Answer: A.) 330 ways
Step-by-step explanation:
We are to determine the number of subsets with 4 elements that can be formed from a set containing 11 elements.
Since the arrangement doesn't matter, it's a combination problem.
We are to take out a subset containing 4 elements at a time ; from a set with 11 elements
Recall :
nCr = n! / (n-r)! r!
11C4 = 11! / (11 - 4)! 4!
11C4 = 11! / 7!4!
11C4 = (11 * 10 * 9 * 8) / 4 * 3 * 2 * 1
11C4 = 7920 / 24
11C4 = 330 ways
What is the distance between (-2. 1/2,-3) and (1, -3)?
Answer:
3 1/2 (in fraction form but 11.2... something) hope this helps
Step-by-step explanation:
Match the justification to each statement in the solution of x + 12.7 = -25.2.
Answer:
1) x+12.7=-25.2 is given
2)x+12.7-12.7=-25.2-12.7 is the subtraction property of equality(subtracting on both sides)
3)x+0=-37.9(add. inverse/simplification since we're simplifying the equation)
x=-37.9(identity property of addition since x+0 is just x)
Hope this helps!
hi :) how to do 10(iii) ?:)
(i) AB and DC are parallel, so the lines containing these sides have the same slope.
The line containing AB has slope (2 - (-1))/(10 - 4) = 3/6 = 1/2.
Use the point-slope formula to find the equation of the line containing CD:
[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2\implies\boxed{2y=x+4}[/tex]
AP is perpendicular to both AB and CD, and perpendicular lines have slopes that are negative reciprocals of one another. This means the line containing AP has slope -1/(1/2) = -2. Using the point-slope formula again, the equation of the line containing AP is
[tex]y-(-1) = -2(x-4)\implies \boxed{y=-2x+7}[/tex]
(ii) D lies on the x axis, so its y-coordinate is 0. Find the x-coordinate by plugging y = 0 into the equation for the line containing CD:
[tex]2\cdot0=x+4\implies x=-4[/tex]
So D is the point (-4, 0).
P is the intersection of the lines containing CD and AP, so set them equal and solve for x and y :
[tex]y=\dfrac x2+2\text{ and }y=-2x+7[/tex]
[tex]\implies\dfrac x2+2=-2x+7\implies 5x=10\implies x=2[/tex]
[tex]\implies y=-2\cdot2+7\implies y=3[/tex]
So P is the point (2, 3).
(iii) For ASBC to be a parallelogram, we need to find the coordinates of S such that the line containing AS is parallel to the line containing BC, and the line containing SC is parallel to the line containing AB.
BC has slope (8 - 2)/(12 - 10) = 6/2 = 3. Then the line containing AS has equation
[tex]y-(-1)=3(x-4)\implies y=3x-13[/tex]
We already know AB has slope 1/2. Then the line containing SC has equation
[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2[/tex]
S is the intersection of these two lines:
[tex]3x-13=\dfrac x2+2\implies\dfrac{5x}2=15\implies5x=30\implies x=6[/tex]
[tex]\implies y=3\cdot6-13\implies y=5[/tex]
So S is the point (6, 5), and *not* (2, -7) as the answer key suggests. In fact, (2, -7) is located lower than the point A and slightly to the left; if you draw that point and connect it to the other three, there's no way to get a parallelogram.
(iv) Find the lengths of AB, CD, and AP. Then the area is (AB + CD)*AP/2.
[tex]AB=\sqrt{(4-10)^2+(-1-2)^2}=3\sqrt5[/tex]
[tex]CD=\sqrt{(12-(-4))^2+(8-0)^2}=8\sqrt5[/tex]
[tex]AP=\sqrt{(4-2)^2+(-1-3)^2}=2\sqrt5[/tex]
so the area is
[tex]\dfrac{(3\sqrt5+8\sqrt5)2\sqrt5}2=\boxed{55}[/tex]
on monday it took 5 builders to 3 1/2 hours to build a wall
on tuesday an identical wall was built but only 2 builders were available
each builder is paid £9.30 for each hour or part of and hour they work
work out how much each builder will be paid for the work completed on tuesday
Answer: £ 81.38
Step-by-step explanation:
Given: On Monday,
5 builders took [tex]3\dfrac{1}{2}[/tex] hours ( i.e. [tex]\dfrac{7}{2}[/tex] hours ) to build a wall.
On Tuesday, only 2 builders were available.
As workers are inversely proportional to the time if the job remains constant.
Inverse variation equation : [tex]x_1y_1=x_2y_2[/tex]
Let x be the time taken by 2 builders, then
[tex]2\times x =5\times \dfrac{7}{2}[/tex]
[tex]\Rightarrow\ x=\dfrac{35}{2}\times\dfrac{1}{2}=\dfrac{35}{4}=8.75[/tex]
So, 2 builders will take 8.75 hours.
Each paid £9.30 for each hour.
Then, each builder will be paid for the work completed on Tuesday = £9.30 x 8.75
≈ £ 81.38
Hence, each builder will be paid £ 81.38 for the work completed on Tuesday .
What is 5π/6 radians converted to degrees? If necessary, round your answer to the nearest degree.
Answer:
300 degrees
Step-by-step explanation:
we know that [tex]\pi = 360 degrees[/tex][tex]\pi = 360 \ degrees[/tex]
we have to find value of [tex]5\pi /6[/tex]
for that we have to multiply 5/6 to [tex]\pi[/tex] and 360 degrees
[tex]\pi = 360 \ degrees\\5\pi /6 = 5/6 *360 = 300[/tex]
Thus, [tex]5\pi /6[/tex] = 300 degrees.
Answer:
150
Step-by-step explanation:
Need Help Please I'm Out Of Time ;(
Which of the following questions are statistical questions? Select all that apply
How far does Mary live from school?
How many students were absent from Mrs. Jenssen's class today?
How tall are the sixth-grade students in your school?
How many pull-ups can each student in your class do?
What was the temperature at 4 p.m. each day this week?
Answer:
last three questions are statistical question
Answer:
The last three questions
Step-by-step explanation:
How many times will the digit '1' appear if we write all whole numbers from 1 to 999?
Answer: The number one occurs 300 times while writing the numbers from 1 to 999.
Step-by-step explanation:
Write 2.37 correct to 1 decimal place
Answer:
2.4
Step-by-step explanation:
The first decimal place is 3, the digit after that is 7 which is more or equal to 5. So add +1 to the 3, followed by zeros.
2.37 ⇒ 2.40
*PLEASE ANSWER* If a town has a density of 8 houses per block and there are 65 blocks in the town, how many houses are in the town? a.) 840 houses b.) 520 houses c.) 1040 houses d.) 2080 houses
Answer:
520
Step-by-step explanation:
65 blocks multiplied by 8 houses per block
Translate into an algebraic expression: p% of m
Answer:
p/100 * m
Step-by-step explanation:
The algebraic expression of p% of m is pm/100.
What is expression?Expression is combination of numbers, fraction, symbols , coefficients, indeterminants or determinants. It shows a relationship between variables. It is mostly not found in equal to form.
How to form algebraic expression?We have been given p% of m and we have to form an expression of this.
To express this we have to just solve the percentage and because we donot have any number so will only write p/100 in place of p%.
p% of m=p/100*m
=pm/100
Hence the algebraic expression of p% of m is pm/100.
Learn more about expression at https://brainly.com/question/723406
#SPJ2
Find the missing length to the attached triangle.
Answer:
x = 135
Step-by-step explanation:
Use the right triangle altitude theorem and similar triangles.
x/81 = 225/x
x^2 = 81 * 225
x = 9 * 15
x = 135
Answer:
135
Step-by-step explanation:
PLS ANSWER BEFORE 7/12/18 THANK YOU!!!
Mrs. Herby bought some carrots. She put 2/5 of them on a platter and the rest in a plastic bag. If there were 8 carrots on the platter, how many carrots were there in the plastic bag?
Answer:
12
Step-by-step explanation:
I need help with number 12
Answer:
C.
Step-by-step explanation:
add up all of the angles correct ft im not sure but i think its C.
Graph: f(x) = 22-1
Step 1: Find the value of x that makes the exponent zero
by solving this equation: x-1 = 0
Answer:
Step-by-step explanation:
To graph an exponential function f(x) = [tex]2^{x-1}[/tex],
Step - 1 :
Find the value of x that makes the exponent 0.
x - 1 = 0
x = 1
f(1) = 2⁰ = 1
Similarly, for other input values (x- values),
For x = 2,
f(2) = [tex]2^{2-1}[/tex]
= 2¹
= 2
For x = 3
f(3) = [tex]2^{3-1}[/tex]
= 2²
= 4
For x = 4
f(4) = [tex]2^{4-1}[/tex]
= 2³
= 8
Therefore, table for input - output values will be,
x 1 2 3 4
f(x) 1 2 4 8
Answer:
:>
Step-by-step explanation:
Determine the function's value when x = -1.
O g(-1) = -3
O g(-1) = 0
O g(-1) = 1
O g(-1) = 27
Ryan had $80. He spent $32 on a book. what percentage of his money did he spend on the book? What percentage of his money did he have left?
Answer:
40% spent. 60% left.
Step-by-step explanation:
To find the percentage spent, divide the two values, then multiply by 100.
$32 / $80 = 0.40 0.40 x 100 = 40% spent.
To find the percentage of money left, subtract the two values.
$80 -$32 = $48
Then, divide the two values and multiply by 100.
$48 / $80 = 0.60 0.60 x 100 = 60% left.
The diagram shows a wedge in the shape of a prism.
Angle BCF is a right angle.
A string runs diagonally across the wedge
from A to F.
Calculate the length A F.
Give your answer correct to 3 significant figures.
*PLEASE ANSWER* (: Find the measure of angle A.
Answer:
B. 120°
Step-by-step explanation:
If two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
m∠A° = 1/2(300 - 60)
m∠A° = 1/2(240)
m∠A° = 120
Which graph represents the solution set for the system x + y> 5 and -3x + 2y< -2.
One zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0. What are the zeros of the polynomial function?
0, −5, −4
0, −5, 4
0, 5, −4
0, 5, 4
Answer: 0, −5, 4
Step-by-step explanation:
The given function is
[tex]f(x)=x^3+x^2-20x[/tex]
One of the zero of the given polynomial function is x=0.
To find other zeroes put f(x)=0
[tex]x^3 + x^2 - 20x=0\\\\\Rightarrow\ x(x^2+x-20)=0\ \ \ [\text{Taking x as common}][/tex]
That is
[tex]x^2+x-20=0[/tex] or [tex]x=0[/tex]
if [tex]x^2+x-20=0[/tex]
then [tex]x^2+5x-4x-20=0\ \ \ [\text{By using middle term splitting method}][/tex]
[tex]\Rightarrow\ x(x+5)-4(x+5)=0\\\\\Rightarrow\ (x+5)(x-4)=0\\\\\Rightarrow\ x=-5, 4[/tex]
So, the zeroes of f(x) are 0, −5, 4 .
Hence, the correct option is 0, −5, 4.
Rewrite the function by completing the square
Answer:
[tex](x+10)^2-186[/tex]
Step-by-step explanation:
which is the recursive formula for this geometric sequence? -16, -7, 2, 11,
Answer:
A
Step-by-step explanation:
[tex]a_{1}=-16\\c.d. d=-7-(-16)=-7+16=9\\a_{n}=a_{n-1}+d\\a_{n}=a_{n-1}+9[/tex]
Answer:
a1=-16
an=an-1+9
Step-by-step explanation:
This is for clarification for the person above who probably made it confusing for some people
Remember, the letter doesnt matter, because everyones test is in a different order.
Drag each tile to the correct box. Order the quadratic functions from least to greatest based on the number of x-intercepts of each function.
Answer:
Leftmost box: Graph, because it has zero x intercepts
Middle box: Function f with a vertex at 2, 0
Rightmost box: g(x)=x^2+x-2
Answer:
g(x)=x^2+x-2
Step-by-step explanation:
Please help me with question eightttt thank you
Answer:
Question 8 should be 25.6 hours
Step-by-step explanation:
Since time = distance/speed.
We just replace the words with the appropriate numbers.
time =
[tex] \frac{ 3.84 \times {10}^{5} }{1.5 \times {10}^{4} } [/tex]
which equals 25.6
Help will mark brainliest!
Answer:
2 : 3Step-by-step explanation:
Total number of cards = 48
Red cards/black cards = 1/1
(so, 24 each of read and black cards)
8 red cards are removed.
Now, there will be (24-8) number of cards left in the pack which equals to 16 cards.
So, now the number of red cards in the pack= 16
Number of black cards = 24
Ratio of red card/ black card
[tex] = \frac{16}{24} [/tex]
[tex] = \frac{2}{3} [/tex]
= 2 : 3Hope this helps...
Good luck on your assignment...
I need an answer please
Answer:
=434.86
Step-by-step explanation:
The radius = 4.7cm
this means that using the equation that is given (V=4/
3πr^3)
add the radius where it says r
it also says you are allowed to use a calculator so put the equation into your calculator to give you the answer.
i hope this helped :)
Answer:
volume of sphere is 4 thirds pie r squared. Google it!
Step-by-step explanation:
Given the parent function of f(x) = x^(4, what change will occurr when the function is changed to f((1)/(2) x))
Answer:
The graph of the function f( (1/2)x ) will expand across x-axis
Step-by-step explanation:
We have been given the function:
f(x) = x⁴
If we substitute x = (1/2)x into the given equation, we get:
f((1/2)x) = ( (1/2)x )⁴
We can simplify the equation
f((1/2)x) = = (1/2)⁴ x⁴
f((1/2)x) = = (1/16) x⁴
Graph of both of the functions is shown below. We can clearly see that that the graph of the function f((1/2)x) = = (1/16) x⁴ expands horizontally on x-axis as compared to the graph of f(x) = x⁴
how to solve which number completes the square of the expression below? 2x^2-3x+
1. 9/8
2. 9
3. -9/2
4. 9/16
Answer:
see below
Step-by-step explanation:
2x^2-3x+
Factor out 2
2( x^2 -3/2x)
Take the coefficient of x
-3/2
Divide by 2
-3/4
Square it
(-3/4) ^2 = 9/16
This is the number inside the square
2( x^2 -3/2x + 9/16)
Multiply by 2 since that is factored on the outside
9/16 *2 = 9/8
Add to the equation
2x^2-3x+9/8
6d-\dfrac{11}2=2d-\dfrac{13}26d− 2 11 =2d− 2 13
Answer:
So your answer is d = -1/4 = -0.250
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*d-11/2-(2*d-13/2)=0
13
Simplify ——
2
11 13
(6d - ——) - (2d - ——) = 0
2 2
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
2d 2d • 2
2d = —— = ——————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2d • 2 - (13) 4d - 13
————————————— = ———————
2 2
11 (4d - 13)
(6d - ——) - ————————— = 0
2 2
11
Simplify ——
2
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
6d 6d • 2
6d = —— = ——————
1 2
4.2 Adding up the two equivalent fractions
6d • 2 - (11) 12d - 11
————————————— = ————————
2 2
5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(12d-11) - ((4d-13)) 8d + 2
———————————————————— = ——————
2 2
6.1 Pull out like factors :
8d + 2 = 2 • (4d + 1)
4d + 1 = 0
4d + 1 = 0
7.1 Solve : 4d+1 = 0
Subtract 1 from both sides of the equation :
4d = -1
Divide both sides of the equation by 4:
d = -1/4 = -0.250
Answer:
d = -1/4 = -0.250
Step-by-step explanation:
Randall built a scale model of a barn he wants to construct. What is the total volume of the model Round your answer to the nearest tenth.
3,254.0 cm^3
326.4 cm^3
3,100.8 cm^3
4,243.2 cm^3
1,305.6 cm^3
Answer:
2764.8cm³
Step-by-step explanation:
Looking at the diagram, the barn is a combination of 2 geometric shapes, a cuboid and Triangular prism
Step 1
Find the volume of the cuboid
Volume of the cuboid = Length × Width × Height
Length = 10cm
Width = 20.4cm
Height = 11.2cm
Volume = 10cm × 20.4cm × 11.2cm
Volume = 2284.8cm³
Step 2
Volume of Triangular prism = 1/2 × base × height × length
= 1/2 × 8 × 12 × 10
= 480cm³
Total volume = 2284.8cm³ + 480cm³
= 2764.8cm³