speed of slower jet is 685 miles/hr.
Now we will check the answer;
Distance traveled by faster jet = speed × time = 756 × 4 = 3024 miles.
Distance traveled by Slower jet = speed × time = 685 × 4 = 2740 miles
Hence Total Distance = 3024 + 2740 = 5764 miles.
A random sample of 384 people in a mid-sized city (city one) revealed 112 individuals who worked at more than one job. A second random sample of 432 workers from another mid-sized city (city two) found 91 people who work at more than one job. Find a 99% confidence interval for the difference between the proportions of workers in the two cities who work at more than one job.Select one:a. (0.003, 0.159)b. (0.021, 0.141)c. (-0.159, 0.004)d. (0.031, 0.131)e. Sample sizes aren't large enough to justify using z-procedures
Answer:
99% confidence interval is:
(0.00278 < P1 - P2< 0.15921)
Step-by-step explanation:
For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:
[tex][(p_{1} - p_{2}) \pm z_{\alpha/2} \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}} + \frac{p_{2}(1-p_{2})}{n_{2}} }[/tex]
Where [tex]p_{1}[/tex] : proportion sample of individuals who worked
at more than one job in the city one
[tex]n_{1}[/tex]: Number of respondents in the city one
[tex]p_{1}[/tex] : proportion sample of individuals who worked
at more than one job in the city two
[tex]n_{1}[/tex]: Number of respondents in the city two
Then
α = 0.01 and α/2 = 0.005
and [tex]z_{\alpha/2} = 2.575[/tex]
[tex]p_{1} = \frac{112}{384} = 0.2916[/tex]
[tex]p_{2} = \frac{91}{432} = 0.2106[/tex]
[tex]n_{1}= 384[/tex] and [tex]n_{2}= 432[/tex]
The confidence interval is:
[tex][(0.2916 - 0.2106) \pm 2.575 \sqrt{\frac{0.2916(1-0.2916)}{384} + \frac{0.2106(1-0.2106)}{432} }[/tex]
(0.00278 < P1 - P2< 0.15921)
Please Help me!!!!!! Thank you so much
Answer:x1 = 1, x2 = - 1, x3 = 3
Step-by-step explanation:
x1 + 2x2 - x3 = - 4 - - - - - - - - - -1
x1 + 2x2 + x3 = 2 - - - - - - - - - -2
- x1 - x2 + 2x3 = 6 - - - - - - - - - -3
Let us eliminate x1 and x2. Subtracting equation 2 from equation 1, it becomes
-2x3 = - 6
x3 = -6/-2
x3 = 3
Adding equation 2 to equation 3, it becomes
x2 + 3x3 = 8 - - - - - - - - - - - 4
Substituting x3 = 3 into equation 4, it becomes
x2 + 3 × 3 = 8
x2 + 9 = 8
x2 = 8 - 9 = -1
Substituting x2 = -1 and x3 = 3 into equation 2, it becomes
x1 + 2 × -1 + 3 = 2
x1 - 2 + 3 = 2
x1 + 1 = 2
x1 = 2 - 1 = 1
Let us check by substituting x1 = 1, x2 = -1 and x3 = 3 into equation 1. It becomes
1 + 2 × - 1 - 3 = - 4
1 - 2 - 3 = - 4
-1 - 3 = - 4
-4 = - 4
Find the indicated term of the geometric sequence. a8 for 4, -12, 36, ...
Answer:
76
Step-by-step explanation:
Answer:
The 8th term of geometric sequence is -8748
ie., [tex]a_{8}=-8748[/tex]
Step-by-step explanation:
Given geometric sequence is 4,-12,36,...
Geometric sequence can be written as
[tex]a_{1},a_{2},a_{3},..,[/tex]
[tex]a_{1}=4=a[/tex]
[tex]a_{2}=-12=ar[/tex]
[tex]a_{3}=36=ar^2[/tex]
and so on.
common ratio is [tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]r=\frac{-12}{4}[/tex]
[tex]r=-3[/tex]
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]r=\frac{36}{-12}[/tex]
[tex]r=-3[/tex]
Therefore [tex]r=-3[/tex]
Geometric sequence of nth term is [tex]a_{n}=ar^{n-1}[/tex]
To find the 8th term:
[tex]a_{8}=ar^{8-1}[/tex]
[tex]a_{8}=ar^{7}[/tex]
here a=4 and r=-3
[tex]a_{8}=ar^{7}[/tex]
[tex]=4\times (-3)^7[/tex]
[tex]=4\times (-2187) [/tex]
[tex]=-8748[/tex]
[tex]a_{8}=-8748[/tex]
Therefore the 8th term of geometric sequence is -8748
4n-12=12-4n(If there is no solution, type in "no solution") n= Answer
Answer:
n = 3
Step-by-step explanation:
Which graph represents the solution set of the system of inequalities? How do you know?
{x+y<1 2y≥x−4
Answer:
Step-by-step explanation:
It is the fourth one
Hope this helps
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At a popular theme park, there were 2,000,000 visitors last year. This year, there were 2,100,000 visitors. What is the percent increase in visitors from last year to this year? (Enter an exact number.)
Answer:
There was 5% increase in visitors from last year to this year.
Step-by-step explanation:
Given:
Number of Visitors at theme park last year = 2000000
Number of Visitors at theme park this year = 2100000
We need to find the percent increase in visitors from last year to this year.
First we will find Number of increase in visitors from last year to this year.
Number of increase in visitors is equal to Number of Visitors at theme park this year minus Number of Visitors at theme park last year.
Framing in equation form we get;
Number of increase in visitors = 2100000 - 2000000 = 100000
Now Percent of increase in visitors is can be calculated by dividing Number of increase in visitors with Number of Visitors at theme park last year and then multiplied with 100.
Framing in equation form we get;
Percent of increase in visitors = [tex]\frac{100000}{2000000}\times 100 = 5\%[/tex]
Hence There was 5% increase in visitors from last year to this year.
There was a 5% increase in visitors to the theme park from last year to this year, calculated using the formula for percent increase.
Explanation:The question is asking for the percent increase in visitors from one year to the next at a popular theme park. To find this, we'll use the formula for percent increase: ((new value - old value) / old value) * 100%.
In this case, the 'old value' is the number of visitors last year, which is 2,000,000. The 'new value' is the number of visitors this year, which is 2,100,000. Substituting these numbers into our formula gives us: ((2,100,000 - 2,000,000) / 2,000,000) * 100%.
This simplifies to: (100,000 / 2,000,000) * 100%. Then, converting 100,000 / 2,000,000 to a decimal gives us 0.05. Multiplying 0.05 by 100% gives us a 5% increase in visitors from last year to this year.
Learn more about Percent Increase here:https://brainly.com/question/18960118
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