Answer:
[tex]x=21 ways[/tex]
Step-by-step explanation:
From the question we are told that:
Bike space [tex]N=7[/tex]
Number of Bike [tex]n=5[/tex]
Generally the equation for This combination is mathematically given by
[tex]x=^NC_n[/tex]
[tex]x=^7C_5[/tex]
[tex]x= \frac{7!}{5!2!}[/tex]
[tex]x= 7*6/2[/tex]
[tex]x=21 ways[/tex]
Anna needed to let everyone in the music club know the time of its next meeting. She called two people and asked each of them to call two other people, and so on. if it takes one minute to call two people, how many phone calls were made during the fifth minute?
Answer:
62
Step-by-step explanation:
In one minute Anna called 2 people
the next minute the 2 people each called 2 people making it 4 so I'll draw something like a branch chain to calculate so it will look like the fig above
I'm not too sure but I tried my best.
Find the measure of angle 'y'. 49° A. 60 degrees B. 70 degrees C. 80 degrees D. 110 degrees
Answer:
70°
Step-by-step explanation:
61° + 49° + y = 180° (sum of angles of a triangle is always 180°)
so,
y= 180° - 61° - 49° = 70°
What is the slope of the line that contains the points in the table?
A. -6
B. 2
C.-3
D. 3
Answer:
-3
Step-by-step explanation:
change in y over the change in x
pick to points and use slope formula
9-3
0-2
that's 6/-2 = -3
The table shows how many male and female students attended two different movies. What is the probability that a randomly chosen person from this group is mail and attended an action movie? Round your answer to two decimal places.
Answer:
the answer is d trust me 0.22
Step-by-step explanation:
help me plz
this is very important for me
Step-by-step explanation:
A line with the specific numbers plotted on it, numerical order
Answer:
1- Put the letter A on positive 7
2- Put the letter B on positive 5
3- Put the letter C on 0
4- Put the letter D on negative 4
5- Put the letter E on negative 9
Alex wants to arrange chairs in such a way that the number of chairs in a row is equal to the number of the columns.He has ordered 5100 tables.
a)How many more tables needed to arrange in such a way that he planned? Justify your answer
b)How many chairs can he remove to arrange in a way that he wants? Justify your answer.
Answer:
84
59
Step-by-step explanation:
In other to have the same number of chayes in both rows and columns ;
If the Number of chairs per row = x ; then number of chairs per column = x
Then the total number of chairs needed = x * x = x²
Hence, if there are 5100 chairs ;
Number of chairs needed more ;
Take the square root of 5100 ;the round to the next whole number :
B.) For number of chairs to be removed ;
Take the square root of 5100 and round down to the whole number.
Hence,
A.) = √5100 = 71.414 = 72
72² - 5100 = 84
B.) 5100 = 71.414 = 71
5100 - 71² =
Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.L1: x / 1 = y - 1 / -1 = z - 2 / 3L2: x - 2 / 2 = y - 3 / -2 = z / 7
The lines are skew
Step-by-step explanation:
To make things clearer, rewrite the given lines as follows;
[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3}[/tex]
[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7}[/tex]
(i) Test if the lines are parallel.
Two lines are parallel if the cross product of their directional vectors is equal to the zero vector 0 (which is equal to <0, 0, 0>). For example, if their directional vectors are m and n, then;
m x n = 0
Where;
m, n and 0 are vectors
In the given lines, L₁ and L₂, their directional vectors are given by the denominators of their symmetric equation.
For L₁, the directional vector = <1, -1, 3>
For L₂, the directional vector = <2, -2, 7>
Let
m = <1, -1, 3> = i - j + 3k
n = <2, -2, 7> = 2i - 2j + 7k
Now, find the cross product of the vectors;
m x n = | i j k |
| 1 -1 3 |
| 2 -2 7 |
m x n = i(-7 + 6) -j(7 - 6) + k(-2 + 2)
m x n = i(-1) -j(1) + k(0)
m x n = -i -j + 0k
Since the cross product does not give a zero vector, then the lines are not parallel.
(ii) Test if the lines intersect
To do this:
(a) First, we express the lines in parametric form rather than the symmetric form. Therefore
[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3}[/tex] is equated to say a;
and
[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7}[/tex] is equated to say b;
We have;
[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3} = a[/tex]
[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7} = b[/tex]
Split the lines into system of three equations in terms of a and b
For L₁
=> [tex]\frac{x}{1}[/tex] = a which gives x = a
=> [tex]\frac{y-1}{-1}[/tex] = a which gives y = 1 - a
=> [tex]\frac{z-2}{3}[/tex] = a which gives z = 3a + 2
∴ L₁ has these three equations
x = a -------------------------(i)
y = 1 - a --------------------------(ii)
z = 3a + 2 --------------------------(iii)
For L₂
=> [tex]\frac{x-2}{2}[/tex] = b which gives x = 2b + 2
=> [tex]\frac{y-3}{-2}[/tex] = b which gives y = 3 - 2b
=> [tex]\frac{z}{7}[/tex] = b which gives z = 7b
∴ L₂ has these three equations
x = 2b + 2 --------------(iv)
y = 3 - 2b ---------------(v)
z = 7b ----------------(vi)
(b) Secondly, we combine the set of equations of the two lines.
Equations of x : (i) and (iv)
a = 2b + 2
=> a - 2b = 2 --------------------------------------(vii)
Equations of y: (ii) and (v)
1 - a = 3 - 2b
=> - a + 2b = 2 --------------------------------------(viii)
Equations of z: (iii) and (vi)
3a + 2 = 7b
=> 3a - 7b = -2 -------------------------------------(ix)
(c) Thirdly, solve equations (vii), (viii) and (ix) simultaneously to find the values of a and b
Add equations (vii) and (viii)
a - 2b = 2
+
-a + 2b = 2
0 + 0 = 4
Since 0 + 0 ≠ 4, then the values of s and t cannot be determined from the system of equations due to inconsistency. Therefore, the lines L₁ and L₂ do not intersect.
(iii) Test if the lines are skew
Two lines are said to be skew if they are neither parallel nor intersecting.
Since the lines L₁ and L₂ are neither parallel nor intersecting, the lines are skew.
Solve the equation 4x^2 - 5x -33 = -29 to the nearest tenth.
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Answer:
x = {-0.6, 1.8}
Step-by-step explanation:
Adding 33 we have ...
4x^2 -5x = 4
Dividing by 4, we get ...
x^2 -5/4x = 1
We can complete the square by adding the square of half the x-coefficient:
x^2 -5/4x +25/64 = 89/64
(x -5/8)^2 = 89/64
x = (5 ±√89)/8 = {-0.5542, 1.8042}
The solution rounded to the nearest tenth is ...
x = {-0.6, 1.8}
What is the area of this figure?
Answer:
286 mm ^2
Step-by-step explanation:
The figure is a trapezoid
The area of a trapezoid is given by
A = 1/2 ( b1+b2) *h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 28+24) * 11
A = 1/2 (52)*11
A =286 mm ^2
Answer:
The area of this figure is 286
Step-by-step explanation:
The formula for the area of a trapezoid is A = (a+b/2)h, or the top line plus the bottom line divided by 2 times the height. a is given as 24 mm and b is given as 28 mm so 24 plus 28 is 52. 52 divided by 2 is 26. 26 times 11 is 286 therefore the answer and area is 286.
What is the value of cos C?
Answer:
15/17
Step-by-step explanation:
cos=opp/adj
cos C=15/17
Can anyone help !! Please
Answer:
the first question is x=68/3 in standard from it is 3x=68
the second question is x= - 11/10
Step-by-step explanation:
for the second question the negative is beside the fraction.
Below is a frequency distribution for our RCCC sample of men's heights.
Class Class Frequency Midpoint (inches)
64-65 4
66-67 4
68-69 4
70-71 5
72-73 10
74-75 4
a. Fill in the midpoint of each class in the column provided.
b. Enter the midpoints in L, and the frequencies in L2, and use 1- VarStats to calculate the mean and standard deviation of the frequency distribution. Using the frequency distribution, I found the mean height to be ___________with a standard deviation of____________
c. Now, let's compare the mean of the frequency distribution you just found in part (b), which is an estimate of the actual sample mean, to the actual sample mean you found in (#1).
Using the frequency distribution in (a), I found the mean height to be___________ inches, while using the actual data in #1, I found the mean height to be___________ inches. The true sample mean (using all the data) and the sample mean estimated from a frequency distribution can be fairly close to each other or very different. In this case, do you think the two means were close___________ Using complete sentences, explain why you think the two means came out so close, or why they came out so different, whichever the case may be.
Answer:
[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { 64.5} & {64-65} & {4} & {66.5 } & {66-67} & {4} & {68.5 } & {68-69} & {4} &{70.5 } & {70-71} & {5} & {72.5 } & {72-73} & {10} & {74.5 } & {74-75} & {4}\ \end{array}[/tex]
Using the frequency distribution, I found the mean height to be 70.1129 with a standard deviation of 3.2831
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { } & {64-65} & {4} & { } & {66-67} & {4} & { } & {68-69} & {4} &{ } & {70-71} & {5} & { } & {72-73} & {10} & { } & {74-75} & {4}\ \end{array}[/tex]
Solving (a): Fill the midpoint of each class.
Midpoint (M) is calculated as:
[tex]M = \frac{1}{2}(Lower + Upper)[/tex]
Where
[tex]Lower \to[/tex] Lower class interval
[tex]Upper \to[/tex] Upper class interval
So, we have:
Class 64-65:
[tex]M = \frac{1}{2}(64 + 65) = 64.5[/tex]
Class 66 - 67:
[tex]M = \frac{1}{2}(66 + 67) = 66.5[/tex]
When the computation is completed, the frequency distribution will be:
[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { 64.5} & {64-65} & {4} & {66.5 } & {66-67} & {4} & {68.5 } & {68-69} & {4} &{70.5 } & {70-71} & {5} & {72.5 } & {72-73} & {10} & {74.5 } & {74-75} & {4}\ \end{array}[/tex]
Solving (b): Mean and standard deviation using 1-VarStats
Using 1-VarStats, the solution is:
[tex]\bar x = 70.1129[/tex]
[tex]\sigma = 3.2831[/tex]
See attachment for result of 1-VarStats
Solving (c): Compare the calculated mean to the actual mean
The actual mean is missing from the question, so I will make assumptions in this part
Assume they are close
This means that the selected sample is a reflection of the actual population where the samples are selected.
Assume they are not close
This means that the selected sample does not reflect the actual population where the samples are selected.
How many yards did Satomi run?
Answer:
50 yards
Step-by-step explanation:
Have a nice day :)
Answer:
1810 yd
Step-by-step explanation:
Satomi ran 50 more yards than 1/2 of 2 miles.
2 miles ÷ 2 = 1 mile
1 mile = 1760 yd
1760 yd + 50 yd = 1810 yd
If v = 35 , a = 4 , t = 5 and v = u + a t , evaluate u .
v = u + at
=> 35 = u + (4×5)
=> 35 = u + 20
=> 35 - 20 = u
=> 15 = u
Step-by-step explanation:
v = u + a t
35=u+ 4(5)
35-20=u
u=15
8x - (2x - 13) = 42
solve and check the equation
Answer:
x = 29/6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
8x - (2x - 13) = 42
Step 2: Solve for x
[Distributive Property] Distribute negative: 8x - 2x + 13 = 42[Subtraction] Combine like terms: 6x + 13 = 42[Subtraction Property of Equality] Subtract 13 on both sides: 6x = 29[Division Property of Equality] Divide 6 on both sides: x = 29/6Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 8(29/6) - [2(29/6) - 13] = 42Multiply: 116/3 - [29/3 - 13] = 42[Brackets] Subtract: 116/3 - -10/3 = 42Subtract: 42 = 42Here we see 42 does indeed equal 42.
∴ x = 29/6 is the solution.
Answer:
x = 29/6
Step-by-step explanation:
solve for x.
8x - ( 2x - 13 ) = 42
distribute minus sign
8x - 2x + 13 = 42
combine like terms
6x + 13 = 42
subtract 13 from both sides
6x + 13 - 13 = 42 - 13
6x = 29
Divide each side by 6
6x / 6 = 29 / 6
x = 29 / 6
Check the equation :
8x - ( 2x - 13 ) = 42
substitute the value of x in equation
8 ( 29/6) - ( 2(29/6) - 13) = 42
reduce the number with the greatest common factor 2
4 × 29 /3 - ( (29/3) - 13) = 42
calculate the product
116/3 - ( 29/3 - 13 )= 42
calculate the difference
116/3 -( -10/3 )= 42
change the sign
116/3 + 10/3 = 42
add the fractions to get 42.
42 = 42
Hence, verified.
Find the missing side or angle. Round to the nearest tenth. C=53° B= 80° a=2 b=[ ? ]
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Answer:
b ≈ 2.7
Step-by-step explanation:
The missing angle A is ...
A = 180° -53° -80° = 47°
The law of sines tells you ...
b/sin(B) = a/sin(A)
b = sin(80°)×2/sin(47°) ≈ 2.6931
Side b is about 2.7 units.
Answer:
b~ 2.7Step-by-step explanation:
hope it helps much
Need help pls. Kind of struggling to get an answer
Answer:
c. 216 m squared
do 6×6 to find the missing area then do 12×21 to fine whole area then subtract 252 and 36. hope this helps
Which product is positive?
(1) (1943)-3)
(13)04-1)-4)
O
5
3
Answer:
El 5 y el 3
Step-by-step explanation:
La primera y la segunda saldrá un negativo ya que hay un negativo y con eso nunca saldrá positivo.
La tercera es 0, no es positivo ni negativo
La cuarta y quinta es positivo
7. The points P(2, -3), Q(3, -2) and R(8, z) are
collinear, i.e. they lie on a straight line. Find the
value of z.
Answer:
z = 3
Step-by-step explanation:
Since the points are collinear then the slopes between the points are equal.
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = P (2, - 3) and (x₂, y₂ ) = Q (3, - 2)
m = [tex]\frac{-2+3}{3-2}[/tex] = 1
Repeat with
(x₁, y₁ ) = Q (3, - 2) and (x₂, y₂ ) = R (8, z )
m = [tex]\frac{z+2}{8-3}[/tex] = [tex]\frac{z+2}{5}[/tex] , then
[tex]\frac{z+2}{5}[/tex] = 1 ( multiply both sides by 5 )
z + 2 = 5 ( subtract 2 from both sides )
z = 3
In parallelogram DEFG if m FGD=125 find m GDE
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Answer:
55°
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary.
m∠GDE = 180° -m∠FGD = 180° -125°
m∠GDE = 55°
Eyjafjallajökull is a volcano in Iceland. Ina research reuption a projectile is ejected with an initial velcony of 304 feet per second. The height H, in feet is given the equation H=16t^2 + 304t
Answer:
t = 9.5 seconds
Step-by-step explanation:
Given that,
The initial velocity of the projectile is 304 ft/s
The height of the projectile is given by :
[tex]H=16t^2 + 304t[/tex]
For maximum height,
Put h' = 0
[tex]h'=-32t+304[/tex]
or
[tex]-32t+304=0\\\\t=\dfrac{304}{32}\\\\t=9.5 \ s[/tex]
So, the time taken to reach the maximum height is 9.5 seconds.
If the total surface area of hemispher is 7392 square cm. Them find its radius.
Answer: The radius of the hemisphere is (R) = 28 cm
Three more than the product of six and a number, increased by nine in the simplest form
Answer: 12+6x
Step-by-step explanation:
three more means addition +3
the product of 6 and a number means multiplying 6 by a variable 6x
increased by 9 means addition +9
put it together and we have 3+6x+9
now we combine like terms
3+9+6x
12+6x
If you spoke 200 minutes per month, what would your monthly bill be for each plan?
Answer:
it will have 2be 408,99 cent plan so tht u can be able 2 speak the whole month
Find the value of x.
Answer:
9 sqrt(2) /2 = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hypotenuse
sin 45 = x /9
9 sin 45 = x
9 sqrt(2) /2 = x
1 torr is equal to (1 Point)
Answer:
1 torr = 760 atm
1 torr = 1 mmHg
Please help me no links!!
Answer:
Slope = 1
Y-intercept = 4
equation = 1x + 4
Hope this helps!
An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a yellow on your next toss of the die
Answer:
[tex]P(Yellow) = \frac{29}{147}[/tex]
Step-by-step explanation:
Given
[tex]Brown = 27\\Purple = 47\\Yellow = 29\\Green = 44[/tex]
Required
[tex]P(Yellow)[/tex] --- next roll to be yellow
This is calculated as:
[tex]P(Yellow) = \frac{Yellow}{Total}[/tex]
So, we have:
[tex]P(Yellow) = \frac{29}{27 + 47 + 29 + 44}[/tex]
[tex]P(Yellow) = \frac{29}{147}[/tex]
m/
Tim is an elementary school art teacher. His students are sculpting a replica of a shark out of clay. Tim has given them one block of clay to make 20 conical shark
teeth for the sculpture. The block contains 81 cm3 of clay. If each tooth is solid and has a 2.5 cm base diameter, what is the maximum height each tooth can be?
Assume that the students use all the clay.
A.
1.25 cm
Св.
2.27 cm
c.
2.47 cm
D
3.57 cm
E. 4.50 cm
=====================================================
Explanation:
We have 81 cm^3 of clay. Divide this among the 20 students and each gets 81/20 = 4.05 cm^3 of clay
--------------
The volume of a cone is
V = (1/3)*pi*r^2*h
Solving for h gets us
3V = pi*r^2*h
(3V)/(pi*r^2) = h
h = (3V)/(pi*r^2)
--------------
The diameter is 2.5 cm which cuts in half to 1.25 cm, so this is the radius.
We'll plug this radius in, along with V = 4.05 and pi = 3.14
h = (3V)/(pi*r^2)
h = (3*4.05)/(3.14*(1.25)^2)
h = 2.4764
This value is approximate. Rounding down to the nearest hundredth gets us 2.47
We round down because rounding up to 2.48 will lead to a volume larger than 4.05
The maximum height of each tooth is 2.47 cm and this can be determined by using the formula of the volume of the cone.
Given :
Tim is an elementary school art teacher. His students are sculpting a replica of a shark out of clay. Tim has given them one block of clay to make 20 conical shark teeth for the sculpture. The block contains 81 cm3 of clay. If each tooth is solid and has a 2.5 cm base diameter.The following steps can be used in order to determine the maximum height of each tooth:
Step 1 - The formula of the volume of the cone can be used in order to determine the maximum height of each tooth.
Step 2 - The formula of the volume of the cone is given below:
[tex]\rm V = \dfrac{1}{3}\pi r^2h[/tex]
where r is the radius and h is the height of the cone.
Step 3 - Substitute the values of the known terms in the above expression.
[tex]\rm \dfrac{81}{20}= \dfrac{1}{3}\times \pi \times (1.25)^2\times h[/tex]
Step 4 - Simplify the above expression.
h = 2.47 cm
For more information, refer to the link given below:
https://brainly.com/question/1578538
Use mapping notation to describe a translation up 8 units.
A. (x,y) → (x 8, y-8)
B. (x,y) → (x,y+8)
C. (x,y) = (x+8, y+8)
D. (x,y) → (x+8, y)
