Women can be seated in 89 ways.
Let Sn be the number of possible seating arrangements with n women. Consider n≥3 and focus on the rightmost woman. If she goes back to her seat, then there are Sn−1 ways to seat the remaining n−1 women. If he is sitting in the penultimate seat, then the woman who was sitting there before must now sit in the rightmost seat.
This gives us Sn−2 ways to seat another n−2 woman, so we get the recursion Sn=Sn−1+Sn−2. Starting with S1=1 and S2=2 we can calculate S10=89.
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Given that
x
= 8 cm and
y
= 23 cm, work out
∠
BCA rounded to 3 SF.
The value of the angle ∠BCA when approximated to 3 significant figures is; 20.4°
How to use Trigonometric Ratios?From the attached image of the triangle ABC showing the side lengths x and y, we can see clearly that it is a right angle triangle.
Now, since we want to find the value of the angle ∠BCA, then it means we have to use trigonometric ratio to get;
x/y = sin BCA
Plugging in the relevant values gives us;
8/23 = sin BCA
∠BCA = sin⁻¹(8/23)
∠BCA = 20.355
Approximating to 3 significant figures gives us;
∠BCA = 20.4°
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Match each formula on the left with an equivalent formula on the right.
W = X-Y
W = X - //
W = 4 - Y
W = XY
Y
X =W₁ + ½
X = Z(W + Y)
X = WZ+Y
X = // +Y
The formulas and the equivalent formulas are
W = X - Y X = W +Y
W = X/Z - Y X = Z(W + Y)
W = (X - Y)/Z X = WZ+Y
W = XY X =W/Y
How to match the formulas?To do this, we simply make X the subject of the formula in expressions on the left.
So, we have:
W = X - Y
This gives
X = W + Y
W = X/Z - Y
This gives
X/Z = W + Y
X = Z(W + Y)
W = (X - Y)/Z
This gives
X - Y = WZ
X = WZ + Y
W = XY
This gives
X =W/Y
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Complete question
Match each formula on the left with an equivalent formula on the right.
W = X - Y X =W/Y
W = X/Z - Y X = Z(W + Y)
W = (X - Y)/Z X = WZ+Y
W = XY X = W +Y
Look at this table.
Hours of Monthly
Pay
1220
1420
1620
1820
2020
2220
2420
Training
10
20
30
40
50
60
70
According to the table, how many hours of training would you need to have a
monthly pay of $1500?
Using a linear function, it is found that you would need roughly 24 hours of training to have a monthly pay of $1500.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Looking at the table, the pay increases $200 each 10 hours of work, hence the slope is:
m = 200/10 = 20
Then:
y = 20x + b
When x = 10, y = 1220, hence:
y = 20x + b
1220 = 20(10) + b
b = 1020.
Then the pay for x hours of training is:
y = 20x + 1020.
For a pay of $1500, we have that:
y = 20x + 1020.
1500 = 20x + 1020.
20x = 480
x = 24
You would need roughly 24 hours of training to have a monthly pay of $1500.
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The following table shows a proportional relationship between jjj and mmm.
jjj mmm
444 333
121212 999
202020 151515
Write an equation to describe the relationship between jjj and mmm.
Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
Writing an Equation to Represent a Proportional Relationship
What is proportional relationship?
A proportional relationship between two quantities is when the two quantities vary directly with one and other. Meaning if one item is doubled, the other item is also doubled.
Going back to the given problem above, we have the table showing the proportional relationship between j and m.
j | 4 | 12 | 20 |
m | 3 | 9 | 15 |
Solution:
Step #1
The proportional relationship can be written as:
m/j = ¾ = 9⁄12 = 15⁄20 = ¾
Step #2
So, the equation representing this proportional relationship is:
m = ¾ × j/1 = 3j/4
Final Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
if another line is perpendicular to the line shown on the graph, what must be its slope
It's B
Slope is negative, the other must be positive due to m1 x m2 = - 1
m1 = -2/5
The diagram shows a gradient of -2/5. So, the
reciprocal of this valve to make - 1 is 5/2 (which is the - 2/5 flipped upside down, but positive)
-2/5 x 5/2 = - 10/10 (or - 1)
Thus, the perpendicular line to this has a gradient of 5/2.
Hope this helps!
Translate into an algebraic expression:
How much 50% of sugar syrup can you make if you have x grams of sugar?
(Need Urgent Help)
Answer:
Que is talking about a syrup which contains 50% of sugar .
Que asked : amount of sugar syrup from X grams of sugar.
Explanation :
if a sugar syrup contains 50% of sugar , that means that the half of the solution contains sugar and half is solvent .
means , 2 × amount of sugar = solution (syrup)
now , we are given x grams of sugar
then , solution can be made with x grams of sugar = 2 × (X grams) = 2X gram of solution or sugar syrup.
.
.
Mark BRAINLIEST!
A boy walks 58 feet up a ramp having a 22.5 degree inclination. how high is he standing from the ground?
Boy is 22.5 feet high from the ground
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
The given question can be solved by sin, as value of perpendicular is to be evaluated and height and angle is provided. Let height from the ground be x
sin(22.5°) = x / 58
x = 58sin22.5 = 58(.38258) = 22.5 feet high.
Thus the Boy is 22.5 feet high from the ground.
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(−7)^-2 and more letters cause needed
Answer:
1/49.
Step-by-step explanation:
(−7)^-2
= 1 /(- 7)^2
= 1/49.
A student wants to sell 18 cookies for a fundraiser. She knows that she only has 3 days left to sell her cookies. Write an equation to find out how many cookies she must sell each day to reach her goal.
Answer:
6 cookies per day.
Step-by-step explanation:
if she is going to sell 18 cookies within 3 days, would divide that problem, (18 divided by 3) which will get you selling 6 cookies per day during that 3-day challenge.
Which ratio is equivalent to 4:5 ?
Answer:
Step-by-step explanation:
Maybe..
8/10
12/15
16/20
20/25
24/30
28/35
32/40
36/45
40/50
Any one of these is equal to the ratio of 4 over 5.
Answer:
No, the person who answered first is wrong
I'll give you the correct answer
Step-by-step explanation:
He the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.
thank you, this is the correct answer
hope that hepls
look at image............
Answer:
f(x)=2x-3
Step-by-step explanation:
cause fir example if you put x=2 the y became 1.
triangle abc is equal to
triangle pqr, angle p=8X+4,
angle a=5x+16 , and angle
q=10x+2. find angle r
a. 36
b.not enough info
c. 42
d 102
Answer:
d. 102°
Step-by-step explanation:
We can use the relations ...
corresponding angles in congruent triangles are congruentthe sum of angles in a triangle is 180°to write equations that let us find x and all of the angles in ∆PQR.
Corresponding anglesThe congruence relation ∆ABC ≅ ∆PQR tells us that ∠P = ∠A. Using the given expressions for these angles, we have ...
∠P = ∠A
8x +4 = 5x +16
3x = 12 . . . . . . . . . subtract (5x+4)
x = 4 . . . . . . . . . divide by 3
Then the measure of angle P is ...
∠P = 8x +4 = 8(4) +4 = 36 . . . . . degrees
Other anglesAngle Q in ∆PQR is given as ...
∠Q = 10x +2 = 10(4) +2 = 42 . . . . . degrees
Then the measure of angle R needed to make the total of angles in ∆PQR be 180° is ...
∠R = 180° -36° -42° = 102°
Angle R is 102°.
__
In summary:
x = 4∠P = ∠A = 36°∠Q = ∠B = 42°∠R = ∠C = 102°A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.
----------------------
The car is 120 miles away when the motorcycle starts.
The bike gains on the car at 30 mph (70-40).
It takes 4 hours for the bike to close the gap (120/30).
In 4 hours, the bike and the car are 280 miles from the starting point.
---------
4*70 = 280
7*40 = 280
Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)
70T = 40T + 120
30T = 120
T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).
It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.
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Find the value of x:
X
4
10
Applying the definition of similar triangles, the value of x is determined as: 12.5.
What are Similar Triangles?In a triangle like the one shown above, the line that intersects the two sides of the triangle divides the two sides of the triangle to form similar triangles. Thus, their corresponding sides are proportional to each other.
Therefore, we would have:
(x + 5) / 5 = (10 + 4) / 4
(x + 5) / 5 = 14/4
4(x + 5) = 5(14)
4x + 20 = 70
4x = 70 - 20
4x = 50
x = 50/4
x = 12.5
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4
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
PLEASE HELP I AM REALLY CONFUSED
Answer:
Step-by-step explanation:
y = 3 (x-1)(x+ 7 ) this graph will intercept the x axis when y = 0
0 = 3 ( x-1)(x+7) so you can see this = 0 when x =1 or when x = -7
these are the x-axis intercepts
the vertex will be right in the middle between the intercepts found above ....... at x = -3
plug this value in to find the y coordinate 3 ( -3-1)(-3+7) = -48
vertex is -3, -48
the axis of symmetry is the value of the x coordinate of the vertex
x = - 3
direction of opening will be upward.....
see attached graph
In Angle FGH, the measures of angles F, G, and
H, respectively, are in the ratio 4:4:10. Find
the measure of each angle.
Answer:
40 40 100°
Step-by-step explanation:
Is that TRIANGLE FGH?
the angles add to 180
180 / ( 4 + 4 + 10 ) = 10
then each angle is 4 x10 4 x 10 and 10 x10
CAN ANYONE HELP PLSS
Answer:
CD = 13
Step-by-step explanation:
since Δ ABD and Δ CBD are congruent , then corresponding sides are congruent, so
CD = DA = 13
Answer:
13
Step-by-step explanation:
We know that if two triangles are congruent, the corresponding element of those are also equal.
Given that,
ABD Δ ≡ CBD Δ
Therefore, the corresponding elements are also equal.
AD = CD
AD = 13 units
∴ CD = 13 units
What are the two binomial factors for x2 – 25? (x – 5)(x – 5) (x 5)(x 5) (x – 20)(x 5) (x – 5)(x 5)
Answer:
(x - 5)(x + 5)
Step-by-step explanation:
x² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 25
= x² - 5²
= (x - 5)(x + 5)
Answer:
Step-by-step explanation:
(x-5) +(x+5)
In a group of 60 students, 18 students take Algebra I, 20 students take
Algebra II, and 10 students take both subjects. How many students don't take
either of these subjects?
A. 12
B. 32
C. 34
D. 36
Answer:
32...................
Given: BC bisects ZABD
mZABD = 52°
Prove: mABC = 26°
A
D
B
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Statements Reasons
mZABD = 52
mZABC+ m ZABC = 52
Statements
mZABC=mZCBD
m/ABC+mZC=52
Reasons
BC bisects ZABD
mZABC+mZCBD =
m ZABD
A bisector is a line that divides a given line or angle into two equal parts or measures. So that the required statements and reasons are given below:
STATEMENT REASONS
1. BC bisects <ABD Given
2. m<ABC = [tex]26^{o}[/tex] Bisection property of an angle
3. 2(m<ABC) = [tex]52^{o}[/tex] Sum of angles of a bisected angle
4. m<ABC = m<CBD Congruent parts of a bisected angle
5. <mABC + m<ABC = [tex]52^{o}[/tex] Sum of an individual angle of a bisected angle
6. m<ABC + m<CBD = [tex]52^{o}[/tex] Sum of angles of a bisected angle
7. m<ABC + m<CBD = m<ABD Sum of the angles of a bisected angle
The above statements and reasons are majorly centered on a bisector, the angles formed due to the bisection of a given angle, and the bisected angle.
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Answer:
1. BC bisects <ABD | Given
2.m<ABD=52 | Given
3.m<ABC = m<CBD | Definition of Bisector
4.m<ABC + m<CBD = m<ABD | Angle Addition Postulate
5.m<ABC + m<CBD =52 | Substitution Property
6.m<ABC + m<ABC =52 | Substitution Propery
7.2(m<ABC)=52 | Addition
8.m<ABC=26 | Division Property
Step-by-step explanation:
Edge 2022
Can someone pls help me?
Answer:
[tex] \frac{8}{24} [/tex]
Step-by-step explanation:
If Adam's family uses 8lb of apples to make pie. We know that 3 x 8 = 24, so it's probably approximately 3 out of 18.
a square room has a area of 49 square feet the height of the room is 4 feet. what is the area of one wall
Answer:
28 ft^2
Step-by-step explanation:
The room is in the shape of a square. That means the base of the room (width and length) will have the same dimensions.
Length x Width = 49 ft^2
Length = Width
Length^2 = 49 ft^2
Length = 7 feet
Width is also 7 feet
The height of the room is 4 feet, plenty for non-humans. One wall area would be (7 ft)*(4 ft) = 28 ft^2
3. Segment RU is an angle bisector. m/QRU = 70°.
What is mzQRS?
Q
70°
□A 70°
B 140°
C 35°
OD 20°
A
U
S
PLS HELP ME OUT
Answer:
b - 140
Step-by-step explanation:
an angle bisector divides an angle in half
so
half of the angle is 70
the other half is 70
so
70 + 70 = 140
b is your answer
Answer: B. 140°
Step-by-step explanation:
Hi!
An angle bisector just cuts the angle in half.
Therefore, if one half is 70°, the other half is also 70°!
To find the measure of the angle just add them!
70° + 70° = ?
= 140°
So, your answer is B. 140°
Hope this helps and have a great day!
help me i im not good in math
Number of shirts = dependent variable
Cost of the purchases = independent variable
the milligrams of aspirin in a persons body is given by the equation a=500x(3/4)t, where t is the number of hours since the patient took the medicine.
A. how much aspirin will bein the patients body after two hours?
B. in the equation, about what does the 500 tell us the situation
C. in the equation, what does the 3/4 tells us about the situation.
The amount of aspirin that would be in the patient's body is; 281.25.
What is the amount of aspirin in the patient's body after 2 hours?A) The amount of aspirin in the patient's body after 2 hours can be evaluated as follows;
a = 500×(3/4)² = 4500/16 = 281.25.
B) The number 500 as used in the equation represents the amount of aspirin in the patient's body prior to taking the medicine, at time, t= 0.
C) The fraction 3/4 as used in the task content is the factor of change in aspirin content in the patient's body.
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Name the ordered pair that would be a reflection of (9, 2) over the y axis
Answer:
(- 9, 2 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(9, 2 ) → (- 9, 2 )
35.149 = 30+5+0.1+ ____ +0.009
how to find the missing sum
Answer:
0.04
Step-by-step explanation:
30+5+0.1+0.009 is 35.109
35.149 - 35.109= 0.04
35.149 = 30+5+0.1+ ____ +0.009
= 30 + 5 + 0.1 + x + 0.009
= 35.109 + x
x is the unknown value, so what number add to the 35.109 gives 35.149? That's what we're after.
35.149 = 35.109 + x
- 35.109 both side
0.04 = 0 + x
Thus, x = 0.04
(35.109 - 35.109 cancles each other & we get x on its own because 0.04 - 0 gives you 0.04)
Hope this helps!
a ramp is 17 feet long, rises 8 feet above, and a covers a horizontal distance of 15 feet as showed in the figure. the ratio of to is equal to tan B
Using relations in a right triangle, it is found that:
The ratio of 8 to 15 is equals to tan B.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Researching the problem on the internet, we have that:
The side opposite to angle B has a length of 8 feet.The side adjacent to angle B has a length of 15 feet.Hence the tangent of B is:
tan(B) = 8/15.
Which means that:
The ratio of 8 to 15 is equals to tan B.
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Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water.
represents the volume of water Andrei uses (in liters) if he uses marbles.
What is the glass tank's volume?
______________liters
Answer: the amount of liters that would fill the glass tank's volume can not be found
Step-by-step explanation:
there is not enough information to find out how many liters could fill the glass tanks volume
The required volume of glass tank = Vb +Vw liters
Volume, is defined as the ratio of the mass of object to its density.
Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water.
Volume of pebbles = Vb
Volume of water = Vw
Volume of glass tank = Vg
Vg = Vb + Vw
Thus, the required volume of glass tank is = Vb + Vw liters
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