Answer:
1. Equivalent: [tex]p(1+0.20),\ 1.20p;[/tex]
2. Not equivalent: [tex]2p+0.20,\ 0.80p,\ 2.20p,\ 1.02p.[/tex]
Step-by-step explanation:
Consider the expression [tex]p+0.20p.[/tex]
Use the distributive property
[tex]a\cdot (b+c)=a\cdot b+a\cdot c.[/tex]
Then
[tex]p+0.20p=p\cdot 1+p\cdot 0.20=p\cdot (1+0.20)=p(1+0.20).[/tex]
Expression [tex]p(1+0.20)[/tex] is equivalent to the expression [tex]p+0.20p.[/tex]
Since [tex]1+0.20=1.20,[/tex] then expression [tex]p(1+0.20)=1.20p[/tex] is equivalent to the expression [tex]p+0.20p.[/tex]
All the rest expressions are not equivalent to the expression [tex]p+0.20p.[/tex]
Final answer:
The expressions equivalent to Paul's original expression p + 0.20p for calculating a meal's cost plus a 20% tip are p(1+0.20) and 1.20p. The other expressions provided do not accurately represent the original expression's intent to include a 20% tip.
Explanation:
The expression p + 0.20p can be simplified by combining like terms. As both terms contain 'p', we can add them together. Since 0.20 is the decimal form of 20%, this expression can be rewritten as 1p + 0.20p, which simplifies to 1.20p. This means that to find the total cost of the meal including the tip, you multiply the price of the meal 'p' by 1.20. Therefore, the equivalent expressions to p + 0.20p are p(1+0.20) and 1.20p, because both represent Paul adding a 20% tip to the cost of his meal.
Let's identify which of the given expressions are equivalent:
2p + 0.20 - Not equivalent, as it suggests doubling the price plus 20 cents.
0.80p - Not equivalent, as it represents only 80% of the original price.
p(1+0.20) - Equivalent; this is simply another way of writing the original expression.
1.20p - Equivalent; this is the simplified form of the original expression.
2.20p - Not equivalent, as it incorrectly represents an additional 220% of the meal cost.
1.02p - Not equivalent, as it only adds an additional 2% to the original price, not the 20% intended for the tip.
A punter kicks a football upward with an initial velocity of 48 feet per second. After how many seconds does the ball hit the ground? Use the formula h=rt−16t2, where h represents height in feet and r represents the initial velocity (rate) in feet per second.
A. 3
B. 6
C. 8
D. 12
A. 3
Step-by-step explanation:Fill in the given values in the formula (h=0, r=48) and solve for t.
... 0 = 48t -16t²
... 0 = 16t(3 -t)
This is true for t = 0 and for t = 3.
The ball will take 3 seconds to hit the ground.
Answer:
A.3
Step-by-step explanation:
PLZ HELP WILL MARK BRAINLEST SOLVE FOR X
[tex]\frac{x}{8} + 19 = 30[/tex] - subtract 19 from both sides
[tex]\frac{x}{8} = 11[/tex] - multiply both sides by 8
[tex]x = 88[/tex]
In this equation, x = 88.
please help me asap!
Answer:
24 units
Step-by-step explanation:
Given is a circle with two chord BE and CD
BE and CD intersect at A
By circle chords intersection theorem we have
DA*AC = EA*AB
i.e. 8(15) = 5(AB)
Divide by 5 both the sides
AB =8(15)/5 = 8(3) = 24 units
Verify:
Let us check now whether chord intersection theorem is satisfied.
DA*AC = 8(15) = 120
EA*AB = 5(24) = 120
Since these two equal, we verify that answer is right.
The fee for a balance transfer is 2% of the amount of the transfer. If b represents the amount of the balance transfer and ƒ represents the amount of the fee, which of the following equations represents the relationship between b and ƒ?
b = 0.2ƒ
ƒ = 0.02b
b = 0.2 + ƒ
ƒ = b + 2
Answer:
f=0.02b
Step-by-step explanation:
So we want to figure out the fee (f) therefore our answer will be in terms of f=(something). Now since the fee is 2% and 2% is decimals is 2÷100=0.02 then:
f=0.02b
Meaning that the fee is 2% of the balance (b).
The ratio AB to CB is
Answer:
1/3
Step-by-step explanation:
The ratio of AB to CB
AB/CB
3/9
Simplifying by dividing the top and bottom by 3
1/3
A line has __________ dimension and is usually represented with two arrowheads.
one
two
three
Points that lie in the same plane are known as ___________ points.
collinear
coplanar
coordinate
1. A line has only a length dimension. It has no width or height. It is a one-dimensional object.
2. Points on the same line are collinear. On the same plane, they are called coplanar. Coordinates locate a point relative to some measurement reference.
the temperature in Tampa was 55°F at 5a.m . It rose 7°every hour for the next 2 hours and then rose 8° every hour for 3 hours after that. It then remained constant until 3p.m. what was the temperature at noon.
Answer:
93 °F
Step-by-step explanation:
At 7 am, the temperature was 55 °F + 2×7 °F = 69 °F.
At 10 am, the temperature was 69 °F + 3×8 °F = 93 °F.
Since the temperature was constant until 3 pm, it was 93 °F at noon.
What is the property of addition that is illustrated by the equation 0+34=34?
Answer:
Additive identity.
Step-by-step explanation:
The zero is the additive identity. It is so named because when you add 0 to anything, you leave the unchanged. To give you a better idea about what this is, the multiplication identity is 1
One times anything does not change anything's value. 1 * 33 = 33. 33 is left unchanged.
Carter has balance of -2,096.37 on his bank loan.He makes a payment and subtracts $500 of his debt.Then he decides to make a monthly payment to subtract $250 of the debt each month.What is the least number of months that Carter needs to make the monthly payment to pay off the original debt? Explain your thinking
7 months
Step-by-step explanation:After Carter makes his $500 payment, the balance on the loan is -1596.37. We want to find the number of months (m) such that ...
... -1596.37 +250m ≥ 0
... m ≥ 1596.37/250 . . . . add 1596.37, divide by the coefficient of m
... m ≥ 6.4
The least number of months that is more than 6.4 is 7 months.
_____
Comment on this answer
Carter's loan balance may also be affected by interest charged on the loan amount. We don't expect those charges to be so high as to require an additional month's payment.
Please help me if you can
(4x10^6) - (2x10^5)
Simplify!
78.2% of the students study more that one day for the chapter test. Find the probability that a randomly selected student did not study more than one day for the test.
A. 0.218 (this one is right)
B. 0.782
C. 0.328
D. 0.391
Answer:
A
Step-by-step explanation:
Total is ALWAYS 100%.
It says that 78.2% DO STUDY. It means the REST (100-78.2) DO NOT STUDY.
What is 100 - 78.2 ? It is 21.8%
To get the answer in decimal, we divide by 100:
[tex]\frac{21.8}{100}=0.218[/tex]
Hence, A is the correct answer.
PLEASE HELP, will give brainliest if you answer
consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the independent variable. Must show work for full credit
b=1/4r-3/4
Step-by-step explanation:Divide everything by 16
Leave it a fraction
So ye...
Simplify t^12/t^6 help!
Answer:
t^6
Step-by-step explanation:
The simplified form is [tex]t^{6}[/tex].
What is simplification?Related to "simplification" troubles are a few "solving" issues. just as some expressions contain parentheticals and even nested grouping symbols, so also do a few equations. The simplification manner is equal, whether or not we are running with expressions (and for this reason best simplifying) or equations (so we're additionally fixing).
Like terms: terms which have equal variable elements (identical variable(s) and same exponent(s)). Whilst simplifying using addition and subtraction, you combine “like terms” through retaining the "like term" and including or subtracting the numerical coefficients.
[tex]t^{12}[/tex] divided by [tex]t^{6}[/tex]
[tex]=t^{12-6}\\ = t^{6}[/tex]
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What is the solution to the system of equations?
x+y = 2
x -y =4
(__ , ____)
So with this system of equations, I will be using the elimination method. With the two equations, add them together and you will get:
[tex]2x=6[/tex]
Since the y-variable has been eliminated, we can solve for x. With this, divide both sides by 2:
[tex]x=3[/tex]
Now that we know the value of x, substitute it into either equation to solve for y:
[tex]3+y=2\\y=-1\\\\3-y=4\\-y=1\\y=-1[/tex]
Answer:In (x,y) form, your answer is (3,-1).
Answer:
x=3, y=-1
Step-by-step explanation:
x+y = 2
x -y =4
I will use elimination to eliminate the variable y. Add the two equations together.
x+y = 2
x -y =4
-------------
2x = 6
Divide each side by 2
2x/2 = 6/2
x = 3
But we still don't know y
x+y =2
Substitute x=3 into the equation
3+y =2
Subtract 3 from each side
3-3 +y =2-3
y =-1
Quadrilateral QRST has two pairs of congruentes sides, but it is not a parallelogram. What figure is it? What further condition would have to satisfy to be a parallelogram?
Answer:
The correct answer is: [C]:
________________________________________________
" {The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } ."
________________________________________________
Step-by-step explanation:
________________________________________________
Note that "all" squares are "parallelograms" ; and that "all" rectangles are
"parallelograms" ;
yet: "Not All parallelograms" are "squares" or "rectangles".
________________________________________________
The question asks:
________________________________________________
"Quadrilateral QRST has two pairs of congruent sides, but it is not a parallelogram.
What figure is it?
What further condition would have to satisfy to be a parallelogram? " .
________________________________________________
So; we can rule out:
________________________________________________
"Answer choices:
[A]: "The figure is a square..." ;
________________________________________________
[B]: "The figure is a rectangle..." ; AND :
________________________________________________
[D]: "The figure is a square..." .
________________________________________________
We are left with:
________________________________________________
Answer choice: [C]:
________________________________________________
" { The figure is a kite. To be a parallelogram, it would have to have pairs of opposite congruent sides, not just congruent sides. } " .
________________________________________________________
30 ounces = how many pounds and ounces
Answer: " 1 lb , 14 oz. " .
_________________________________________________
Step-by-step explanation:
_________________________________________________
Note the exact conversion: " 16 oz. = 1 lb. " .
→ {that is: " 16 ounces = 1 pound " .}.
_________________________________________________
30 oz. * ( 1 lb / 16 oz). = [tex]\frac{30}{16}[/tex] lbs. ;
= (30/2) / (16/2) lbs.
= (15 / 8) lbs. ;
_________________________________________________
1
8 ┌ 15
- 8
7 ;
______________________
The answer is equal to: " 1 7/8 lbs. " .
→ (1 lb) + (7/8) (lb). ;
______________________
→ (7/8) lb. = how many "oz." ??
_______________________
Note the exact conversion: " 1 lb. = 16 oz. " .
_______________________
→ [tex]\frac{7 lb}{8}[/tex] * [tex]\frac{16 oz}{1 lb}[/tex] ;
= [tex]\frac{7}{8} * \frac{16}{1}[/tex] oz. ;
→ The "8" cancels to a "1" ; and the "16" cancels to a "2" ;
→ {since: " {16 ÷ 8 = 2 } " ;
and: {since: " {8 ÷ 8 = 1 } " .
_______________________________________________
→ So we can rewrite as:
_______________________________________________
→ [tex]\frac{7}{1} * \frac{2}{1}[/tex] oz. ;
= { 7 * 2 } oz. ;
= 14 oz.
_______________________________________________
→ So:
_______________________________________________
→ " 30 oz. " = " (1 lb) + (7/8) lb. " ;
= " 1 lb. + 14 oz. " ;
= " 1 lb , 14 oz. " .
_______________________________________________
→ The answer is: " 1 lb , 14 oz. " .
_______________________________________________
Let us check our answer:
→ Does: " 1 lb. + 14 oz. = ? 30 oz. ? " ;
_______________________________________________
Note the exact conversion: " 1 lb. = 16 oz. " .
_______________________________________________
→ Does: " 16 oz. + 14 oz. = ? 30 oz. ?? " ;
_______________________________________________
₁
16 oz
+ 14 oz
30 oz.
_______________________________________________
→ Does: " 30 oz. = ? 30 oz. ? " ??? ; → Yes!
_______________________________________________
Hope this helps!
Best wishes to you in your academic endeavors
— and within the "Brainly" community!
_______________________________________________
f divided by 1/4 for f =2/9
Please help FAST
ASAP
[tex]f\div\dfrac{1}{4}=f\times\dfrac{4}{1}=4f\\\\f=\dfrac{2}{9}\to4f=4\times\dfrac{2}{9}=\boxed{\dfrac{8}{9}}[/tex]
Your class wants to know to most typical age of student in your class. It collects the ages of all students and the teacher. Which measures of central tendency would give you the best typical student age
Answer:
Median.
Step-by-step explanation:
Assuming the teacher is not of similar age to the students, their higher age would pull the mean higher than if the teacher were not included, where the median would not be pulled by this extreme value.
once out of every two weeks of the year would be how may days through out the year
Answer:
26 most years; 27 some years
Step-by-step explanation:
1 day out of 14 is 1/14 of the number of days in a year.
The number of days in a year depends on the year or years you're talking about. In all cases, there are not an integer number of weeks in a year, so days are left over. 365/14 = 26 1/14.
For example, if you're concerned with every other Monday, most years, there will be 26 of them, but every few years there will be 27. Over a period of 800 years, there will be exactly 71 years with 27 days of interest instead of 26. 800 is not divisible by 71, so the spacing will be uneven.
find the value of x.
Answer:
71.79 degrees
Step-by-step explanation:
The cosine is (adjacent side to angle) / (hypotenuse)
so the cosine of x = 5/16
to get x you multiply cosine by its inverse
(cos^-1 x)(cos x) = (cos^-1 x)(5/16)
= 71.79 degrees
from the graph; calculate: E=
c) 7π cm
Step-by-step explanation:The length of an arc (s) is related to its central angle (θ) and the radius of the circle (r) by ...
... s = rθ . . . . . . . . . θ in radians
Here, the central angle measures are given in "grads". There are 400 grads in a circle, so 200 grads in π radians. To convert grads to radians, we multiply the number of grads by π/(200g).
Then the lengths of the arcs are ...
... arc AB = (20 cm)·(50g·(π/(200g))) = 5π cm
... arc BC = (10 cm)·(40g·(π/(200g))) = 2π cm
E = arc AB + arc BC = 5π cm + 2π cm = 7π cm
At the produce counter, 71⁄5 pounds of seedless grapes cost $12.89. How much would 3 pounds cost?
A. $3.58
B. $5.16
C. $1.79
D. $5.37
Answer:
D. $5.37
Step-by-step explanation:
We need to figure out how much grapes cost per pound
Change the mixed number to an improper fraction
7 1/5 = (5*7+1) /5 = 36/5
$12.89 / 36/5
Copy dot flip
12.89 * 5/36 = 1.79 per lb
If we are purchasing 3 pounds, we will multiply by 3
3 lbs * $1.79 / lb = $5.37
Evaluate the expression 8 to the second power + 3.8 - 10 * 2
Answer:
47.8
Step-by-step explanation:
8^2+3.8-10*2
64+3.8-20
47.8
the perimeter of a rectangle whose sides are lengths ( 4z + 3 ) units and ( 3z + 5 ) units
Answer:
14z + 16 is your perimeter
Step-by-step explanation:
To solve the perimeter, add all sides together. Note that in a rectangle, the opposite sides are congruent and parallel to each other.
Let Perimter = p
p = 2(4z + 3) + 2(3z + 5)
Simplify. Distribute the numbers.
2(4z + 3) = 8z + 6
2(3z + 5) = 6z + 10
Simplify. Combine like terms
p = 8z + 6 + 6z + 10
p = 14z + 16
14z + 16 is your perimeter
~
If f(x) is a third degree polynomial function and g(x) = f(–2x), which of the following is NOT true?
f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(2) = g(–1)
f(x) and g(x) have the same number of zeros
Answer:
f(x) and g(x) have the same x-intercepts (is not true)
Step-by-step explanation:
g(x) is a reflection across the y-axis and a horizontal compression of f(x). In general those transformations will move the x-intercepts. (The y-intercept and the number of x-intercepts will remain unchanged.)
_____
Comment on the question/answer
f(x) = x^3 is a 3rd degree polynomial. When transformed to g(x) = -8x^2, its only x-intercept (x=0) remains the same. The answer above will not apply in any instance where the only x-intercept is on the line of reflection. (The question is flawed in that it does not make any exception for such functions.)
Trevon is making payments on a car that costs $26,555. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Show your work to justify your answer.
Answer:
$13
Step-by-step explanation:
$26,555 ÷ 36 = 737.6388889 ≈ $738 per month
36 × 738 = $26,568
= $13
Answer:
$13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
Step-by-step explanation:
We are given the following in the question:
Total cost of car = $26,555
Number of equal installments made = 36
Payment of 1 installment =
[tex]\displaystyle\frac{\text{Toatl cost}}{\text{Number of installments}} = \frac{26555}{36} = 737.6389\$[/tex]
Rounding of to nearest whole number, payment of one installment = $738
Value of 36 installments of $738 each =
[tex]36\times 738 = 26568\$[/tex]
Money overpaid after 6 months =
[tex]26568 - 26555 = 13\$[/tex]
Thus, $13 will be overpaid after 36 months if payments are rounded of to nearest whole number dollar.
Which of the following fractions are less than or equal to 0.66? Select all that apply.
D 9/14
C 33/50
A 3/7
B 4/9
All of them
Step-by-step explanation:A. 3/7 ≈ 0.43
B. 4/9 ≈ 0.44
C. 33/50 = 0.66
D. 9/14 ≈ 0.64
All of the above numbers are 0.66 or less.
Annie was given two pieces of information and must write the equation of a line crosses the y-axis at the point (0,5) and has a slope of -4 what is the equation of the line?
A) y = 5x - 4
B) y = -5x + 4
C) y = 4x - 5
D) y = -4x + 5
Answer:
D) y = -4x + 5
Step-by-step explanation:
We know a point and a slope. The point is a special point. It is the y intercept because x = 0. We can use the equation for a line in slope intercept form
y= mx+b
where m is the slope = -4
and b is the y intercept = 5
y = -4x+5
The equation of the line that crosses the y-axis at the point (0,5) and has a slope of -4 is y = -4x + 5. This is found by using the formula of the slope-intercept form of a line, substituting -4 for the slope and 5 for the y-intercept.
Explanation:To find the equation of the line which crosses the y-axis at the point (0,5) and has a slope of -4, we need to use the formula of slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
The slope, m, is given as -4. The y-intercept, b, is where x=0, thus is the y-value of the line where it crosses the y-axis. The point provided (0,5) indicates that b=5.
By substituting the slope and y-intercept into the equation, we get y = -4x + 5. So, the equation of the line is y = -4x + 5. Consequently, the correct answer is D) y = -4x + 5.
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In kite JKLM , MJ=JK and ML=KL . Diagonals JL¯¯¯¯¯ and MK¯¯¯¯¯¯¯ intersect at point P, m∠MLK=48∘ , and m∠JKM=30∘ . What is m∠JML ?
Answer:
96°
Step-by-step explanation:
ΔKLM is isosceles, so base angle KML will be half the supplement of ∠MLK, or ...
.... ∠KML = (180° -48°)/2 = 66°
ΔKJM is also isosceles, so base angle JMK will be the same measure as ∠JKM, 30°.
∠JML = ∠JMK + ∠KML = 30° +66°
∠JML = 96°