Answer:
a) 294
b) 180
c) 75
d) 168
e) 105
Step-by-step explanation:
Given the numbers 0, 1, 2, 3, 4, 5 and 6.
Part A)
How many 3 digit numbers can be formed ?
Solution:
Here we have 3 spaces for the digits.
Unit's place, ten's place and hundred's place.
For unit's place, any of the numbers can be used i.e. 7 options.
For ten's place, any of the numbers can be used i.e. 7 options.
For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.
Total number of ways = [tex]7 \times 7 \times 6[/tex] = 294
Part B:
How many 3 digit numbers can be formed if repetition not allowed?
Solution:
Here we have 3 spaces for the digits.
Unit's place, ten's place and hundred's place.
For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.
Now, one digit used, So For unit's place, any of the numbers can be used i.e. 6 options.
Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.
Total number of ways = [tex]6 \times 6 \times 5[/tex] = 180
Part C)
How many odd numbers if each digit used only once ?
Solution:
For a number to be odd, the last digit must be odd i.e. unit's place can have only one of the digits from 1, 3 and 5.
Number of options for unit's place = 3
Now, one digit used and 0 can not be at hundred's place So For hundred's place, any of the numbers can be used i.e. 5 options.
Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.
Total number of ways = [tex]3 \times 5 \times 5[/tex] = 75
Part d)
How many numbers greater than 330 ?
Case 1: 4, 5 or 6 at hundred's place
Number of options for hundred's place = 3
Number of options for ten's place = 7
Number of options for unit's place = 7
Total number of ways = [tex]3 \times 7 \times 7[/tex] = 147
Case 2: 3 at hundred's place
Number of options for hundred's place = 1
Number of options for ten's place = 3 (4, 5, 6)
Number of options for unit's place = 7
Total number of ways = [tex]1 \times 3 \times 7[/tex] = 21
Total number of required ways = 147 + 21 = 168
Part e)
Case 1: 4, 5 or 6 at hundred's place
Number of options for hundred's place = 3
Number of options for ten's place = 6
Number of options for unit's place = 5
Total number of ways = [tex]3 \times 6 \times 5[/tex] = 90
Case 2: 3 at hundred's place
Number of options for hundred's place = 1
Number of options for ten's place = 3 (4, 5, 6)
Number of options for unit's place = 5
Total number of ways = [tex]1 \times 3 \times 5[/tex] = 15
Total number of required ways = 90 + 15 = 105
Determine what type of quadrilateral ABCD is, given the following points. A(1,−1) B(7,1) C(8,−2) D(2,−4). 1.Parralellogram 2.rectangle 3.rhombus 4.square
Answer:
.
Step-by-step explanation:
Answer:
Rectangle
Step-by-step explanation:
You graph them. From Point A to Point B it's rise 2 run 6 just like Point C to Point D. From Point D to Point A it's rise 3 run -1 just like Point C to Point B
On a pice of paper graph Y + 2 > -3x - 3
Answer:
Copy this onto a piece of graph paper
Step-by-step explanation:
when graphing you want to make sure that the slope is correct and the y-intercept is the same
Graph the equation y = -x2 + 5x + 24. How do the values of x = 8 and x = -3 on the graph relate to this situation? Find the width of the archway.
Answer:
The values of x = 8 and x = -3 are the x-intercepts of this equation. The width of the archway is 11 units.
Step-by-step explanation:
Let be [tex]y = -x^{2}+5\cdot x +24[/tex], which is now graphed with the help of a graphing tool, the outcome is included below as attachment. The values of x = 8 and x = -3 are the x-intercepts of this equation, that is, values of x such that y is equal to zero. Algebraically speaking, both are roots of the second-order polynomial.
The width of the archway ([tex]d[/tex]) is the distance between both intercepts, which is obtained by the following calculation:
[tex]d = |x_{1}-x_{2}|[/tex], where [tex]x_{1} \geq x_{2}[/tex].
If [tex]x_{1} = 8[/tex] and [tex]x_{2} = -3[/tex], then:
[tex]d = |8-(-3)|[/tex]
[tex]d = 8 +3[/tex]
[tex]d = 11[/tex]
The width of the archway is 11 units.
AYOOO PLZ HELP ASAP!!!
Answer:
B.
Step-by-step explanation:
Well we know that
[tex]224=2^{5} *7[/tex]
so we can get the 2 outside of the radical
[tex]x^{11} =(x^{5} )^{2} *x[/tex]
and we can get the x^2 outside too.
[tex]y^8=y^5*y^3[/tex]
and we also can get y outside.
so we have:
[tex]2x^{2}y\sqrt[5]{7xy^3}[/tex]
HELP PLEASEEEE!!!!!
find y-intercept on the graph
Answer:
-4
Step-by-step explanation:
When looking at the graph look at the y axis and look to see where the line passes through
Answer:
-4 is the y intercept.
Step-by-step explanation:
Brainliest? Have a great day!
2.A 1998 Pontiac Grand-Am depreciates in value by 18% on average each year. If the car originally sold for $19995 in 1998, how much would the car be worth in 2012?
Answer:
Amount of car in 2012 = $1,242.55 (Approx)
Step-by-step explanation:
Given:
Rate of depreciation(d) = 18% = 0.18
Amount of car in 1998 = $19,995
Find:
Amount of car in 2012
Computation:
Number of year(n) = 14 year
[tex]Amount\ of\ car\ in\ 2012 = Amount\ of\ car\ in\ 2012 [1-d]^n[/tex]
Amount of car in 2012 = 19,995[1-0.18]¹⁴
Amount of car in 2012 = 19,995[0.82]¹⁴
Amount of car in 2012 = 19,995[0.0621432458]
Amount of car in 2012 = 1,242.5542
Amount of car in 2012 = $1,242.55 (Approx)
PLS HELP I NeED to finish this
Answer:
D. 15
Step-by-step explanation:
Use proportions.
[tex]\frac{35}{25} = \frac{21}{x} \\\\35x = 525\\x = 15[/tex]
Evaluate \dfrac32y-3+\dfrac53z 2 3 y−3+ 3 5 zstart fraction, 3, divided by, 2, end fraction, y, minus, 3, plus, start fraction, 5, divided by, 3, end fraction, z when y=6y=6y, equals, 6 and z=3z=3z, equals, 3.
Answer:
11
Step-by-step explanation:
Given:
3/2y - 3 + 5/3z
When
y=6
z=3
3/2y - 3 + 5/3z
Substitute the value of y and z
3/2(6) - 3 + 5/3(3)
=18/2 - 3 + 15/3
=9-3+5
=6+5
=11
I don't understand this question! Please help me!!
Answer:
262°Step-by-step explanation:
[tex]m\angle OFB=m\angle OCB=90^o\\\\so\ from\ BCOF:\\\stackrel{\big{\frown}} {CDF} =m\angle COF=360^o-2\cdot90^o-82^o=98^o \\\\\\ \stackrel{\big{\frown}} {CGF} =360^o-\stackrel{\big{\frown}} {CDF} =360^o-98^o=262^o[/tex]
the value of a plot of land is $18000. Land tax charged at the rate of $0.70 per $100 value. What is the total amount of tax paid for land
Answer:
126 $
Step-by-step explanation:
1- 18000 / 100 = 180
2- 180 x 0.7 = 126$
Write the number in standard notation. 4.16 × (10) ^–5
Answer:
.0000416
Step-by-step explanation:
Since 10 is squared by a negative number, the number (4.16) will be smaller. To find the answer, move the decimal 5 places to the left
Answer:
0.0000416.
Step-by-step explanation:
When 10 is raised to a negative power, that means that the decimal point will be moved to the left a certain number of units.
In this case, it is 10^-5, so the decimal point will move to the left by 5 units.
4.16 * 10^-5 = 000004.16 * 10^-5 = 0.0000416.
Hope this helps!
please helllppppp........
8% lower means the gauge is showing 92% of the original pressure
( 100% - 8% = 92%)
Divide the pressure the gauge is showing by 92%
33.58 / 0.92 = 36.5
The actual pressure is 36.5
If v1 = (2,5) and V2 = (4,-3), then the angle between the two vectors is
Round your answer to two decimal places,
Answer:
105.07°
Step-by-step explanation:
The angle of v1 is ...
arctan(5/2) ≈ 68.199°
The angle of v2 is ...
arctan(-3/4) ≈ -38.870°
The angle difference between the two vectors is ...
68.199° -(-38.870°) = 105.07°
Hawaii has an area of 1.1 x 104 square miles and a
population of 1.2 x 10% people.
Which key strokes on a calculator will give the population
density of Hawaii?
Answer:
A i think its a A try. it it that looks correct
Answer:
Its B, 1.2EE6/1.1EE4
Step-by-step explanation:
The density is 109.9, and this is the only equation that gives you this answer
i also took the test!
value of k, if (x – 1) is a factor of 4x3
+ 3x2
– 4x + k.
Answer:
k = - 3
Step-by-step explanation:
Given that (x - 1) is a factor of the polynomial then x = 1 is a root
Substitute x = 1 into the polynomial and equate to zero, that is
4(1)³ + 3(1)² - 4(1) + k = 0, that is
4 + 3 - 4 + k = 0
3 + k = 0 ( subtract 3 from both sides )
k = - 3
PLEASE I NEED THE ANSWERS ASAP!!! Simplify the following:
1.√7 × √7
2.√18 × √2
3.√45
4.√50/5
5.2√2 × 4√5
6.√48 - √12
7.(2-√3) (1+√3))
1. √7 × √7 = √[7×7] = √[7²] = 7
2. √18 × √2 = √[18×2] = √36 = √[6²] = 6
3. √45 = √[9×5] = √9 × √5 = √[3²] × √5 = 3√5
4. [tex]\dfrac{\sqrt{50}}{5}=\dfrac{\sqrt{25\cdot2}}{5}=\dfrac{\sqrt{25}\cdot\sqrt2}{5}=\dfrac{5\cdot\sqrt2}{5}=\bold{\sqrt2}[/tex]
5. 2√2 × 4√5 = (2×4) × (√2×√5) = 8×√[2×5] = 8√10
6. √48 - √12 = √[16×3] - √[4×3] = √16×√3 - √4×√3 = 4√3 - 2√3 = 2√3
7. (2 - √3)(1 + √3) = 2×1 + 2×√3 + (-√3)×1 + (-√3)×√3 =
= 2 + 2√3 - √3 - √[3×3] = 2 + √3 - 3 = √3 - 1
Please answer this question now
Answer:
[tex] Area = 400.4 m^2 [/tex]
Step-by-step Explanation:
Given:
∆UVW,
m < U = 33°
m < V = 113°
VW = u = 29 m
Required:
Area of ∆UVW
Solution:
Find side length UV using Law of Sines
[tex] \frac{u}{sin(U)} = \frac{w}{sin(W)} [/tex]
U = 33°
u = VW = 29 m
W = 180 - (33+113) = 34°
w = UV = ?
[tex] \frac{29}{sin(33)} = \frac{w}{sin(34)} [/tex]
Cross multiply
[tex] 29*sin(34) = w*sin(33) [/tex]
Divide both sides by sin(33) to make w the subject of formula
[tex] \frac{29*sin(34)}{sin(33)} = \frac{w*sin(33)}{sin(33)} [/tex]
[tex] \frac{29*sin(34)}{sin(33)} = w [/tex]
[tex] 29.77 = w [/tex]
[tex] UV = w = 30 m [/tex] (rounded to nearest whole number)
Find the area of ∆UVW using the formula,
[tex] area = \frac{1}{2}*u*w*sin(V) [/tex]
[tex] = \frac{1}{2}*29*30*sin(113) [/tex]
[tex] = \frac{29*30*sin(113)}{2} [/tex]
[tex] Area = 400.4 m^2 [/tex] (to nearest tenth).
easy question i will mark braineliest
Answer:
0.67Step-by-step explanation:
[tex]5(y - 3.8) = 4.7(y - 4)[/tex]
Distribute 5 through the parentheses
[tex]5y - 19 = 4.7(y - 4)[/tex]
Distribute 4.7 through the parentheses
[tex]5y - 19 = 4.7y - 18.8[/tex]
Move ' 4.7 y ' to L.H.S and change it's sign
[tex]5y - 4.7y - 19 = - 18.8[/tex]
Move constant to R.H.S and change it's sign
[tex]5y - 4.7y = - 18.8 + 19[/tex]
Collect like terms
[tex]0.3y = - 18.8 + 19[/tex]
Calculate
[tex]0.3y = 0.2[/tex]
Divide both sides of the equation by 0.3
[tex] \frac{0.3y}{0.3} = \frac{0.2}{0.3} [/tex]
Calculate
[tex]y = 0.67[/tex]
Hope this helps...
Best regards!!
Answer:
[tex]y = 0.67[/tex] (To 2 dps)
y = 0.7 (To 1 dps)
y = 1 (To nearest whole no.)
Step-by-step explanation:
[tex]5(y-3.8) = 4.7 (y-4)[/tex]
Distribute the terms
[tex]5y - 19 = 4.7y-18.8[/tex]
Combining like terms
[tex]5y - 4.7y = -18.8+19[/tex]
Adding and subtracting
[tex]0.3y = 0.2[/tex]
Dividing both sides by 0.3
[tex]y = 0.2/0.3[/tex]
[tex]y = 0.67[/tex]
What is the simplified expression for
2^2 • 2^3 over
24
O 20
O 21
O 22
O 23
Answer:
(B)[tex]2^1[/tex]
Step-by-step explanation:
We are to simplify the given expression: [tex]\dfrac{2^2 \cdot 2^3}{2^4}[/tex]
Step 1: Apply the addition law of indices to simplify the numerator.
[tex]\text{Addition Law: }a^x \cdot a^y=a^{x+y}[/tex]
Therefore:
[tex]\dfrac{2^2 \cdot 2^3}{2^4} \\\\=\dfrac{2^{2+3}}{2^4}\\\\=\dfrac{2^5}{2^4}[/tex]
Step 2: Apply the Subtraction law of indices to simplify the expression
[tex]\text{Subtraction Law: }a^x \div a^y=a^{x-y}\\\\\implies \dfrac{2^5}{2^4} =2^{5-4}\\\\=2^1[/tex]
The correct option is B.
Please help it’s urgent
[tex]\bold{\text{Answer:}\quad \dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]
Step-by-step explanation:
[tex].\quad \dfrac{-5x}{8x+7}-\dfrac{6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}+\dfrac{-6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}\bigg(\dfrac{3x+1}{3x+1}\bigg)+\dfrac{-6x^3}{3x+1}\bigg(\dfrac{8x+7}{8x+7}\bigg)\\\\\\=\dfrac{-15x^2-5x}{(8x+7)(3x+1)}+\dfrac{-48x^4-42x^3}{(8x+7)(3x+1)}\\\\\\=\large\boxed{\dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]
Find each difference.
(2x2-5x-7)-(7x2+3)
PLEASE HELP!!!
Answer: [tex]-5x^{2} -5x-10[/tex]
Step-by-step explanation:
[tex](2x^{2} -5x-7)-(7x^{2} +3)[/tex]
subtract by terms.
2x^2 - 7x^2 = -5x^2
-5x is the only term so leave it alone
-7-3= -10
-5x^2 -5x -10
Answer:
-5x-48
Step-by-step explanation:
First, simplify the first half,
(2x2-5x-7) --> (4-5x-7) --> (-5x-7+4) --> (-5x-13)
Then, simplify the second half,
(7x2+3) --> (7x5) --> (35)
Finaly put them together
-5x-13-35, subtract like terms
-5x-48
This is the most simplifyed it can get because of the variable.
Hope this helps, if you have a question if you are confused,
Have a good day and if you can, please give me brainliest, it will help a lot. :)
PLS HELP! A rectangle has a height of 2 and a width of 5x^2-2x+3. Express the area of the entire rectangle. Expression should be expanded.
Answer:
Expanded expression of the area of the rectangle = 10x² - 4x + 6 square units
Step-by-step explanation:
Area of a rectangle = Length × Width
Area of the rectangle = 2 × (5x² - 2x + 3)
= 2 × 5x² - 2× 2x + 2×3
= 10x² - 4x + 6 square units
Please answer this question now
Answer:
469.4ft² of 469.4 square feet
Step-by-step explanation:
In the above question, we are given ∆ WXY
In the question, we have the following values already:
Angle W = 27°
Angle X = unknown
Angle Y = 40°
Side w = unknown
Side x = unknown
Side y = 38ft
Area of the triangle= it is unknown as well
First Step
We would determine the third angle = Angle X
Sum of angles in a triangle = 180°
= Angle X= 180° - (27 + 40)°
= 180° - 67°
Angle X = 113°
Second step
Determine the sides w and x
We find these sides using the sine rule
Sine rule =
a/ sin A = b/ Sin B
Hence for triangle WXY
w/ sin W = x/ sin X = y/ sin Y
a) side w
w/ sin W= y/ sin Y
w/sin 27 = 38/sin 40
Cross Multiply
sin 27 × 38 = w × sin 40
w = sin 27 × 38/sin 40
w = 26.83879ft
w = 26.84ft
Finding side x
x / sin X= y/ sin Y
x/ sin 113 = 38/sin 40
Cross Multiply
sin 113 × 38 = x × sin 40
x = sin 113 × 38/sin 40
x = 54.41795ft
x = 54.42ft
To find the area of triangle WXY
We use heron formula, which is given as:
= √s(s - w) (s - x) (s - y)
Where S = w + x + y/ 2
s = (38 + 26.84 + 54.42)/2
s = 59.63
Area of the triangle
= √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)
Area of the triangle = √220343.61423
Area of the triangle = 469.40772706541ft²
Therefore, approximately to the nearest tenth , the Area of ∆WXY =469.4yd²
Suppose a triangle has sides 3, 4, and 6. Which of the following must be true? A: The triangle in question is not a right triangle. B: The triangle in question may or may not be a right triangle. C: The triangle in question is a right triangle.
Answer:
A: The triangle in question is not a right triangle.
Step-by-step explanation:
If the triangle is a right triangle, then the Pythagorean theorem would hold
a^2 + b^2 = c^2
3^2 + 4^2 = 6^2
9+16 = 36
25 = 36
This is not true so this is not a right triangle
Answer:
A: The triangle in question is not a right triangle.
Step-by-step explanation:
We can use Pythagorean theorem to check.
a² + b² = c²
3² + 4² = 6²
9 + 16 = 36
25 = 36 (not true)
what is 1/8 - 7/8 ? ( its a fraction)
Answer:
1/8-7/8= -3/4
Step-by-step explanation:
1/8-7/8 is just like 7/8-1/8 but is the opposite
7/8-1/8=6/8 or 3/4
1/8+6/8=7/8
1/8-1/8=0
0-6/8= -6/8 or -3/4
A college requires all freshmen to take Math and English courses. Records show that 24% receive an A in English course, while only 18% receive an A in Math course. Altogether, 35.7% of the students get an A in Math course or English course. What is the probability that a student who receives an A in Math course will also receive an A in English course
Answer:
7.3%
Step-by-step explanation:
Let M = Maths
E = English
P(M ∪ E) = P(M) + P(E) - P( M ∩ E)
From the question:
P(M ∪ E) = 35.7%
P(M) = 18%
P(E) = 24%
P( M ∩ E) = unknown
35.7% = 18% + 24% - P( M ∩ E)
35.7% = 42% - P( M ∩ E)
P( M ∩ E) = 42% - 35.7%
P( M ∩ E) = 7.3%
Therefore, the probability that a student who receives an A in Math course will also receive an A in English course is 7.3%.
819 : 17 =?
Write your answer as a whole number and remainder.
R
Answer:
117 R=0
Step-by-step explanation:
819:7= 117 R=0
Plz help asap 10x^2+11x+3
Answer:(2x+1)(5x+3)
Step-by-step explanation:
Please answer in two minutes
Answer:
Toa
48/55
Step-by-step explanation:
O/A
48/55
Is anyone here good at geometry? please help
Answer:
Sin 24 = 0.4067366431 = 0.4
Cos 45 = [tex]\frac{\sqrt{2} }{2}[/tex] = 0.7071067812 = 0.7
Tan 88 = 28.63625328 = 28.6