The fundamental counting principle is used to count the total number of possible outcomes that are in a situation.
What does the fundamental counting principle state?The fundamental counting principle states that if there are n ways of doing something, as well as m ways of doing another thing, then there are n×m ways to perform both of these actions.
The Fundamental Counting Principle helps when determining the sample space of probability as it figures out the total number of ways the combination of events can occur. Therefore, it is used as a guide when determining the sample space of a probability.
Lastly, the limitation is that the Fundamental Counting Principle is that it assumes that each basic event is equally probable, which does not necessarily have to be true.
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Answer:
The fundamental counting principle is used to count the total number of possible outcomes that are in a situation
Step-by-step explanation:
Find the missing side lengths. Round all answers to the nearest tenth.
Answer:
81
Step-by-step explanation:
90+25= 115
115 - 34 = 81
Find three consecutive odd integers such that the product of the second and the third integers is twenty-six more than three times the first integer.
Step-by-step explanation:
first number=x
second number=x+2
third number=x+4
(x+2)(x+4)=3x+26
x(x+4)+2(x+4)=3x+26
x²+4x+2x+8=3x+26
x²+6x+8=3x+26
x²+6x-3x=26-8
x²+3x=18
x²+3x-18=0
you can use that to find the numbers
Answer:
6, 8 and 10
Step-by-step explanation:
Let the 3 consecutive odd numbers be x, x+2, x+4
product of the second and the third integer
(x+2)(x+4)
twenty-six more than three times the first integer is expressed as;
3x + 26
Equate
(x+2)(x+4) = 3x + 26
x²+4x+2x+8 = 3x + 26
x²+6x +8= 3x+26
x²+3x +8-26 = 0
x²+3x-18 = 0
Factorize
x²-6x+3x-18 = 0
x(x-6)+3(x-6) = 0
x+3 = 0 and x-6 = 0
x = -3 and 6
The first 3 number is are 6, 8 and 10
Can someone help me? It's urgent and thank you!
Answer:
480,700
Step-by-step explanation:
C(25,7)
25!/(7!*(25-7)!)
15511210043330985984000000/(6402373705728000*5040)
480700
please help me, it would be really nice
Of the teacups in Bonnie's Tea Shop, 1/12 are blue and another 1/12 are orange. What fraction of the teacups are either blue or orange?
Answer: 1/6
Step-by-step explanation:
This is a question that has to do with the addition of a fraction. Since we are given the information that of the teacups in Bonnie's Tea Shop, 1/12 are blue and another 1/12 are orange.
Then, the fraction of the teacups that are either blue or orange will be calculated as:
= 1/12 + 1/12
= 2/12
= 1/6
Therefore, the fraction of the teacups that are either blue or orange is 1/6.
1
Solve these simultaneous equations using the elimination method
4x + y = 23
x + y = 8
Answer:
y= 3, x= 5
Step-by-step explanation:
4x+y=23
-x-y=-8
3x/3=15/3
x=5
for y
x+y=8
5+y=8
y=8-5
y=3
x=5
y=3
Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 12 inches, and the width QR is labeled as 6 inches. The side LM of the square is labeled as 6 inches
Sam says that the length of diagonal SQ is two times the length of diagonal OM.
Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
(Sorry for the low quality image)
Answer:
Sam is incorrect
Step-by-step explanation:
We can calculate the lengths of the diagonals using Pythagoras' identity.
The diagonals divide the rectangle and square into 2 right triangles.
Consider Δ SRQ from the rectangle
SQ² = SR² + RQ² = 12² + 6² = 144 + 36 = 180 ( take square root of both sides )
SQ = [tex]\sqrt{180}[/tex] ≈ 13.4 in ( to 1 dec. place )
Consider Δ ONM from the square
OM² = ON² + NM² = 6² + 6² = 36 + 36 = 72 ( take square root of both sides )
OM = [tex]\sqrt{72}[/tex] ≈ 8.5 in ( to 1 dec. place )
Now 2 × OM = 2 × 8.5 = 17 ≠ 13.4
Then diagonal OM is not twice the length of diagonal SQ
the standard unit for measuring mass is the
An arrow is shot vertically upward from a platform 19ft high at a rate of 163ft/sec. When will the arrow hit the ground? Use the formula: h=−16t2+v0t+h0. (Round your answer to the nearest tenth.)
Answer: 10.3 s
Step-by-step explanation:
Given
The height of the arrow is given by [tex]h=-16t^2+v_ot+h_o[/tex]
At [tex]t=0, h=19\ ft[/tex]and [tex]v_o=163\ ft/s[/tex]
When arrow hits ground, h becomes 0 i.e.
[tex]\Rightarrow 0=-16t^2+163t+19\\\Rightarrow 16t^2-163t-19=0\\\\\Rightarrow t=\dfrac{163\pm \sqrt{(-163)^2+4(16)(19)}}{2(16)}\\\\\Rightarrow t=-0.115,10.30\ s[/tex]
Neglecting the negative value of t
So, the arrow hits the ground after 10.30 s
If y varies inversely as x2 and y=6 when x=30, what is y when x=6
Answer:
y = 150
Step-by-step explanation:
y varies inversely as x²
yx² = k
----------------
y = 6 when x = 30
6(30²) = k
6(900) = 5400
--------------------------
what is y when x = 6
y(6²) = 5400
y(36) = 5400
y = 5400/36
y = 150
Answer:
y= 150
Step-by-step explanation:
[tex]y\ \alpha \ \frac{1}{x^2}\\\\y = k \times \frac{1}{x^2}\\\\[/tex]
Given y = 6, and x = 30. Find k.
[tex]6 = k \times \frac{1}{30^2}\\\\6 \times 900 = k\\\\5400 = k[/tex]
Given x = 6 and k = 180. Find y
[tex]y = 5400\times \frac{1}{6^2}\\\\[/tex]
[tex]=5400 \times \frac{1}{36}\\\\=150[/tex]
Suppose the hypotenuse of a right triangle is 13 cm and one of the legs is 10 cm. Use the Pythagorean Theorem to find the measure of the triangle’s other leg.
Answer:
3
Step-by-step explanation:
Pythagorean rule
[tex]hyp = opp + adj \\ therefore. \\ opp = hyp - adj \\ and \\ adj = hyp - opp[/tex]
opp=13-10
opp=3
What are the two possible measures of the angle below?
Answer:
90 or -270
Step-by-step explanation:
1+2+3+....+2012+2013
Answer:
Un=n(n+1)/2
U=2013(2013+1)/2
U=2.027.091
pls tell by step by step
Answer:
x = 50 degree
Step-by-step explanation:
x + 10 + x + x + 20 = 180 degree (being linear pair)
3x + 30 = 180
3x = 180 - 30
x = 150/3
x = 50 degree
find'x' 2log_5x = 1+log_5(x-6/5)
Answer:
x = 2 and x = 3
Step-by-step explanation:
Formulas used :
[tex]log_5 \ 5 = 1[/tex]
[tex]log_5 \ x + log_5 \ y = log_5 \ (xy)[/tex]
[tex]log_5 \ x = log_5 \ y => x = y[/tex]
Steps :
[tex]2 \ log_5 \ x = 1 + log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ 5+ log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ ( 5(x - \frac{6}{5} ))\\\\x^2 = 5(x - \frac{6}{5})\\\\x^2 = 5x - 6\\\\x^2 - 5x + 6 = 0\\\\x^2 - 2x - 3x + 6 = 0\\\\x(x - 2 ) - 3 (x - 2) = 0\\\\(x - 3)(x-2) = 0\\\\x = 3 , x = 2[/tex]
Use this system of linear equations to solve for x. 3x+5y=6 and 2x+y=4
Answer:
x=2
HPT 3x+5y=6 (1) và 2x+y=4 (2)
Nhân phương trình (2) với 5 để hệ số y của 2 phương trình bằng nhau. Ta có:
(2)⇔ 10x+5y=20(3)
Trừ (3) cho (1), có: 7x+0y=14⇒x=2
Answer:
3x+5y=6.....eqn 1
2x+y=4.......eqn 2
y=4-2x.....eqn 3
Step-by-step explanation:
substitute eqn 3 into eqn 1
3x+5(4-2x)=6
3x+20-10x=6
-7x = -14
x=2
3. Which of the following equations has a center of (-4,7) and a diameter of 18?
(1) (x+4)*+(y – 7)' =3
(2) (x+4)* +(y-7)= 324
(3) (x+4)*+(y-7)=9
(4) (x+4)*+(y-7)* = 81
Answer:
option 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (- 4, 7) and r = 18 ÷ 2 = 9 , then
(x - (- 4) )² + (y - 7)² = 9² , that is
(x + 4)² + (y - 7)² = 81
what fraction of 4000 is 800?
Answer:
5
Step-by-step explanation:
Since it says the fraction, just divide 4000 by 800. So,
[tex]\frac{4000}{800}\\=>5[/tex]
That's it for the explanation. Hope it helped.
Solve the simultaneous equation:
8d - 4e = 28
6d + 3e = 3
Answer: d=2 and e= -3
Step-by-step explanation:
(8d-4e=28)*3 => 24d-12e=84
(6d+3e=3)*4 => 24d+12e=12
24d+24d-12e+12e=84+12
=> 48d=96
=> d=2
d=2 => 8*2-4e=28
=> e= -3
7 of 8
The mean temperature for the first 7
days in January was 8°C.
The temperature on the 8th day was -1
°C.
What is the mean temperature for the
first 8 days in January?
°C
Answer:
6.875 degrees
Step-by-step explanation:
[tex]Total=7\times8=56\\56-1=55\\mean for 8 days=\frac{55}{8} =6.875 degrees[/tex]
please answer this !!
x/2 + 50
Answer:
x = 260
Step-by-step explanation:
Add the two angles together. They will sum to 180
x/2+ 50 = 180
Subtract 50 from each side
x/2+50-50 = 180-50
x/2 = 130
Multiply by 2
x/2*2 = 130*2
x = 260
Answer:
260°
Step-by-step explanation:
To calculate the two angles together . They will added to 180°.x / 2 + 50° = 180°
Subtract 50° from each side
x/2 + 50° - 50° = 180° - 50°
x / 2 = 130°
Multiply each side by 2
2 × x/2 = 130° × 2
x = 260°
1)Rút gọn:
(√9+4√5)-(√9-4√5)-√5+(√23-8√7)
2)Chứng minh:
x²+x√3+1 luôn luôn dương với mọi x.
Answer:
si sumas 9+4×5 te da la respuesta
4. In slope-intercept form, what is the equation of a line perpendicular toy - 2x + 7 that passes
through the point (5,8)?
a y - 4x + 21
b. y - 2x ***
a.y=2x-31
Answer:
y = (-1/2)x + 21/2
Step-by-step explanation:
Given equation:
y - 2x + 7
Coordinates = (5,8)
Find:
Perpendicular equation
Computation:
y = mx + c
y - 2x + 7
y = 2x - 7
So,
m = 2
The negative reciprocal of 2 is -1/2
So,
For,
Coordinates = (5,8)
y = mx + c
8 = (-1/2)(5) + c
8 = -5/2 + c
c = 8 + 5/2
c = 21 /2
So,
y = mx + c
y = (-1/2)x + 21/2
Can somebody help I’ll give brainless plss
Answer:
$93.22
Step-by-step explanation:
bill = $79
tip = 18%
tip amount = tip % of bill
=18/100 * $79
=$1422/100
=$14.22
total cost = $79 + $14.22
=$93.22
Answer:
93.22
Step-by-step explanation:
Find the amount of the tip
79*18%
79 * .18
14.22
Add this to the amount of the bill
79+14.22
93.22
Using f(x) = 8x + 5 and g(x) = 7x - 2, find:g(f(6))
Answer:
369
Step-by-step explanation:
g(f(x)) simply means to put the whole expression of function f(x) into the place of "x" in g(x).
and to find the functional value for a specific x we just need to calculate functional value for f(x) and use that result as input for g(x).
f(6) = 8×6 + 5 = 48 + 5 = 53
and now
g(53) = 7×53 - 2 = 371 - 2 = 369
to check we do the general functional substitution :
g(f(x)) = 7×(8x+5) - 2 = 56x + 35 - 2 = 56x + 33
g(f(6)) = 56×6 + 33 = 336 + 33 = 369
correct
a rectangular swimming pool is 15 meters long, 12 1/2 meters wide and 2 1/2 meters deep. what is the pools volume?
Answer:
468.75 Cubic meters
Step-by-step explanation:
15 x 12.5 x 2.5 = volume
187.5 x 2.5 = volume
468.75 = volume
Answer:
its 393.75 cubic meters
Step-by-step explanation:
I hope this helps
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+119x+57
Answer:
Time required to hit the ground is 7.9 s.
Step-by-step explanation:
The height of the rocket is given by
[tex]y =- 16 x^2 + 119 x + 57[/tex]
For the time to hit the ground, put y = 0
[tex]-16x^2+119x+57=0\\\\16 x^2 - 119 x - 57 = 0 \\\\x = \frac{119\pm\sqrt{14161+3648}}{32}\\\\x = \frac{119\pm133.45}{32}\\\\t = - 0.45 s, 7.9 s[/tex]
Time cannot be negative, so time to hit the ground is 7.9 s.
2. If the sales tax on a $825 television set is 7%, how
much will you pay in total?
Please help!!Either question is fine!
Answer:
$882.75
Step-by-step explanation:
In order to calculate tax, you need to multiply the percentage by the purchase costs. First, start by finding the decimal value of the percentage.
7 ÷ 100 = 0.07 — Percentage converted to a decimal.
[tex]825 \times 0.07 = 57.75[/tex]
— The tax. Now, in order to find the whole price, the tax and retail price must be added together.
[tex]825 + 57.75 = 882.75[/tex]
As per linear equation, the amount I have to pay in total is $645.
The simplified value of the given expression is (8 - 17x).
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
1. Given, the cost of television is $825.
The sales tax rate is 7%.
Therefore, total price of the television is
= $[tex][825 + (\frac{825(7)}{100})][/tex]
= $[tex](825+57.75)[/tex]
= $[tex]882.75[/tex]
2. The given expression is:
[tex]-4(3x - 2)- 5x\\= -12x + 8-5x\\= 8-17x[/tex]
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Class width is 2
Find mode
Answer:
7.22
Step-by-step explanation:
solved in the diagram
Determine whether the dilation from the figure on the left to the figure on the right is an enlargement or a reduction. Then find the scale factor of the dilation.
A : Reduction scale factor 1/14
B : Enlargement; scale factor 14
C : Enlargement scale factor 0.5
Answer:
A.
Step-by-step explanation:
we are going from a large shape to a smaller shape. the proof is that the side lengths go down from 7m to 0.5m. so, it is a reduction.
and the scaling factor s ? what do we need to multiply the original side lengths with to get the new ones ?
7 × s = 0.5 = 1/2
s = (1/2)/7 = (1/2)/(7/1) = (1×1)/(2×7) = 1/14
=> answer A is correct
The dilation from the figure on the left to the figure on the right is a reduction.
Reduction scale factor 1/14.
The correct option is A.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
We have given that two figures.
The dilation from the figure on the left to the figure on the right is a reduction.
And the scale factor is,
= actual / scale
= 1/(7 / 0.5)
= 1/14
Therefore, the scale factor is 1/14.
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