Given:
Total number of coins (Quarters and dimes) = 60
Total amount = $12.45
To find:
The number of quarters and dimes.
Solution:
Let x be the number of quarters and y be the number of dimes.
We know that,
1 quarter = 0.25 dollar
1 dime = 0.10 dollar
Total coins: [tex]x+y=60[/tex] ...(i)
Total amount: [tex]0.25x+0.10y=12.45[/tex] ...(ii)
From (i), we get
[tex]y=60-x[/tex] ...(iii)
Putting this value in (ii), we get
[tex]0.25x+0.10(60-x)=12.45[/tex]
[tex]0.25x+6-0.10x=12.45[/tex]
[tex]0.25x-0.10x=12.45-6[/tex]
[tex]0.15x=6.45[/tex]
Divide both sides by 0.15.
[tex]x=\dfrac{6.45}{0.15}[/tex]
[tex]x=43[/tex]
Putting x=43 in (iii), we get
[tex]y=60-43[/tex]
[tex]y=17[/tex]
So, the number of quarters is 43 and the number of dimes is 17.
Therefore, the correct option is b.
6. A basketball team averaged 105 points per
game. How many points did the team score
ed
Bernd Melman Alamy
in 6 games?
What is the area of the figure. PLS I NEED THIS FAST
Answer:
252 B
Step-by-step explanation:
45 + 18 + 189
Answer:252
Step-by-step explanation:
Give one verbal expression (VE) and its equivalent algebraic expression (AE).
Example: VE: my age increased by half the age of Ellie AE: x + 1/2y
Answer:
A few examples:
VE: Three more than two times the temperature.
AE: 2x+3
VE: The money I have decreased by two thirds of the money you have.
AE: x - (2/3)y
VE: The number of friends I have increased by four times the amount of friends you have.
AE: x + 4y
Let me know if this helps!
HELPPPPPP!!!!! Classify each pair of numbered angles.
Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more than once.
Linear pair
Vertical
Adjacent
None of these
9514 1404 393
Answer:
1, 2: Vertical
5, 6: Adjacent
Step-by-step explanation:
Vertical angles are formed from opposite rays and share a vertex. Angles 1 and 2 are vertical angles.
__
Adjacent angles share a vertex and have one ray shared between them. Angles 5 and 6 are adjacent angles.
_____
Additional comment
In a polygon, interior angles that share a side of the polygon are also called adjacent angles..
Amanda is researching her ancestry. She records names and birth dates for her parents, their parents and so on, in an online research tool. If she can locate all of the information, how many names will Amanda record in the generation that is 5 generations before her?
Answer:
Step-by-step explanation:
Amanda will record 32 names for the five previous generations.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Amanda is researching her ancestry. She records names and birth dates for her parents, their parents and so on, in an online research tool.
We can write the series as -
Amanda
{M} {F}
{M} {F} {M} {F}
.
.
so on
We can write the sequence as -
2, 4, 8, ....
It is a geometric sequence. For n = 5, we can write -
a(5) = arⁿ⁻¹
a(5) = 2 x (2)⁴
a(5) = 2⁵
a(5) = 2 x 2 x 2 x 2 x 2
a(5) = 32
Therefore, she will record 32 names for the five previous generations.
To solve more questions on functions, expressions and polynomials, visit the link below -
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f(x) = 7x² + 21x - 70
factor
Answer:
Step-by-step explanation:
f(x)=7(x^2+3x-10)=7(x+2)(x-5)
a boat travels 438 km in 8 hours with a constant speed, how far can it travel in 5 hours
Answer:
its the first one
Step-by-step explanation:
You jog 3 kilometers in 12 minutes.
At this rate, how long will it take you to complete a 7-kilometer race?
Answer:
It will take 28 minutes to complete a 7-kilometer race
Step-by-step explanation:
If you can job 3 kilometers in 12 minutes, that means you can jog 1 kilometer in 4 minutes. so if you multiply 7 times 4, you would get 28. So your answer is 28 minutes.
Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 55% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 15% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis. (Round your answer to three decimal places.)
Answer:
0.71 = 71% probability that she or he used the lab on a regular basis.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Student got an A
Event B: Used the lab on a regular basis.
Probability of an student getting an A:
55% of 40%(go to the lab on a regular basis).
15% of 100 - 40 = 60%(do not go to the lab on a regular basis).
So
[tex]P(A) = 0.55*0.4 + 0.15*0.6 = 0.31[/tex]
Probability of getting an A and using the lab on a regular basis:
55% of 40%, so:
[tex]P(A \cap B) = 0.55*0.4 = 0.22[/tex]
Probability that she or he used the lab on a regular basis.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.22}{0.31} = 0.71[/tex]
0.71 = 71% probability that she or he used the lab on a regular basis.
find the slope and the y intercept
Y=1/3x + 2
Answer:
m = 1/3, b = 2
Step-by-step explanation:
The equation is already written is slope-intercept form, y = m x + b.
Kristin has 3 2/3 yards of plaid ribbon. She has 2 5/6 yards of polka-dot ribbon.
Part A
Estimate how many yards of ribbon Kristin has in all.
I don't know :/ sorry hold on wait
Evaluate 2x + 9y -9, when x= 6 and y= 6
Answer:
57
Step-by-step explanation:
2x + 9y -9
2(6) + 9(6) - 9
12 + 54 - 9 = 57
good luck, i hope this helps :)
Answer:
57
Step-by-step explanation:
2*6+9*6-9=
12+54-9=
66-9=
57
PLEASE HELP TIMED
Do you want to install the updates
Understanding Expressions
Assignment
Active
Explaining Algebraic Expressions
o
Describe the parts of this algebraic expression using the
lesson's vocabulary.
-x+102-3x+y
Done
· 00000000
9 of 10
1. Javier scored 78% on the test. Write this
percent as a fraction in simplest form and
as a decimal.
Answer:39/50
Step-by-step explanation:
Please help me!! Thank you!!
Answer:
[tex]Solution,\\PQ = \sqrt{(1-3)^2+(3-1)^2} = \sqrt{2^2+2^2} = \sqrt{8} = 2\sqrt{2} \\P'Q' = \sqrt{(3-9)^2+(9-3)^2} = \sqrt{6^2+6^2} = \sqrt{72} = 6\sqrt{2}\\Also,\\RQ = \sqrt{(1-3)^2+(1-1)^2} = \sqrt{2^2} = 2\\R'Q' = \sqrt{(3-9)^2+(3-3)^2} = \sqrt{6^2} =6\\Again,\\PR = \sqrt{(1-1)^2+(3-1)^2} = \sqrt{2^2}=2\\P'R' = \sqrt{(3-3)^2+(9-3)^2} = \sqrt{6^2} = 6\\Here, P'R' = 3PR, P'Q'=3PQ ~and~ Q'R'=3RQ~\\In~other~words~each~side~of~triangle~P'Q'R' ~is~three~times~the~length~of~triangle~PQR.\\[/tex][tex]So,~the~algebraic~rule~of~diliation(enlargement)~is~(x,y)----(3x,3y)[/tex]
If my answer did not help you, comment below but please don't delete it.
Use order of operations to simplify 6 squared - (5 -4) + 2( 8 - 2 squared) divided by 8
Determine the MEDIAN of the following numbers: 8, 11, 11, 12, 13, 15, 16, 16,
18, 21
15
13
14
21
Answer:
Step-by-step explanation:
Determining Median is super easy!
1. Order the numbers, in ascending order.
8, 11, 11, 12, 13, 15, 16, 16, 18, 21
2. Cross off one number from both ends until you reach the middle number, whether you're left with one or two.
11, 11, 12, 13, 15, 16, 16, 18
11, 12, 13, 15, 16, 16
12, 13, 15, 16
13, 15
3. Determine the average of these two numbers.
(13 + 15) / 2
28 / 2
14
The median for this set of data is 14.
P.S. the average only needs to be calculated when left with two numbers, if you are left with only one, that number is your answer!
Hope this helps :)
Answer:
The median of the following numbers is 14
Step-by-step explanation:
the range for a list of numbers is 7. the smallest value is 4. what is the largest value in the list
Answer:
7
Step-by-step explanation:
The largest value in the list is 11.
What is list?A list is a structure consisting of an ordered set of numbers.
What is the range?"The range is the difference between the smallest and highest numbers in a list."
For given example,
The range for the given list is 7 and the smallest value is 4.
Let R be the range of the list.
⇒ R = 7
Let S be the smallest value in the list.
⇒ S = 4
Let the largest value in the list be L.
⇒ R = L - S
⇒ 7 = L - 4
⇒ L = 7 + 4
⇒ L = 11
Therefore, the largest value in the list is 11.
Learn more about the range of the list here:
https://brainly.com/question/14814262
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Find the distance between the two points rounding to the nearest tenth (8,−9) and (2,−7)
Answer:
negative 7 is first then comes 2. negative 9 is first then comes 8.
Step-by-step explanation:
Answer:
6.3
Step-by-step explanation:
PLS HELP !!! I need this question done quick
Answer:
a. 17 b. 51
Step-by-step explanation:
Follow Order of Operations (PEMDAS):
Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
a. 9 + 4² - (4-2) • 4
9 + 4² - (4-2) • 4 –––Start with (4-2) = 2 (parentheses)
9 + 4² - 2 • 4 ––– 4² (exponents)
9 + 16 - 2 • 4 ––– 2 • 4 (multiplication)
9 + 16 - 8 ––– 9 + 16 (addition)
25 - 8 ––– 25 - 8 (subtraction)
17
b. 15 - 4 + 2(7-3) • 5
15 - 4 + 2(7-3) • 5 ––– Start with 2(7-3)
~ Note: this can be done using distributive property (2•7 - 2•3) OR solving the parentheses first and then multiplying 2(4). Both get 8 and same end result.
15 - 4 + 8 • 5 ––– 8 • 5 (multiplication)
15 - 4 + 40 ––– 15 - 4 (subtraction) *Note: Subtraction and addition are interchangeable in the order because you do it left to right*
11 + 40 ––– 11 + 40 (addition)
51
Answer:
(a. 7) (b. 51)
Step-by-step explanation:
A.
[tex]9 + 4^{2} - (4-2) * 4\\\\9 + 4^{2} - (2) * 4\\9 + 16 - 2 * 4\\9 + 16 - 8\\25 - 8\\17 \\[/tex]
B.
[tex]15 - 4 + 2 (7 - 3) * 5\\15 - 4 + 2 (4) * 5\\15-4+(2*4*5 )\\15-4+40\\11 + 40\\51[/tex]
(I don't know the numerical values)
Look at the formula for finding distance. Which of the following is the formula to find time? [picture included]
Answer:
A.
Step-by-step explanation:
Answer:
[tex] \huge \: \boxed { \boxed{ \red{ a)t = \frac{d}{r}}}}[/tex]Step-by-step explanation:
to understand thisyou need to know about:equationPEMDASgiven:[tex]d = rt[/tex]to find[tex]t[/tex]let's solve:[tex]step - 1 :define[/tex]
[tex]d = rt[/tex]
[tex]step - 2 : solve[/tex]
[tex]rewrite : \\ rt = d[/tex][tex]divide \: both \: sides \: by \: r : \\ \frac{rt}{r} = \frac{d}{r} [/tex][tex]simplify : \\ t = \frac{d}{r} [/tex][tex] \huge \: \boxed { \boxed{ \red{ \therefore t = \frac{d}{r}}}}[/tex]
Raul started a plant garden and started collecting lots of soil to grow his plants. His supply of soil grows by 8% per week. If he starts with 14 kg of soil, how much does he have after 16 weeks? Round your answer to the nearest hundredth (two decimal places). I
Please help me
-(8x)^2
-x/4=3
-8x-5=35
-4(z+7)=36
Help pls !!! Answer u don’t have to explain
Answer:
B
Step-by-step explanation:
6 miles............
HELP
Write an equation in slope-intercept form for a line with a slope of -2 and a 8 points
y-intercept of 7. *
Answer:
y=-2x+7
Step-by-step explanation:
slope intercept form is equal to y=mx+c
where y is the y value
x is the x value
m is the gradient
and c is the y intercept
so the equation for this set of values is equal to
y=-2x+7
slope will be the m
and b is the y intercept
y=mx+b
y=-2x+7
Select all that may be correct
Answer:
Option (2) and Option (6)
Step-by-step explanation:
Expression representing the error can be given by,
Expected value = Original value ± percentage error
If original value of the ice cream filled in the container = 64 ounce
Percentage error to fill the ice cream in each container = 1.5%
So net error = ± 1.5% of 64
= [tex]64(\frac{1.5}{100})[/tex] ounce
= 64(0.015) ounce
Therefore, expression that can show the maximum maximum amount of ice cream in the container will be
= 64 + 64(0.015) Option (6)
= 64(1 + 0.015)
= 64(1.015) Option (2)
Therefore, Option (2) and Option (6) are the correct options.
$1900 at 9 for 2 years
Answer:
$342
Step-by-step explanation:
Complete question
Find the simple interest on $1900 at 9% for 2 years.
Simple interest PRT/100
Given
Principal P = 1900
Rate R = 9%
Time T = 2years
Substitute
Simple interest = 1900*9*2/100
Simple interest = 19*18
Simple interest = $342
Hence the simple interest on $1900 at 9% for 2 years is $342
help me out not all just what you can
9514 1404 393
Answer:
1e. 2t² +8t -6
2h. a² +2ab -3b²
3b. 8r +4
4b. 6x +4y -11
5b. e -3
Step-by-step explanation:
1e. Combine like terms.
(3t² +3t -6) +(-t² +5t) = t²(3 -1) +t(3 +5) -6
= 2t² +8t -6
__
2h. (2a² +3ab -4b²) -(a² +ab -b²)
Use the distributive property to eliminate parentheses. Note that all signs change in the second set of parentheses.
= 2a² +3ab -4b² -a² -ab +b² = a²(2 -1) +ab(3 -1) +b²(-4+1)
= a² +2ab -3b²
__
3b. The hash marks indicate sides of the same length. The perimeter is the sum of all side lengths.
P = (4r -2) +2(2r +3)
P = 4r -2 +4r +6 . . . . . . eliminate parentheses
P = 8r +4 . . . . . . . . . . . . combine like terms
__
4b. (3x +4y) +(5x -8) -(2x +3)
Note that the distributive property changes the sign of all terms in the last parentheses.
= 3x +4y +5x -8 -2x -3 . . . . eliminate parentheses
= x(3+5-2) +y(4) +(-8-3) . . . group like terms
= 6x +4y -11
__
5b.
Bill's age - Erin's age = (2e-3) -(e) = e -3
The difference in their ages is (e -3).
Given a point translated from A(1,2) to B(4,4). If a point C at (0,0) is translated in the same way, what will be its new endpoints?
A.(−3,−2)
B.(3,2)
C.(2,2)
D.(3,3)
please help
Answer:
B. (3,2)
Step-by-step explanation:
Step 1) When shifting from A(1,2) to B(4,4), the point shifted 3 units to the right (which means x=3) and 2 units upwards (which means y=2).
Step 2) So when you apply the same movements to point C(0,0), the new point will be (3,2).
See the diagram below. Step 1 is the graph on the left. Step 2 is the graph on the right. The movement is colored in green. Hope this helps!
2. Do the representations below define a function? *
10
1
10
2
10
3
10
4
Yes, it is a function,
No, it is not a function,
Answer:
No it is not a function for sure.