The number of $1, $5 and $10 are 49, 44 and 22 respectively.
How to use equation to find the number of bills?There are 3 denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills.
let
x = number of $1 bills
Hence,
number of $5 bills = x - 5
There are half as many $10-bills as $5-bills.
number of $10 bills = 1 / 2 (x - 5)
Therefore,
x + x - 5 + 1 / 2 (x - 5) = 115
2x - 5 + 1 / 2 x - 5 / 2 = 115
2x + 1 / 2 x - 5 - 5 / 2 = 115
5 / 2 x - 7.5 = 115
2.5x = 115 + 7.5
x = 122.5 / 2.5
x = 49
Number of $1 bills = 49
Number of $5 bills = 49 - 5 = 44
Number of $10 bills = 1 / 2 (49 - 5) = 22
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Juliana is training to run a marathon. in her second week of training she ran 13 km more than she did during her first week of training. she ran a total of 145 km during the first two weeks of training. how far did she run during her first week of training?
Suppose a researcher conducts an A-B-A-B study. She records baseline observations and then administers a treatment and records behavior during treatment. What will she do next
If we suppose a researcher conducts an A-B-A-B study. She records baseline observations and then administers a treatment and records behavior during treatment. Her next step would be administering the treatment again.
Reason Behind the Next Step of the Study
It is given the the researcher conducts an A-B-A-B study.
Her first step was recording the baseline observations.
Hence, first A indicates the first step here that is, recording the observations
In the next step of the study, she administers a treatment.
Thus, B denotes the administering treatment step.
Again, for the third step of the study, she again records behavior during the treatment.
This is again denoted by A.
Hence, we can conclude that in the A-B-A-B study, A denotes recording observation or behavior, B denotes administering a treatment.
Now, since, A, B, and A steps of the study have already been followed, the next phase is B which is concerned with reintroducing or re-administering the treatment.
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PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP
Answer:
We multiply by 2 and add 4
Step-by-step explanation:
To find the pattern, we find the slope
m = ( y2-y1)/(x2-x1)
m = ( 10-6)/(3-1)
m = 4/2
m =2
We are multiplying by 2
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Using the point (1,6)
6 = 2(1)+b
6 = 2+b
The y intercept is 4
y = 2x+4
We multiply by 2 and add 4
My Uncle ordered 5 Pizzas, we were 20 people in all. I was just thinking how many pieces of
Pizza will each one of us will get if divided equally? (Each Pizza has 8-pieces)
3. A square garden plot has an area of 24 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot
The length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft
Area of a squareArea of square = Length ²
Area of the square garden plot = 24 ft²Area of square = Length ²
24 = length ²
find the square root of both sides√24 = √length²
√24 = length
length = 4.898979485566356196394568149411782783
Approximately,
length = 4.9 ft
In radical form
length = √24
= 2√6
Therefore, the length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft
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(04.01 LC)
Which set of ordered pairs represents a function?
{(0, 1), (1, 3), (1, 5), (2, 6)}
{(0, 0), (1, 2), (2, 4), (3, 4)}
{(0, 1), (1, 2), (2, 3), (2, 4)}
{(0, 0), (0, 2), (2, 2), (2, 4)}
PLEASE HELP ASAP
ÐA in cos A = 0.7715 in degrees? (not sure if the way I worded that makes sense but yea)
The value of A such that cos A = 0.7715 is 39.5 degrees
How to solve for A in the equation cos A = 0.7715?The equation is given as:
cos A = 0.7715
Where the angle is in degrees
There are several ways to solve this equation, some of which include:
Using a scientific calculatorUsing a graph or a graphing toolUsing the cosine tableIn this case, we make use of the first option; using a scientific calculator
Recall that the equation is represented as:
cos A = 0.7715
Next, we take the arccos (or anti cosine) of the above equation.
This is represented as
arccos(cos A) = arccos(0.7715)
Evaluate the expression on the left-hand side
A = arccos(0.7715)
Evaluate the expression on the left-hand side using the scientific calculator
A = 39.5112207183
Approximate the above expression
A = 39.5
Hence, the value of A such that cos A = 0.7715 is 39.5 degrees
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JDIDJRJDJF PLS HELP IM STUCK
Step-by-step explanation:
we have
B = J + 2
as the number of laps Bill ran.
to get the number of laps Jill ran we need to transform this equation, so that we get
J = ...
or
... = J
J has to be on one side, and the rest on the other (just as it is with B = ...).
so,
B = J + 2
B - 2 = J
or
J = B - 2
hey ! we are finished already !
Type the missing number in this sequence: 4, , 144, 864, 5,184, 31,104
The missing number in the given series is 24.
What is missing number in the given sequence?Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places.
Given the series,
4, ?, 144, 864, 5184, 31104
Multiplying with 6 in each term in the given sequence.
4×6 = 24
24×6 = 144
144×6 = 864
864×6 = 5184
5184×6 = 31104
Following the above sequence, we get the 2nd term is 24.
Hence the missing number is 24.
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[tex]3y - 5x = 10[/tex]
Find the gradient of the linear relation
Isolate y
3y=5x+10y=5/3x+10/3Compare to slope intercept form y=mx+b
Slope=m=5/3
Answer:
[tex]\dfrac{5}{3}[/tex]
Step-by-step explanation:
To find the gradient (slope) of the given linear relation, use arithmetic operations to isolate y:
Given relation:
[tex]3y-5x=10[/tex]
Add 5x to both sides:
[tex]\implies 3y-5x+5x=10+5x[/tex]
[tex]\implies 3y=5x+10[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
[tex]\implies y=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
Slope-intercept form of a linear equation
[tex]y = mx+b[/tex]
where:
m is the slope (gradient)b is the y-interceptComparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.
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. [Multiples / Factors / Primes] *
What is the highest
common factor (HCF)
of 24 and 45?
Does anyone know the answer? I want to make sure I did it right. Evaluate the expression using the given values type your answer in the open box
=======================================================
Explanation:
Replace x with 4 and y with 5.
Then use the order of operations (PEMDAS) to simplify until you get a single number.
Something like 9x means "9 times x", and a similar situation happens with the 8y term as well.
---------
Here's what the steps look like:
9x + 8y
9*4 + 8*5
36 + 40
76
Therefore, 9x+8y = 76 when x = 4 and y = 5.
The point (4,5) is located on the line 9x+8y = 76
In what kind of an event does a choice made for one decision affect the choices available for
the other decisions?
Let's say you want to go on a vacation this summer because you finally saved enough money for it. While at the store to buy more hairbands (you just can't seem to figure out where they all went) you see something that you have been wanting for ages. The item is a bit on the more expensive side but you don't know when you will see it again. You decide to buy the item but you had to use some of the money planned for your trip to pay for it. But because you bought the item you now can't do all the activities you wanted on your trip.
The choice of buying the item affected your choices available on your trip.
Answer:
dependent events
Step-by-step explanation:
A sales team estimates that the number of new phones it will sell is a function of the price that it sets. It estimates that if it
sets the price at.x dollars, it will sell f(x) = 2,712 - 3x phones. Therefore, the company's revenue is x (2,712 - 3x). Find
the price x that will maximize the company's revenue.
The price x which will maximize the company's revenue is 904
How to determine the priceThe price x which will maximize the company's revenue is 240
Let
Price of the good = x
Number of goods sold = 2712- 3x
The formula for revenue is given as;
Revenue = Price × Quantity
= x( 2712 - 3x)
Expand the bracket
2712x - 3x^2
Therefore, the price x which will maximize the company's revenue will be:
2712x - 3x^2 =0
Collect like terms
3x² = 2712x
3x = 2712
Divide both side by 3
3x/3 = 2712/3
x = 904
Hence, the price x which will maximize the company's revenue is 904
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Please Help me i will give brainlist !Which of the choices below show the pre-image quadrilateral ABCD, rotated 180° about the origin?
Answer:
The first choice.
Step-by-step explanation:
The second choice is a translation and the third choice is a reflection.
25points if u solve these questions
Answer:
Step-by-step explanation:
1. yes
2. 0.048955
3. equal, not equal, less than and equal to, less than, greater than and equal to, greater than
4. 9 51/250
5. 387.5%
please answer quickly
will give brainliest for right answer
Slope-Intercept Form: y = mx + b
---Where m is the slope and b is the y-intercept
Correct Answer: y = -5/4x + 2
---Option A
Hope this helps!
Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
Using the permutation formula, the number of different options for the top three finishers is given as follows:
[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]
The order in which the players are chosen is important, as A, B, C is a different outcome than C,B,A for example, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 students will be chosen from a set of 14, hence the number of ways is:
[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]
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1)give your answer in terms of π
2) give your answer using 3.14 for π
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
Volume of a cylinderA cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes
The volume of the composite cylinder is expressed as shown below;
V = πr²h
where
r is the radius
h is the height
According to the given diagram;
V = Vl - Vs
V = π(10)²*15 - π(5)²*15
V = 1500π - 375π
V = 1125π cubic inches
If the value of π is 3.14, hence;
V = 1125(3.14) cubic inches
V = 3532.5 cubic inches
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
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I NEED ANSERS AND SOLUTIONS PLSS DUE TMR. NEED HELP
The solutions using the relevant theorems are:
13. x = −3 or x = 4
14. x = 12
15. x = 12
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6
What is the Triangle Midsegment Theorem?The midsegment of a triangle that joins two sides of a triangle divides the two sides proportionally based on the triangle midsegment theorem.
What is the Angle Bisector Theorem?
The angle bisector of a triangle, according to the angle bisector theorem divides the opposite angles sides in a proportional manner.
What is the Parallel Lines and Proportionality Theorem?The theorem states that when three or more lines that are parallel is cut across by two transversals, they are divided by the transversal proportionally.
13. Apply the angle bisector theorem:
x/3 = (x + 4)/(x + 2)
Cross multiply
x(x + 2) = 3(x + 4)
x² + 2x = 3x + 12
x² + 2x - 3x - 12 = 0
x² - x - 12 = 0
Factorize
x = −3 or x = 4
14. Apply the angle bisector theorem:
16/x = 12/9
x(12) = (16)(9)
12x = 144
x = 12
15. Apply the angle bisector theorem:
(x - 4)/6 = x/9
9(x - 4) = 6x
9x - 36 = 6x
9x - 6x = 36
3x = 36
x = 12
16. Apply the triangle midsegment theorem:
3x/(x + 4) = (x - 1)/(x - 2)
Cross multiply
3x/(x + 4) = (x - 1)/(x - 2)
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² + 3x - 4 - 3x² + 6x = 0
-2x² + 9x - 4 = 0
Factorize
x = 1/2 or x = 4
17. Apply the Parallel Lines and Proportionality Theorem:
(x + 3)/(2x + 2) = (2x + 2)/(4x - 2)
Cross multiply
4x² + 10x - 6 = 4x² + 8x + 4
4x² + 10x - 6 - 4x² - 8x - 4 = 0
2x - 10 = 0
2x = 10
x = 5
18. Apply the angle bisector theorem:
(2x + 3)/x = (x + 4)/(x - 2)
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize
x = −1 or x = 6
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Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.
What is the value of x?
9
10
14
16
The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).
We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.
Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.
We are also given that EC (a part of diagonal AC) is 8 units long.
As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).
Now, we are told that DB (a part of diagonal BD) is x - 1 units long.
To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is
(x - 1) units + (x - 1) units = 2x - 2 units.
The area of a rhombus is given by the formula:
Area = 1/2 × Product of Diagonals.
Substituting the given values, we have:
72 = 1/2 × 16 × (2x - 2).
Now, we can simplify the equation:
72 = 8x - 8.
Move the constant term to the right side:
8x = 72 + 8.
Combine the constants:
8x = 80.
Finally, solve for x by dividing both sides by 8:
x = 80 / 8 = 10.
So, the value of x is 10 units. The correct answer is B).
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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.
What is the value of x?
9
10
14
16 "--
Find the ratio of the areas of to squares whose sides are 3cm and 5cm, respectively
Answer: 9 cm² : 25 cm²
Step-by-step explanation:
The area of a square can be found with x² where x is the length of one side.
x² : x²
3² : 5²
9 : 25
9 cm² : 25 cm²
Select the correct answer from each drop-down menu.
Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.
Prove: WXYZis a square.
Using the distance formula, I found that
…
A. all four sides have a length of 5
B. all four sides have different lengths
C. only 2 sides have the same length
D. all four sides have a length of 10
Answer: A
Step-by-step explanation:
[tex]WX=\sqrt{(-1-3)^2 +(1-4)^2}=5[/tex]
Since WXYZ must be a square, all the sides must have a length of 5.
Complete the steps to solve this linear equation: 2x 9(x – 1) = 8(2x 2) – 5 1.apply the distributive property: 2x 9x– 9 = 16x 16 – 5 2.combine like terms on each side: 11x – 9 = 16x 11 3.use the subtraction property of equality to isolate the variable term: –9 = 5x 11 use the subtraction property of equality to isolate the constant: –20 = 5x 4. use the division property of equality to solve: = x
Answer:
x= 5/2
Step-by-step explanation:
Answer:
-4 =x
Step-by-step explanation:
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need help!! (check picture)
Answer:
N = 2.1
M = 4.5
Step-by-step explanation:
<p is 25 degrees. I know this because the exterior angle of p corresponds with 155. Since this is a straight angle, angle p must be 25 (180-155). Now I can use the cos and the sin of 25 to find M and N
sin 25 = N/5 multiply both sides by 5 to get
5 sin 25 = N Use your calculator put in 5 sin 25
2.1 rounded to the nearest tenth.
cos 25 = M/5 Multiply both sides by
5 cos 25 = M Use your calculator
4.5
The minor arc measures of circle Z are shown in the figure.
Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.
Use the drop-down menus to complete each statement.
Angle UZT is congruent to angle
.
Angle VZW is congruent to angle
.
The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.What is the angle about?Part A:
Angle UZT is congruent to angle TZY.
Using the image attached figure, we can see that:
∠UZT = 54°
∠TZY = 54°
Hence one can say that ∠TZY = ∠UZT are both congruent angles.
Part B:
Angle VZW is congruent to angle YZX.
Using the image attached attached, we can see that:
∠VZW = 71°
∠YZX = 71°
Hence, ∠YZX = ∠VZW are both regarded as congruent angles .
Therefore, The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.Learn more about Angles from
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Answer: a, c
Step-by-step explanation:
Two equations are shown Y equals four over X +3 and Y equals negative 2X subtract four which statement best describes the graph of the two equations
The graph for the given system of equations is shown below
Graph of System of Linear equationsFrom the question, we are to determine the graph that describes the given system equations
First, we will graph the given system of linear equations.
The given equations are
Y equals four over X +3
and
Y equals negative 2X subtract four
That is,
y = 4/(x+3)
y = -2x -4
The graph for the given system of equations is shown below
The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below
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The importance of mendel's work is that it made a connection between observed patterns of ____________ and probability.
Answer:
blank = inheritance
Step-by-step explanation:
Hope that helps
which recursive formula can be used to represent the sequence
2,6,10,14,18...?
Answer:
a(1) = 2
a(n) = a(n-1)+4
Step-by-step explanation:
Using the given arithmetic sequence,
a1 is 2
a2 is 6
a3 is 10
a4 is 14
a5 is 18
and to get from a1 to a2 you have to +4, to get from a2 to a3 you have to +4 and so on.
In a reclusive formula you need to find two pieces of information:
1. The first term of the sequence
2. The pattern rule to get any term from the term that comes before it
Using the given sequence, the first term is 2 and the rule to get any term from its previous term is +4.
So, putting that information in the form of a recursive formula will read as the following:
an+1 = an+4
a1 = 2, n is greater or equal to 1 (n is an interger)
Which can be rearranged to
a(1) = 2
a(n) = a(n-1)+4
A road sign says:
Beaston: 10 mi (17 km)
Assuming that each of these numbers is rounded to the nearest unit, what is the actual range of possible miles to Beaston? Give your answer in interval notation, rounded to 2 decimal places.
(1 mile is exactly 1.609344 kilometers.)
Based on the fact that the road sign's distance to Beaston is rounded to the nearest unit, the actual range of possible miles to Beaston is 9.50 ≤ x ≤ 10.49.
How far is it to Beaston?Based on the fact that the miles to Beaston are rounded to the nearest mile, the first thing to do is to find the lowest and highest numbers that can be rounded to 10 miles.
The lowest number that you can round to 10 miles is:
= 9.5 miles
Because of the 0.5 attached to the 9 miles, you will round up to 10 instead of down to 9.
The highest number that you can round to 10 miles at two decimal places is 10.49 miles.
The reason this is the highest is that the 0.4 is the tenths number just before 0.5. This means that you round the whole number down to 10.
Assuming the distance to Beaston is x, the interval would then be:
9.50 ≤ x ≤ 10.49.
In conclusion, the range of miles of Beaston is 9.50 ≤ x ≤ 10.49.
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