Answer:
[tex]4,060[/tex]
Step-by-step explanation:
[tex]\binom{30}{3}=\boxed{4060}[/tex]
There are 30 teachers for the principal to choose from initially. After the principal chooses one, there will be 29, 28, 27, and so on.
Since the principal is only choosing 3, there are [tex]30\cdot 29\cdot 28=24,360[/tex] permutations. However, the order of which the principal chooses the teachers does not matter. In other words, without loss of generality, let the name of three of the teachers be Adam, Bernie, and Carla. Regardless of whether the principal chooses Adam then Bernie then Carla or Carla then Adam then Bernie, etcetera, the same three teachers are still being chosen.
Thus, we must divide by the number of ways you can rearrange three distinct teachers, which is [tex]3![/tex].
Therefore, the desired answer is [tex]\frac{24360}{3!}=\frac{24360}{6}=\boxed{4,060}[/tex]
A company bought a piece of machinery for $16 200. In the first it depreciated 15%, and in the second year 10%. How much was it worth when two years old?
Https://imgur.com/a/n3PRcMY
Scientists found that a certain particle of dust doubles every 30 minutes. If the scientists tests this out with 21 grams of the specific dust, how many grams would they have after 2 days?
Answer: [tex]1.663\times 10^{30}\ gm[/tex]
Step-by-step explanation:
Given
Population of dust particle doubles every 30 minutes
If the initial sample is 21 grams
The model to predict the population will be
[tex]\Rightarrow P=21\cdot 2^{2t}[/tex]
Where t=time in hours
A day has 24 hours . So, for 2 days time is 48 hours
Population is given by
[tex]\Rightarrow P=21\cdot 2^{2\times 48}\\\\\Rightarrow P=21\times 2^{96}\\\\\Rightarrow P=1.663\times 10^{30}\ gm[/tex]
There are 3 red, 1 blue and 2 yellow marbles in a bag. Once a marble is selected it is not replaced.Find P(red then yellow). *
A.1/6
B.1/5
C.5/6
D.2/5
Answer:
B) 1/5
Step-by-step explanation:
P(R then Y) = 3/6 · 2/5 = 6/30 or 1/5 simplified
A sculptor needs to lift a piece of marble it’s a cuboid with dimensions 1 by 0.2 by 0.5 marble has a density of 2.7 what’s the mass in kg
Answer:
Mass of piece of marble = 0.27 kilogram
Step-by-step explanation:
Given:
Dimensions of cuboid = 1 x 0.2 x 0.5
Density of marble = 2.7
Find:
Mass of piece of marble
Computation:
Volume of cuboid = (l)(b)(h)
Volume of marble = 1 x 0.2 x 0.5
Volume of marble = 0.1
Mass = Density x Volume
Mass of piece of marble = Density of marble x Volume of marble
Mass of piece of marble = 2.7 x 0.1
Mass of piece of marble = 0.27 kilogram
A rectangular park is 260 m by 480 m. Danny usually trains by running 5 circuits around the edge of
the park. After heavy rain, two adjacent sides are too muddy to run along, so he runs a triangular path
along the other two sides and the diagonal. Danny does 5 circuits of this path for training. Show that
Danny runs about 970 metres less than his usual training session
Answer:
971 m to nearest metre
Step-by-step explanation:
training distance = 5*2*(260 + 480) m
Diagonal distance = √(2602 + 4802) m
Heavy rain training distance = 5*(260 + 480 + √(2602 + 4802)) m
Difference between these:
5 × 2 × ( 260 + 480 ) - 5 ×( 260 + 480 + √ 260 ^ 2 + 480 ^ 2 )
= 970 . 5311872087638744
difference = 971 m to nearest metre
Hope this answer helps you :)
Have a great day
Mark brainliest
Two lines are intersecting. What is the value of X? And to your answer in the box
Answer:
x = 51
Step-by-step explanation:
The two angles form a straight line
Angles that form a straight line add up to equal 180
Hence, 2x + 4 + x + 23 = 180
( note that we just created an equation that we can use to solve for x )
we now solve for x using the equation we created
2x + 4 + x + 23 = 180
step 1 combine like terms
2x + x = 3x
4 + 23 = 27
we now have 180 = 27 + 3x
step 2 subtract 27 from each side
180 - 27 = 153
27 - 27 cancels out
we now have 153 = 3x
step 3 divide each side by 3
153 / 3 = 51
3x / 3 = x
we're left with x = 51
B
5
6
100° 5
A
Ta
60°
4 120°
W
D
w = [? 1°
Answer:
I'm sorry but this is very wordy and hard for people to understand.
please reconsider fixing it and submitting it again for assistance.
Nadia is investigating rotations about the center of regular polygons that carry the regular polygon onto itself. She claims that there are rotations about the center that will carry both a regular hexagon and a regular nonagon (9-sided polygon) onto itself. Determine whether each angle of rotation below can be used to support Nadia's claim. Select Yes or No for each angle of rotation
Answer:
[tex]\theta_1 \ n\ \theta_2 = 120, 240[/tex]
Step-by-step explanation:
The question is incomplete, as the angles of rotation are not stated.
However, I will list the angles less than 360 degrees that will carry the hexagon and the nonagon onto itself
We have:
[tex]Nonagon = 9\ sides[/tex]
[tex]Hexagon = 6\ sides[/tex]
Divide 360 degrees by the number of sides in each angle, then find the multiples.
Nonagon
[tex]\theta = \frac{360}{9} =40[/tex]
List the multiples of 40
[tex]\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320[/tex]
Hexagon
[tex]\theta = \frac{360}{6} =60[/tex]
List the multiples of 60
[tex]\theta_2 = 60, 120, 180, 240, 300[/tex]
List out the common angles
[tex]\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320[/tex]
[tex]\theta_2 = 60, 120, 180, 240, 300[/tex]
[tex]\theta_1 \ n\ \theta_2 = 120, 240[/tex]
This means that, only a rotation of [tex]120, 240[/tex] will lift both shapes onto themselves, when applied to both shapes.
The other angles will only work on one of the shapes, but not both at the same time.
what property 8 + 43 = 43 + 8
Answer:
commutative property
Step-by-step explanation:
It's basically just changing the order of the equation.
The length of a rectangle is 3 yd less then twice the width, and the area of the rectangle is 27 yd^2. Find the dimensions of the rectangle.
Answer:
4.5yards and 6 yards is your rectangle measurement
4. Multiply the following fractions and reduce to the lowest form.
(a)9/4 8/81
(b)20 x 4/5
Please help me i would give more points but i dont have much (Giving brainlest)
Answer:
Step-by-step explanation:
First, put them in order.
5.3x+3.6x+9.8-8.14
Add 5.3x and 3.6x
8.9x
Subtract 8.14 from 9.8
1.66
(140-x)/(7)+70 = 120. Please answer correctly.
write an equation of the line in slope intercept form
Answer:
[tex]y=-2x+2[/tex]
Step-by-step explanation:
[tex]y=mx+b[/tex] is the slope intercept
[tex]m[/tex] is the slope
[tex]b[/tex] is the y-intercept
The slope in the graph is 4/2 or 2 simplified. From point (-2,6), you have to go down 4 and right 2 to get to the point (0,2)
The y-intercept is 2 because the line crosses the y axis at exactly 2.
Hope this helps
if g(x) = 3x + 7 what is the value of g(-2)?
1- -1
2- 1
3- 8
4- 12
Answer:
12
Step-by-step explanation:
3x+7 = 12
PLEASE PLEASE PLEASE SOMEONE HELP ME THIS IS DUE TODAY
EXPLAINING YOUR ANSWER = BRAINLIEST
What is m∠E?
Answer:
try 144
Step-by-step explanation:
m<E is basically just ot asking you to find the angle of E, i think :').
And since all angles equal to 180, 180-36=144
(hope ots right)
Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?
Answer:
So , 41 years ago, Mothers age is 3 times of Sally's age. When Sally's age was 13 , and her mom age was 39 (
What is the amplitude in the graph of y = 5sin(2x - 1) + 3?
Answer:
The amplitude is 5
Step-by-step explanation:
The function [tex]y=asin(bx-c)+d[/tex] has an amplitude of [tex]|a|[/tex]. Therefore the amplitude of the function [tex]y=5sin(2x-1)+3[/tex] is [tex]|a|=|5|=5[/tex].
Any of you guys know this answer?
If the farm has 10,000 spinach plants, Describe a method that would produce a random sample and how many in your sample study?
Answer:
Take an even number of random samples from the 10000 spinach plants
lets assume you take ; 100 random samples each sample will contain = 10,000 / 100 = 100 spinach plants
Step-by-step explanation:
Given that the total number of spinach plants in the farm = 10,000
To obtain a random sample, take a census of the number of farms wherein the spinach plants are planted, determine the mean size and standard deviation of the farm that way you can apply the central limit theorem.
After determining these Take an even number of random sample from the 10000 spinach plants
lets assume you take ; 100 random samples each sample will contain = 10,000 / 100 = 100
Put these numbers in order from least to greatest.
0.78
8.7
0.078
Answer:
Least:0.078
In between: 0.78
Greatest: 8.7
Step-by-step explanation:
pls help middle school math
Given ,
5<x<10 and 8<y<19
For y-x,
8-5<y-x<19-10
3<y-x<9
Which choice is equivalent to the expression below when x 0?
√328 – 116x + 428 – 12x
O A. 3x12x
O B. 4x/2x
O c. 18x
O D. 32x
the answer is d hopes this helps you
Analyze the diagram below and complete the instructions that follow.
Find the exact value of sin(O)
=====================================================
Explanation:
Use the pythagorean theorem
a^2+b^2 = c^2
to find that c = 13 when a = 12 and b = 5.
So that makes the hypotenuse MO = 13 units long.
The opposite side is MN = 12 units long as this side is furthest we can get from angle O.
The sine ratio involves opposite over hypotenuse
sin(angle) = opposite/hypotenuse
sin(O) = MN/MO
sin(O) = 12/13
Answer:
C. 12/13
Step-by-step explanation:
a² + b² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
c = 13
------------
sin = opp/hyp
sinO = 12/13
Find WX. Assume that segments which appear to be tangent are tangent.
Answer:
Step-by-step explanation:
Tangent from the point outside the circle are equal
WX = XY
7x - 29 = 2x + 16 {Add 29 to both sides}
7x = 2x + 16 +29
7x = 2x + 45 {Subtract 2x from both sides}
7x - 2x = 45
5x = 45 {Divide both sides by 5}
x = 45/5
x = 9
WX = 7x - 29
= 7*9 - 29
= 63 - 29
WX = 34
The following table shows the probability of rolling the numbers 1 through 7
on a fair 7-sided die.
х
1
2
3
4
5
6
7
P(X) 1/71/71/71/71/71/71/7
What is the standard deviation of the random variable X, "the number that
comes up on the die"?
A. 1.708
OB. 3.745
O C. 2.917
Оооо
D. 3.5
E. 2.0
Answer:
2.0
Step-by-step explanation:
Couldn't really understnd what you wrote but I'll assume it's the standard deviation of a fair, 7-sided die
The standard deviation is just the square root of the variance (which is just the second moment minus the first moment squared)
The first moment (AKA the average is..)
[tex]\frac{1+2+3+4+5+6+7}{7}=4[/tex]
The second moment is..
[tex]\frac{1^2+2^2+3^2+4^2+5^2+6^2+7^2}{7}=20[/tex]
[tex]\sqrt{20-4^2}=2[/tex]
help......................
Answer:
17.
[tex] 7 \times {10}^{ - 6} [/tex]
18. 8 sides (and 8 corners)
19. the chance is 50% or 0.5, and yes, both colors have the same chance.
20. on a coordinate grid make a point at x=1 and y=5. and then simply draw a line through that point.
Step-by-step explanation:
17. the defining digit is 7. and it is at the the 6th position after the decimal point. that is how you write this.
18. the more corners or sides a polygon has, the closer it gets to a circle. that means that the outside angles always add up to 360 degrees.
so, with the inside angles being 135 degrees, the outside angles are 180-135 = 45 degrees.
his many such outside angles can we add together until we reach 360 degrees ?
360/45 = 8 (just imagine : 2×45 = 90, and 90×4 = 360)
so, this polygon has 8 corners and therefore 8 sides.
19. 12 balls are in the bag. the chance for a single ball to be pulled is therefore 1/12.
but there are 6 red balls. we don't care which specific ball we pull, as long as it's red. so, we have 6/12 chances to achieve that.
and yes, for exactly the same reason, black balls have the same chance.
area of the triangle ABC
Answer:
180
Step-by-step explanation:
hope this answer be right :)
My mama got me doing freaking school work pls help me out
Answer:
x=50
Step-by-step explanation:
corresponding angles