Answer:
A. 1/8 of the semester
B. 3/20 of the semester
Step-by-step explanation:
A professor wants to divide the remaining 3/4 of the semester evenly into 6 different units. A. What fraction of the semester should be spent on each unit?
B. The professor drops one unit. What fraction of the semester should be spent on each unit?
Solution
A.
A professor wants to divide the remaining 3/4 of the semester evenly into 6 different units
Total semester=3/4
Total units=6 units
Fraction of the semester that will be spent on each units = 3/4 ÷ 6
=3/4 × 1/6
=3/24
=1/8
1/8 of the semester will be spent on each units
B. If the professor drops one unit
That is 6 units - 1 unit = 5 units
Fraction of the semester that will be spent on each units=3/4 ÷ 5
=3/4 × 1/5
=3/20
Write an equivalent expression by applying the distributive property (x + y + 3) x (y + 1) = A: 2y2+xy+4 B: 2y + x + 4 C: y2+xy+4y+x+3 Please help math makes me go insane
Answer:
C
Step-by-step explanation:
So we have the expression:
[tex](x+y+3)\times(y+1)[/tex]
To multiply, use the distributive property. Multiply (y+1) to each term on the left:
[tex]=x(y+1)+y(y+1)+3(y+1)[/tex]
Distribute the variables:
[tex]=(xy+x)+(y^2+y)+(3y+3)[/tex]
Rearrange them to combine like terms:
[tex]=y^2+xy+y+3y+x+3\\=y^2+xy+4y+x+3[/tex]
The correct answer is C.
Edit: Typo
[tex](x+y+3)\cdot(y+1)=\\\\=(x+y+3)\cdot y+(x+y+3)\cdot1=\\\\=xy+y^2+3y+x+y+3=\\\\=\boxed{y^2+xy+4y+x+3}[/tex]
Answer C.
Mr Gupta has some rice of worth RS 3000. He sold 1/3 of it with 10% loss .By how many percent must the selling price be increased for making 10% profit on the outlay?
Answer:
20% more of cost price, or 30% more of initial selling price
Step-by-step explanation:
Given:
Product CP = Rs. 3000Sold 1/3 at a loss of 10%Target profit = 10%SP for the rest = ?SolutionTotal money to be obtained:
3000 + 10% = 3000*1.1 = Rs. 3300Money already got:
1/3*3000 - 10% = 1000 - 10% = Rs. 900Money left to obtain:
3300 - 900 = Rs. 2400Product left to sell, worth of:
3000*2/3 = Rs. 2000The difference:
2400 -2000 = Rs. 400Required selling price increase:
400/2000* 100% = 20% of CPOr compared to initial price, new SP to be increased by 30%
How can you tell from the graph of Molly’s garden on the previous slide that it represents a proportional relationship?
Answer:
The graph of a proportional relationship has the same unit rate, is a straight line, and starts at the origin.
Step-by-step explanation:
this the answer
The graph of a proportional relationship is a straight line.
What is the equation of a straight line? What do you mean by domain and range of a linear function?The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have a graph of Molly’s garden.
Since, the graph is not given, i will write the condition for proportional relationship. The graph of a proportional relationship is a straight line whose equation is given by -
y = mx + c
Therefore, the graph of a proportional relationship is a straight line.
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can someone plz help? idk properties in math
Alicia had $-11 in her checking account. She did a few chores and made $44.50. She
decided to pay for her and a friend to go to the movies, and each ticket cost $6.25. How
much money does she have left in her checking account?
Answer:
she would have 21 dollars left
Step-by-step explanation:
44.50-11
33.50-12.50
Answer:
[tex]\Huge \boxed{\$ \ 21}[/tex]
Step-by-step explanation:
She had $-11 initially and gained $44.50.
-11 + 44.5 = 33.5
She has $33.5 in her account.
She buys two tickets for $6.25 each.
33.5 - (2)6.25 = 21
She has $21 left in her account.
Calculate the perimeter of the trapezium
Answer:
P = 26
Step-by-step explanation:
see attached
to get the side 5,
sqrt((10-7)² + 4²)
side = 5
P = 4 + 7 + 5 + 10
P = 26
Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.
Answer:
1/7
Step-by-step explanation:
From the above question, we have the following values:
White socks = 2
Brown socks = 4
Black socks = 2
Total number of socks = 8
We are told in the question that:
You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot.
From above question, we can see that this is a probability with dependent events. This means have a white sock on your left foot and brown sock on your right are events that depend on each other, hence, the probability will occur with replacement.
The probability ( having a white sock on your left foot and brown sock on right) =
2/8 × 4/7
= 8/56
= 1/7
Therefore, the probability of this occuring is 1/7
I need sum help with math
Answer:
Step-by-step explanation:
1) (1÷5)*5*14 = [tex]\frac{1}{5}*5*14[/tex] = 1*14 = 14
2) 6 + 4(19 - 5) = 6 + 4 * 14
= 6 + 56
= 62
Or
Use distributive property. a(b+c) = a*b + a*c
6 + 4( 19 - 5) = 6 + 4* 19 - 4*5
= 6 + 76 - 20
= 82 - 20
= 62
3) 5(14- 5) + 6 (3 +7) = 5 * 9 + 6 *10
= 54 + 60
= 114
A coordinate axis is drawn with a parabola pointing up that has vertex of 0,3. Determine the intervals on which the function is increasing, decreasing, and constant. Increasing x < 0; Decreasing x > 0 Increasing x > 0; Decreasing x < 0 Increasing x < 3; Decreasing x > 3 Increasing x > 3; Decreasing x < 3
Answer:
Option (2). Increasing x > 0; decreasing x < 0
Step-by-step explanation:
Equation of the parabola having vertex (0, 3) will be,
y = (x - 0)² + 3
y = x² + 3
To check the function is increasing or decreasing in the given intervals we will find the derivative of the function,
[tex]\frac{dy}{dx}=\frac{d}{dx}(x^{2}+3)[/tex]
y' = 2x
For x < 0 Or x = -1
y' = 2(-1)
= -2 < 0
Therefore, function is decreasing in x < 0
For x > 0 Or x = 1
y' = 2(1) + 3
= 5 > 0
Therefore, function is increasing in x > 0
Option (2) is the answer.
find the value of f(12) if f(x)=-2x+4
Answer:
f(12) = - 20
Step-by-step explanation:
To evaluate f(12), substitute x = 12 into f(x), that is
f(12) = - 2(12) + 4 = - 24 + 4 = - 20
The required value of function at x = 12 is f(12) = -20.
Given that,
A function is given,
f(x) = -2x + 4
The solution of the function at x = 12 is to be determined.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
the given function is,
f(x) = -2x + 4
At x = 12
put x = 12 in the function
f(12) = -2 * 12 + 4
f(12) = -24 + 4
f(12) = -20
Thus, the required solution of the function at x = 12 is -20.
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A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on two numbers pays 17 to 1 (that is, if you bet $1 and one of the two numbers you bet comes up, you get back your $1 plus another $17). How much do you expect to win with a $1 bet on two numbers
Answer:
-$0.05
Step-by-step explanation:
The computation is shown below:
The loss case = -1
The win case = 11 + 17 + 1 = 17
Now the number of pairs could be formed from (1 to 356, 0, 00) i.e.
[tex]= \frac{38!}{2!36!}[/tex]
= 703
Now
Pr (x = 17) is
[tex]= \frac{1\times37}{703}\\\\ = \frac{37}{703}[/tex]
And, Pr (x = -1) is
[tex]= 1 - \frac{37}{703}\\\\ = \frac{666}{703}[/tex]
Now
E(x) = (-1) Pr (x = -1) + (17) Pr (x = 17)
[tex]= -1 \times \frac{666}{703} + 17 \times \frac{37}{703} \\\\ = \frac{-37}{703}[/tex]
= -$0.05
hence, the -$0.05 would be expected to win that associated with a $1 bet on two numbers
Problem: What values of a and b make this statement false? |a-b|=|a|-|b|
Answer:
All (a,b) that satisfy a.b < 0 will make that statement false
Step-by-step explanation:
It is only right when:
|a-b| = |a| - |b|
<=> ( |a-b| ) ^ 2 = ( |a| - |b| ) ^ 2
<=> a^2 - 2ab + b^2 = a^2 - 2.|ab| + b^2
<=> ab = |ab|
<=> ab ≥ 0
So, when ab < 0, it's wrong
If you were in charge of the money, how would you recommend your friends spend it? Explain why you choose the solution you did. Why do you think it's the most fair? (3 points:1 point for stating your recommendation and 2 points for explaining your reasoning)
Answer:
I would recommend them to go out with their family and spend it because i feel that people always dream about ways to bring their family close again so that can be a good way to bond and do things that often cost a lot of money.
Step-by-step explanation:
Dwayne had 136 songs on his phone. He deleted 56 songs. What is the
ratio of songs he kept to songs he deleted (in its simplest form)?
136 - 56 = 80 songs kept
Ratio of songs kept to songs deleted is:
80:56
Simplify by dividing each number by 8:
The simplest form is: 10/7
Factor the expression 343y^6+64
Answer: 343y^6+64= (7y^2+4)(49y^4-28y^2+16)
Step-by-step explanation:
Answer: The answer is shown in the picture down below.
solve 5u– 5(1–u)=u+8
Answer:
u= -3
Step-by-step explanation:Solve for
u by simplifying both sides of the equation, then isolating the variable.
Answer : 5u– 5(1–u)=u+8
5u - 5+ 5u = u+ 8
10u -5 = u+ 8
9u = 13
u = 1.44
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution. F(x) = x2 + 2 F(x + h) =
Answer:
F(x-h) = x² + 2xh +h² +2
Step-by-step explanation:
F(x) = x² + 2, x∈R
F(x + h) = (x + h )² + 2 = x² + 2xh + h² + 2
Answer:
F ( x ) = x^2 + 2
Domain = R
F ( x - h ) = ( x - h )^2 + 2xh + h^2 + 2
which is a function? {(8,9),(−2,9),(7,5),(−4,−7)} {(−5,−7),(−5,4),(−2,−8),(3,5)} {(8,0),(−4,−2),(7,1),(0,0)} {(−8,3),(−5,−7),(−4,5),(9,3)}
Answer:
All but the second {(8,9),(−2,9),(7,5),(−4,−7)} {(8,0),(−4,−2),(7,1),(0,0)} {(−8,3),(−5,−7),(−4,5),(9,3)}Step-by-step explanation:
Function means that for each x we get y, and no no x gives two different y-es
{(−5,−7),(−5,4),(−2,−8),(3,5)} for x = -5 we have two different y-es therefore its not function
Board 1
C
(3x + 16)°
7
(5x - 54)
Board 2
Enter the measure of ZC.
Answer:
59°
Step-by-step explanation:
From the question given, we obtained the following:
C + (3x + 16) = 180 (sum of angle on a straight line)
5x – 54 = 3x + 16 (Altanate angles are equal)
Next, we shall determine the value of x.
This can be obtained as follow:
5x – 54 = 3x + 16
Collect like terms
5x – 3x = 16 + 54
2x = 70
Divide both side by the coefficient of x i.e 2
x = 70/2
x = 35
Finally, we shall determine the value of C as shown below:
C + 3x + 16 = 180
But, x = 35
C + 3(35) + 16 = 180
C + 105 + 16 = 180
C + 121 = 180
Collect like terms
C = 180 – 121
C = 59°
Therefore, the value of C is 59°
Given that 110ₓ = 40₅ , find the value of x.
110x=405
1*x^2 +1*x^1 +0*x^0=4*5^1+0*5^0
x^2+x=4*5
x^2+x=20
x^2+x-20=0
x^2 +5x-4x-20=0
x(x+5)-4(x+5)=20
(x-4)(x+5)=20
x= 4 or -5
But a base cannot be negative so
x=4
I need help finding the intersection of the line and plane
Answer:
the line is making a kite like shape
Chicken is on sale for $3.90 per pound. If
Ms. Gellar buys 2.25 pounds of chicken, how
much will she spend? Round to the nearest
penny.
Answer:
$8.78
Step-by-step explanation:
Hello!
To find how much she will spend we multiply the cost per pound by the amount of pounds
3.90 * 2.25 = 8.775
Round to the nearest penny
$8.78
The answer is $8.78
Hope this helps!
A restaurant adds a 20% tip to the bills of parties of 6 or more people. Suppose a server waits on five such tables. The bill
without the tip for each party is listed in the table. How much did the server make in tips during this shift?
Distributive Property: a(b + c) = ab + ac and (b + c)a = ba = ca
Party 1
Party 2
Party 3
Party 4
Party 5
$185.45 $205.20 $195.05 $245.80 $262.00
Answer:
$218.70
Step-by-step explanation:
You need to first convert the percentage to the decimal.
20% = 0.2
Now, you need to find 20% of each bill by multiplying each bill by 0.2.
0.2(185.45) + 0.2(205.20) + 0.2(195.05) + 0.2(245.80) + 0.2(262.00)
Because of the distributive property, you can add up the bills and multiply the sum by 0.2.
0.2(185.45 + 205.20 + 195.05 + 245.80 + 262.00)
0.2(1093.50)
218.7
The waiter made $218.70 in tips.
What is the product of complex conjugates? The product of complex conjugates is a difference of two squares and is always a real number. The product of complex conjugates is the same as the product of opposites. The product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero. The product of complex conjugates is a sum of two squares and is always a real number.
Answer:
Last given option is the correct answer:
"The product of complex conjugates is a sum of two squares and is always a real number."
Step-by-step explanation:
The product of two conjugates can be described and solved like this:
[tex](a + b\,i) \,(a - b\,i)= a^2-a\,b\.i+a\,b\,i-b^2\,i^2=a^2+0-b^2\,(-1)= a^2+b^2[/tex]
so, no matter what the values for the real values a and b are, the product is always a real number and the sum of two squares.
Answer:
(a + bi)(a – bi) = a2 – (bi)2 = a2 + b2
The product of a complex number and its complex conjugate is
✔ always
a real number.
Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her allowance every day. Formulate and then graph the equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, X.
Answer:
125+2x=y (take 125 add 2x for $2 a day and then = y for amount saved)
Points on Graph:
(125,0)
(135,5)
(145,10)
(155,15)
(165,20)
(175,25)
(185,30)
(195,35)
(205,40)
(215,45)
(225,50)
Answer:
Step-by-step explanation:
Evaluate the following expressions if a = 2, b = -3, c = -1, and d = 4. then solve for
2a + C
Answer:
3
Step-by-step explanation:
2a + C
Let a = 2 and c = -1
2* 2 + -1
4 -1
3
Answer:
3Step-by-step explanation:
[tex]a = 2\\ b = -3\\c = -1\\ d = 4\\\\2a+c =?\\2(2) +(-1)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:2\left(2\right)\::\quad 4\\=4+\left(-1\right)\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:4+\left(-1\right)\:\\:\quad 3[/tex]
After a baby was born, he began to gain weight at a rate of 2 pounds per month. The weight of the baby at birth was 10 pounds. write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby tt months after birth.
Answer:
[tex]W(t) = 2t[/tex]
Step-by-step explanation:
Given
Weight = 2 pounds
Rate = monthly
Required
Determine the weight of the baby in t months
When the baby is 1 month old, t = 1;
[tex]Weight = 2\ pounds * 1[/tex]
[tex]Weight = 2\ pounds[/tex]
When the baby is 2 months old, t = 2;
[tex]Weight = 2\ pounds * 2[/tex]
[tex]Weight = 4\ pounds[/tex]
When the baby is t months old;
[tex]Weight = 2\ pounds * t[/tex]
[tex]Weight = 2t\ pounds[/tex]
Represent Weight as a function of t
[tex]W(t) = 2t[/tex]
Hence, the formula is [tex]W(t) = 2t[/tex]
Please hurry simplify the problem a i b 5i c -i
Answer:
[tex]\frac{90}{5} i[/tex]
Step-by-step explanation:
10 * sqrt(81/25 * -1) = 10 sqrt(81/25) * sqrt(-1) = 10 *9/5 * i
What is the slope of the line that passes through the points (10, 3)(10,3) and (2, 3) ?(2,3)? Write your answer in simplest form.
Answer:
0
Step-by-step explanation:
The y's are the same so they do not go up or down so the slope is 0.
The slope of the line passes through points (10, 3) and (2, 3) is 0.
Given that,
The slope of the line that passes through points (10, 3) and (2,3) is to be determined.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
The slope of the line passes through the point (10, 3) and (2, 3).
Now, put the point in the equation of the slope,
m =(y₂ - y₁) / (x₂ - x₁)
m = 3 - 3 / (2 - 10)
m = 0 / -8
m = 0
Thus, the slope of the line passes through the points (10, 3) and (2, 3) is 0.
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Preview: 5 People fit comfortably in a 2 foot by 2 foot area. Use this value to estimate the size of a
crowd that is 4 feet deep on both sides of the street along a 1-mile section of a parade route.
Answer:
The estimate size of the crowd is 52800 people
Step-by-step explanation:
The given information are;
The number of people that fit comfortably in a 2 by 2 foot area = 5
Therefore, we have;
The area occupied by the 5 people = 2 × 2
The crowd ratio = 5/(2 × 2) = 5/4
The area occupied by the crowd = 4 feet deep, and 1 mile long on both sides of the street
By conversion factors, 1 mile = 5,280 feet
Therefore, the area occupied by the crowd = 4 × 5280 × 2 = 42240 ft²
The number of people in the crowd = Crowd ratio × The area occupied by the crowd
The number of people in the crowd = 5/4 × 42240 = 52800 people
Therefore, The estimated size of the crowd = 52800 people.