Assignment
Section (A) 5 Marks
Q.No. 1. Do as directed;
(1) Which one of the following is square of 4;
a) 2
b) 8
c) 16
d) 64
(II)Unit digit in the square of 3457 is;
a) 3
b) 7
c) 4
d) 9
(III) Cube root of 64 is;
a) 8
b) 4
c) 2
d) 10
(IV) Ratio of 2:4 is;
a) 4:1
b) 1:2
c) 1:3
d) None of these
(V) Discount =
a) Marked Price - Sale Price
B) Sale Price - Marked Price
......
After using a 15% off coupon, the price of a sheet cake is $30.94. What was the original price?
Answer:
The original price was 36.40
Step-by-step explanation:
p = original price of cake
using the coupon
p - 15% off = 30.94
p - .15 p = 30.94
Combine like terms
.85p = 30.94
divide each side by .85
p = 30.94/.85
p =36.40
The original price was 36.40
Rosie did the following problem. (7-1) 2 ÷ 6 + 4 · 3 6 2 ÷ 6 + 4 · 3 36 ÷ 6 + 4 · 3 6 + 4 · 3 10 · 3 30 Which statement best describes her answer?
Rosie is incorrect because she needs to do the exponent before subtracting. Rosie is incorrect because she needs to multiply before she divides. Rosie is incorrect because she needs to multiply before she adds. Rosie is correct.
Determine whether the situation involves permutations or combinations. Then solve. How many ways are there to place an algebra book, a geometry book, a chemistry book, an English book, and a health book on a shelf?
Answer:
The situation involves permutationThe number of arrangement is 120Step-by-step explanation:
Given that
Algebra book=1
Geometry book=1
Chemistry book= 1
English book= 1
Health book= 1
Total number of books N = (1+1+1+1+1)= 5
Permutation is used to determines the number of possible arrangements in a set when the order of the arrangements is crucial.
Number of arrangements = N!
Number of arrangements= 5*4*3*2*1= 120
Evaluate -x+(-8) for x= 7.1
Answer:
-15.1
Step-by-step explanation:
Answer:
-15.1Step-by-step explanation:
[tex]-x+(-8) \\\\x = 7.1[/tex]
Substitute 7.1 for x in the given equation
[tex]-(7.1 )+(-8)[/tex]
Remove parentheses (a)=a
[tex]=-7.1-8[/tex]
Subtract the numbers: -7.1-8=-15.1
[tex]-15.1[/tex]
The ratio of adults to children on a field trip is 2:7. If there are 14 adults on the trip, how many children are there?
Answer:
49 children
Step-by-step explanation:
Adult : Child = 2 : 7
Adult = 14
2 = 14
So, 1 = 14/2 = 1 = 7 in the ratio.
So, 7 x 7 = 49 children are there.
Answer:
49
Step-by-step explanation:
Let's set up a proportion!
2 14
-- --
7 x
Now, we cross multiply
14 times 7 = 98
2 times x = 2x
98 = 2x
98 divided by 2 equals 49
I need help with the questions could someone answer them all?
Answer:
circumference= 40.82 cm
Step-by-step explanation:
formula circumference= 2 x pi x radius ( 2 x 3.14x 6.5)
3) shaded region = area circle - area rectangle = 132.665 cm - 60 cm^2= 72.665 cm^2
4) 1 foot = 30.48 cm, 6 feet = 182.88 cm = radius 182.88 cm area circle = pi x square radius = 3.14 x 182.88 ^2 ----------> 3.14 x 33445.0944 =105017.5964 cm^2
if 5.49 = 70% , 100% = x so 5.49 x 100 divided 70 = X so X = 7.844 then 5.49 is the 70 % of 7.844
if 6.99 is 36% of something, 6.99 = 36%
X = 100%
so 6.99 x 100 = X (equis) x 36%
6.99 x 100 / 36 = X, so X = 19.416 . 6.99 is the 36% of 19.416
Help!!! PLEASE Math Hurry I have 10mins to finish
Answer:
x0 is the answer I just did that question and got it right
Answer: Answer is in the steps
Step-by-step explanation:
If we given the angle measure in variables then we will sum them up equal 180 and solve for x to determine the angle measure.
9x + x +x+4 = 180
11x + 4 = 180
-4 -4
11x = 176
x=16
In this case we can find the angle measures by using the expressions.
x = 16 degrees
x+4 = 20 degrees
9x = 144 degrees
Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue paint and 20 cans of yellow paint when he starts. He wants the same green color every time he mixes, so the amounts of blue and yellow must always be proportional to the original mixture. On day 1, he mixes 4 cans of blue and 6 cans of yellow. On day 2, he mixes 6 cans of blue and 9 cans of yellow.
The ratio of blue paints to yellow paint is a mixture of 2 : 3.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
The Total cans of blue paint = 14
Total cans of yellow paint = 20
Day 1:
Yellow paint = 6 cans
Blue paint = 4 cans
The ratio of blue paints to yellow paint
= 2 : 3
Day 2:
Yellow paint = 9 cans
Blue paint = 6 cans
The ratio of blue paints to yellow paint
2 : 3
Day 3:
Cans of yellow remaining after 2 days
Yellow paint = Total cans of yellow paint - day 1 cans of yellow paint - day 2 cans of yellow paint
= 20 - 6 - 9
= 20 - 15
= 5 cans
Cans of blue remaining after 2 days
Blue paint = Total cans of blue paint - day 1 cans of blue paint - day 2 cans of blue paint
= 14 - 4 - 6
= 14 - 10
= 4 cans
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Find the 6 trìg functions
I hope this helps you
let's find AB
AB=square root of 2^2+3^2
AB=square root of 13
cosO=2/sqrt13
sinO=3/sqrt13
tgO=3/2
ctgO=2/3
You are a furniture restorer who is mixing a solution of olive oil and lemon juice. The solution is for polishing wooden furniture to give it a shine and a fresh scent. You fill 50% of a cup with lemon juice and 25% of a quart with olive oil. Afterwards, you mix the olive oil and the lemon juice in another container. How many cups of the solution do you have for polishing wooden furniture? 1.5 2.0 2.5 4.5 5.0
The correct answer is A. 1.5 cups
Explanation:
The total of polishing wooden furniture is equivalent to the total of olive oil plus the total of lemon juice. Additionally, in this case, the result should be given in cups. First, let's consider the values given.
50% of a cup of lemon juice + 25% of a quart with olive oil
The first quantity 50% of a cup of lemon indicates half cup of lemon was added, which is equivalent to 0.5 cups as 1 cup = 100% of a cup and 50% is the half.
Now, the second quantity is provided in quarts, which is not the same as a cup. Indeed 1 quart is equivalent to 4 cups, which represents 100%. This means 100% = 4 cups. Now, to calculate the 25% follow this procedure.
1. Write the values
4 = 100 (total percentage)
x = 25 (percentage to be calculated
2. Solve this by using cross multiplication
x100 = 4 × 25
x100 = 100
x = 100 ÷ 100
x = 1 (cups in 25%)
This means 1 cup of olive oil was added and this plus 0.5 cup of lemon juice is equivalent to 1.5 cups of solution.
please helppppppppppppppppppppppppppppp
Answer:
54
Step-by-step explanation:
angle A+angle B+Angle C =180 degree [ angle sum property of a triangle]
36 +90 + angle B =180 degree
126 +angle B =180 degree
angle B= 180-126
54 degree
Ans
The diagonal of a rectangle is 10 units. The width is 6 units, What is the area of the rectangle in square
units?
Answer:
48 square units
Step-by-step explanation:
Let the length of the rectangle be x units.
By Pythagoras theorem:
[tex]x = \sqrt{ {10}^{2} - {6}^{2} } \\ x = \sqrt{ 100 - 36 } \\ x = \sqrt{64} \\ x = 8 \: units \\ [/tex]
Length of rectangle = 8 units
Area of rectangle
= Length * width
= 8 * 6
= 48 square units
2x-(x-(2x+3)-3x-11 help plssss
Answer:
I'll say x = 8
Step-by-step explanation:
because Simplifying
2x + -3 = 3x + -11
Reorder the terms:
-3 + 2x = 3x + -11
Reorder the terms:
-3 + 2x = -11 + 3x
Solving
-3 + 2x = -11 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-3 + 2x + -3x = -11 + 3x + -3x
Combine like terms: 2x + -3x = -1x
-3 + -1x = -11 + 3x + -3x
Combine like terms: 3x + -3x = 0
-3 + -1x = -11 + 0
-3 + -1x = -11
Add '3' to each side of the equation.
-3 + 3 + -1x = -11 + 3
Combine like terms: -3 + 3 = 0
0 + -1x = -11 + 3
-1x = -11 + 3
Combine like terms: -11 + 3 = -8
-1x = -8
Divide each side by '-1'.
x = 8
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 4x - 14}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2x - x - (2x + 3) - 3x - 11}[/tex]
When there is a ( - ) in front of parentheses in an expression, change the sign of each term
⇒[tex] \sf{2x - x - 2x - 3 - 3x - 11}[/tex]
Collect like terms
⇒[tex] \sf{2x - x - 2x - 3x - 3 - 11}[/tex]
Since the terms having opposite signs adds up to zero, remove them from the expression
⇒[tex] \sf{ - x - 3x - 3 - 11}[/tex]
⇒[tex] \sf {- 4x - 14}[/tex]
Hope I helped!
Best regards!!
What is 3+(−4)−8−(−1)?
Answer:
-8
Step-by-step explanation:
3+(−4)−8−(−1)=-8
x?(y + 1)) if x = -3 and y = 2
Answer:
-9
Step-by-step explanation:
add x and y to the equation.
so now its -3(2+1)
add 2 and 1
now its -3(3)
multiply.
now its -9
Answer:
-9
Step-by-step explanation:
Hello!
It is asking us for the answer when x = -3 and y = 2 so we put in those values for x and y
-3(2 + 1)
Now follow PEMDAS
-3(3) = -9
The answer is -9
Hope this helps!
The expression 6n-3006n−3006, n, minus, 300 describes the amount of profit the school makes from the dance if nnn students buy tickets. What does 6n6n6, n represent in this context? Choose 1 answer: Choose 1 answer: (Choice A) A The amount of money the school charges for all nnn tickets (Choice B) B The amount of money the school spends on the dance (Choice C) C The number of students who buy tickets (Choice D) D The profit the school earns per ticket
Answer:
A The amount of money the school charges for all n tickets
Step-by-step explanation:
The number 6 in the term 6n is the "marginal" profit, the additional profit earned from the sale of 1 more ticket. Then 6n represents the revenue from the sale of all n tickets.
Solve for the variables in each triangle below.
Answer:
A) 41 degrees
Step-by-step explanation:
A) SohCahToa
20 = hyp.
15 = adj.
therefore, use Cos (Cah).
cos x = 15/20
x= cos^-1 (15/20)
x= 41 degrees
The required values are shown below.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.
Since, All the triangle are right angle triangle.
Use right angle properties,
(a)
To find the value of θ,
Use cos θ = base/hypotenuse = 15 / 20 = 3/4
cos θ = 3/4
θ = cos⁻¹ (3/4)
θ = 41.41
The value of θ is 41.41°.
(b)
Use sin θ = 3/10 =
θ = 17.45
The value of θ is 17.45.
(c)
Use Pythagorean theorem,
x² + x² = 5²
2x² = 25
x² = 25/2
x = 5/√2
(d)
sin30 = x / 8
1/2 = x/8
x = 4
cos 30 = y / 8
√3 / 2 = y/8
y = 4√3
The values of x and y are 4 and 4√3 respectively.
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If $x$, $y$, and $z$ are positive integers such that $6xyz+30xy+21xz+2yz+105x+10y+7z=812$, find $x+y+z$.
Answer:
10
Step-by-step explanation:
When we simplify we get [tex]$$z(6xy+21x+2y+7)+30xy+105x+10y=812.$$[/tex]
Then we continue to factor to get: [tex](z+5)(6xy+21x+2y+7)&=847.[/tex]
We then see that we can factor [tex](6xy+21x+2y+7)[/tex] into [tex](z+5)(3x+1)(2y+7)&=847.[/tex]
we then do the prime factorization of 847, which i think is, [tex]7*11*11[/tex]. we have to find the numbers that multiply to 847 and then plug them into z+5, 3x=1,2y+7.
It has to be a positive, non-negative integer, right?
We also see that 3x+1=11 so we see that x=10/3 (which wont work).
So 3x+1=7, so x=2.
So 11 has to be in another term. It has to be in 2y+7=11 so y=2
for the last term we get z+5=11 so z=6
2+2+6=10
Hope this helps and if you want please consider giving me brainliest. :)
The value of x+y+z is 8.83.
Given equation,
[tex]6xyz+30xy+21xz+2yz+105x+10y+7z=812[/tex].
We have to calculate the value of [tex]x+y+z\\[/tex].
Here,
[tex]6xyz+30xy+21xz+2yz+105x+10y+7z=812[/tex]
Adding 35 both sides, we get
[tex]6xyz+21xz+2yz+7z+30xy+105x+10y+35=812+35\\[/tex]
Taking z common we get,
[tex]z(6xy+21x+2y+7)+30xy+105x+10y+35=847[/tex]
On further simplifying, we get
[tex](z+5)(6xy+21x+2y+7+6xy+21x+2y+7)=847[/tex]
[tex](z+5)(12xy+42x+4y+14)=847[/tex]
[tex](z+5)[6x(2y+7)+2(2y+7)]=847[/tex]
[tex](z+5)(2y+7)(6x+2)=847[/tex]
Now the prime factorization of 847 is [tex]11\times11\times7.[/tex]
So,
[tex](z+5)(2y+7)(6x+2)=11\times11\times7[/tex]
Here if [tex]z+5=11\\[/tex]
[tex]z=6[/tex]
And if [tex]2y+7=11\\[/tex]
[tex]2y=4\\y=2[/tex]
Again,
[tex]6x+2=7\\x=\frac{5}{6}[/tex]
Now,
[tex]x+y+z=\frac{5}{6} +2+6[/tex]
[tex]x+y+z=0.83+8\\x+y+z=8.83[/tex]
Hence the value of x+y+z is 8.83.
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Can someone help my solve this?
you can write yd^2 or [tex]yd^{ \ 2}[/tex] to indicate "square yards"
=========================================================
Work Shown:
The triangle has a base of 3+3+2 = 8, and a height of 7
A = area of triangle
A = 0.5*base*height
A = 0.5*8*7
A = 28
The rectangle has a length and width of 3 and 2
B = area of rectangle
B = length*width
B = 3*2
B = 6
The shaded area is the difference of the two areas
C = area of shaded region
C = A - B
C = 28 - 6
C = 22
A manufacturer buys large quantities of certain fuel pumps. He finds that his cost depends on the number of cases, q, bought at the same time according to the table below, where cost(q), measured in dollars, is the total cost of purchasing q cases. Find the marginal cost at q = 108.
9 96 100 104 108 112 116 cost(q)
1780 1850 1920 1990 2060 2120
a) $15.80/case
b) $10.50/case
c) $17.50/case
d) $14.00/case
Answer:
The correct option is c) $17.50/case.
Step-by-step explanation:
Note: The data in the question are merged. The data are therefore sorted and the whole question is represented before answering the question. Please, see the attached pdf file for the sorted data and the represented question.
The explanation of the answer is now given as follows:
Marginal cost refers to the cost incurred in order to produce one more unit of a product.
Therefore, marginal cost is the change in the total cost that is caused by a one-unit increase in the quantity of a commodity that is produced.
From the table in the question, the marginal cost at q = 108 can be calculated as follows:
Change in total quantity at 180 cases = 108 - Number of cases immediately before 108 = 180 - 104 = 4
Change in total cost at 180 cases = Total cost at 108 cases - Total cost immediately before 108 cases = 1990 - 1920 = 70
Marginal cost at 108 cases = Change in total cost at 180 cases / Change in total quantity at 180 cases = 70 / 4 = 17.50 per case
Therefore, the correct option is c) $17.50/case.
Paul purchased 8 computers which cost him a total of $6,016, and Mary purchased 8 printers which cost her $1,080.
Steve purchased 25 DVD movies which cost $350, and Sally purchased 34 CD’s which cost $306. How much would 7 computers, 9 printers, 23 DVD’s, and 30 CD’s cost?
-6= 2(w + 5) PLEASE ANSWER AND SHOW WORK!!!
Answer:
[tex]w=-8[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-6=2(w+5)[/tex]
First, distribute the right side:
[tex]-6=2(w)+2(5)\\-6=2w+10[/tex]
Subtract 10 from both sides. The right cancels:
[tex](-6)-10=(2w+10)-10\\-16=2w[/tex]
Divide both sides by 2. The right cancels:
[tex](-16)/2=(2w)/2\\-8=w[/tex]
Flip:
[tex]w=-8[/tex]
Thus, the value of w is -8.
Answer:
-8 = w
Step-by-step explanation:
-6= 2(w + 5)
Divide each side by 2
-6/2= 2/2(w + 5)
-3 = w+5
Subtract 5 from each side
-3-5 = w+5-5
-8 = w
triangle town wants to build a school that is equidistant from its three cities L,M, and N. Which construction correctly finds the best location of the school? A. Construction Y because point E is the incenter of triangleLMN B. Construction Y because point E is the circumcenter of triangleLMN C. Construction X because point C is the incenter of triangleLMN D. Construction X because point C is the circumcenter of triangleLMN
Answer:
C. Construction X because point C is the incenter of triangle LMN.
Step-by-step explanation:
The construction requires that the school must be at equal distance to cities of the triangle town. Thus, it must be located at the point of intersection of the straight path from the three cities L, M, and N.
To be able to construct the school with the specification, option C is the most suitable. Construction X describe the appropriate method because point C is the incenter of triangle town of cities L, M, and N.
Answer:
A
Step-by-step explanation:
Construction Y because point E is the circumcenter of Triangle LMN
Chen took 54 photos with his digital camera. He stored an equal number of photos in each of 6 folders on his computer. Which multiplication sentence could Chen use to find the number of photos in each folder? 0 6 X 54 = 324 0 54 + 6 = 9 O 6 X 9 = 54 O 5 X 9= 45 plz help me
Answer:
6x9=54
Step-by-step explanation:
6 folders with 9 photos in each = 54 photos all together.
Suppose there are 200 lockers and 200 students. Kayla reasons that since there are 10
lockers opened in the first 100 lockers (i.e. between 1 and 100) there must be 10 lockers
opened in the next 100 (i.e. between 101 and 200). Is Kayla's reasoning correct? Explain
why or why not.
Answer:
Kayla's reasoning is not correct.
Step-by-step explanation:
The locker problem is as follows:
Imagine you are at a school that has student lockers. There are 200 lockers, all shut and unlocked, and 200 students. Suppose the first student goes along the row and opens every locker. The second student then goes along and shuts every other locker beginning with number 2. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it). The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the 200 students have followed the pattern with the 200 lockers. At the end, which lockers will be open and which will be closed? Why?
Solution:
So from the information we know that the first student goes along the row and opens every locker.
Then the second student shuts every other locker, i.e. locker numbers 2, 4, 6, 8, 10, ..., 196, 198 and 200.
Then the third students changes the state of every third locker, i.e. he/she closes an open locker and opens a closed locker.
So the open lockers are: 1, 5, 6, 12,...
Then the fourth students changes the state of every fourth locker.
So the open lockers are: 1, 4, 5, 6, 8,....
So, on we will observe that the open lockers have a perfect square number such as, 1, 4, 9, 16,....
Consider that the pattern is as follows:
Student 1 opens the locker, Student 2 closes it, Student 3 opens it, person 4 Student and so on.
This is because the square numbers always have an odd number of factors, which leads them to be open at the end.
Take any locker number, 40, for example. Its state (open or closed) is changed for every student whose number in line is a factor of the locker number.
Student Locker 40 status
1 Open
2 Close
4 Open
5 Close
8 Open
10 Close
20 Open
40 Close
Like all other lockers numbered with non-square numbers, it ends up closed after all the students have gone through the line because it has an even number of factors.
Consider the locker number 16:
Student Locker 16 status
1 Open
2 Close
4 Open
8 Close
16 Open
Thus, we can conclude that all the doors with square numbers on them will remain open because all square numbers have an odd number of factors and the doors with non-square numbers on them will remain close because they have even number of factors.
There will be a total of 14 lockers open.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 and 196
So, if there are 10 lockers open in the first 100 lockers there must be only 4 other lockers opened in the next 100.
The area of the indoor sports exhibition is shown below. What is its perimeter? m What is its area? m2
Answer:
Area = 3097.96[tex]m^{2}[/tex]
Perimeter = 270.96m
Step-by-step explanation:
Step 1: State the shapes making up the indoor sports exhibiti[tex]\pi[/tex]on
2 rectangles
1 semi circle
Step 2: Find the area and perimeter of the shapes
ARectangle1 = lw = (10)(40) = 400m^2
PRectangel1 = 2l + w = 2(10) + 40 = 60m
ARectangle2 = lw = (33)(68) = 2244m^2
PRectangel2 = l + w = 33 + 68 = 101m
ASemiCicle = [tex]\frac{\pi r^{2}}{2} =\frac{\pi 17^{2} }{2} =\frac{289\pi }{2}=144.5\pi=453.96m^{2}[/tex]
PSemiCircle = [tex]2\pi r=2\pi(17)=35\pi =109.96m[/tex]
Step 3: Add up the areas and perimeters
Area = 400 + 2244 + 453.96
Area = 3097.96[tex]m^{2}[/tex]
Perimeter = 60 + 101 + 109.96
Perimeter = 270.96m
Therefore the area of the indoor sports exhibition is 3097.96[tex]m^{2}[/tex] and the perimeter is 270.96 m
PLEAAASE ANSWER TIMER IS RUNNING OUT
Answer:
the correct answer is 1/2.
How i came to this answer was adding all of the number of medals together for all of the years, coming up to a total of 22. When asking about probability of any given set or amount of things, you always take the selected values and take them out of the whole amount. Years 2009 and 2012 have a whole selected value of 11 (4+7). Therefore you're "taking" 11 from 22, coming up with the fraction 11/22 seeing as that is not a answer choice the next step is to simply the fraction to 1/2.
Answer:
C Mark me as brainliest!!!
Step-by-step explanation:
1. There are 125 juniors at the high school.How many ways can they elect a
president,vice president, and secretary?
2. Determine the number of 4-letter arrangements that can be made using the
word RHOMBUS.
Answer: 1. 1,906,500
2. 840
Step-by-step explanation:
1. Given: There are 125 juniors at the high school.
Total positions = 3 [president,vice president, and secretary]
Then, Number of ways to elect a president,vice president, and secretary( which is in order) out of 125 juniors = [tex]^{125}P_{3}=\dfrac{125!}{(125-3)!}[/tex] [Using permutations]
[tex]=\dfrac{125!}{122!}\\\\=\dfrac{125\times124\times123\times122!!}{122!}\\\\=125\times124\times123\\\\=1906500[/tex]
Hence, Required ways =1906500
(2) Given word : "RHOMBUS"
Total letters= 7
By permutation, the umber of 4-letter arrangements = [tex]^7P_4=\dfrac{7!}{(7-4)!}=\dfrac{7!}{3!}[/tex]
[tex]=\dfrac{7\times6\times5\times4\times3!}{3!}\\\\= 7\times6\times5\times4\\\\=840[/tex]
Hence, required ways = 840
Answer:
1) The number of ways = 1906500.
2) The number of ways = 840.
1) President, vice president, and secretary are 3 different positions.
There are total 125 students.
So we can select them in [tex]125P3=\frac{125!}{\left(125-3\right)!}=1906500[/tex] ways.
2) There are total 7 different letters in RHOMBUS.
We can select 4 different letters from 7 letters in [tex]7P4=\frac{7!}{\left(7-4\right)!}=840[/tex].
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2,793,000,000 in scientific notation
Answer:
2.793109
Step-by-step explanation: