Answer:
a) $160
b) $116.50
Step-by-step explanation:
a) Let the original price of the yellow bicycle be $x.
Since both has the same original price,
original price of yellow bicycle= 100% x
original price of green bicycle= 100% x
Discounted price of yellow bicycle
= (100% -25%) x
= 75% x
Discounted price of green bicycle
= (100% -30%) x
= 70% x
Difference in cost
= 75%x -70%x
= 5% x -----(1)
From 2nd paragraph:
Discounted price of yellow bicycle
= Kyreen's money +3.50
Discounted price of green bicycle
= Kyreen's money -4.50
Difference in cost
= (Kyreen's money +3.50) -(Kyreen's money -4.50)
= Kyreen's money +3.50 -Kyreen's money +4.50
= 3.50 +4.50
= 8.00 -----(2)
Equating (1) and (2) together:
5% x= 8.00
\( \frac{5}{100} x = 8\)
\(x = 8 \div \frac{5}{100} \)
\(x = 8 \times \frac{100}{5} \)
x= 8 ×20
x= 160
Thus, the original price of the yellow bicycle is $160.
_______
b) Amount Kyreen has at first
= discounted price of yellow bicycle -$3.50
= 75%($160) -$3.50
= $120 -$3.50
= $116.50
There will be 175 guests at a wedding. Instead of a wedding cake, the bride wants to serve cheesecake. If each cheesecake serves 12 people, how many should she order?
Answer:
She should order 15 cakes.
Step-by-step explanation:
175/12=14.58
We can't have part of a cake, so round to 15, so we have extra!
Answer:
15
Step-by-step explanation:
14.58 actually but if you round(which is better) it's 15
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Which complex number has a distance of √ 17 from the origin on the complex plane? 2 + 15i 17 + i 20 – 3i 4 – i
Answer:
4-i
Step-by-step explanation:
Answer:
4 - i
Step-by-step explanation:
took the quiz
A movie theatre currently has 49 empty seats. 3
people enter every minute to fill those seats. The
scenario is modeled by the arithmetic sequence
= 46 − 3( − 1)
The number of empty seats based on the arithmetic sequence in 6 minutes is 28.
How to illustrate the information?It should be noted that an expression simply means the function that's given to show the relationship between the variables.
From the information, the movie theatre currently has 49 empty seats. 3 people enter every minute to fill those seats. The scenario is modeled by the arithmetic sequence:
= 46 − 3m.
In this case m = number or minutes.
The empty seats in 6 minutes will be:
= 46 - 3m
= 46 - 3(6)
= 46 - 18
= 28
There are 28 empty seats.
The complete question is written below.
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A movie theatre currently has 49 empty seats. 3 people enter every minute to fill those seats. The scenario is modeled by the arithmetic sequence
= 46 − 3m. Find the numberof empty seats in 6 minutes.
find the distance between each pair of points. (5, -6) and (2, -6)
Answer:
The distance between the two points is 3 units
Step-by-step explanation:
5-2=3
The distance between (5, -6) and (2, -6) is 3 units.
what is Distance Formula?Distance Formula to find distance between two points (a, b) and (c, d) is D = √(c-a)² + ( d- b)²
The distance formula to find the distance of a point P(a, b) from the origin O(0,0) is D = √((a² + b²).
Given:
(5, -6) and (2, -6)
now, if there are two points (a, b) and (c, d) then the distance is
d= √(c-a)² + ( d- b)²
Then, d= √(2-5)² + (-6+ 6)²
d= √ 9+ 0
d= 3
Hence, the distance between two points is 3 units.
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0.58 kilogram of flour each day for 4 weeks. How many grams did Destiny use in those 4 weeks?
1 kg = 1,000 g
Answer: 28.58
Step-by-step explanation: you find 7x4 which is 28 and then 28 + 0.58 and that gives you 28.58
f: A → B, f(x) = (x−2)/3 and B=[-1;2); A=?
A) [-1;4)
B) [-2;3)
C) [-1;8)
D) (-4;1]
Step-by-step explanation:
so, we need to find the x values (A) that create the defined result values (f(x)) of B.
so, when taking the lower interval limit of B as the first f(x), we get
-1 = (x-2)/3
-3 = x - 2
-1 = x
so, the lower interval limit for A is also -1.
-1 as input value for the function delivers also -1 as functional result.
now for the upper limit :
2 = (x-2)/3
6 = x - 2
8 = x
so, the upper interval limit for A is 8.
and since the limit is excluded for B, it is also excluded for A.
so, C) is the correct answer.
how long will it take for the battery to run down one sixth of its capacity of 3600 Milli Ampere hours
Answer:
6 hours
Step-by-step explanation:
\(\frac{1}{6}\) of Total battery life = \(\frac{1}{6} * 3600 = 600\)milliamps
Assuming the battery takes 100 Milliamps per hour,
Time = Battery Capacity / Current hours
Time = 600 / 100 Mah = 6H
difer from the true proportion by more than 2% ? A previous study indicates that the proportion of lefthanded sclontists is 9%. Round up to the nearest whicie number. Duestion 13 A. 1.218 B. 1,109 C. 14 D.767
The total number of samples will be 1109 .
Given ,
Margin of error 0.02
Here,
According to the formula,
\(Z_{\alpha /2} \sqrt{pq/n}\)
Here,
p = proportions of scientist that are left handed
p = 0.09
n = number of sample to be taken
Substitute the values,
\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)
n ≈1109
Thus the number of samples to be taken will be approximately 1109 .
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4 ÷ 5/7 Give your answer as a mixed number in its simplest form.
Answer:
5.6
Step-by-step explanation:
4 ÷ 5/7
is 4 divide 5 over 7
which is 5.6
93) Calculator exercise. Select Float 4 in Document Settings. Store 0.00102 in variable A. See the contents of A = 0.001. How many significant figures in 0.001? How many significant figures in 0.00102? The HW system requires 3 sig. figs. for 1% accuracy. ans: 2
Since the HW system requires 3 significant figures for 1% accuracy, the number 0.00102 with three significant figures satisfies the requirement.
How many significant figures are there in the number 0.001? How many significant figures are there in the number 0.00102? (Enter the number of significant figures for each number separated by a comma.)In the number 0.001, there are two significant figures: "1" and "2".
The zeros before the "1" are not considered significant because they act as placeholders.
Therefore, the significant figures in 0.001 are "1" and "2".
In the number 0.00102, there are three significant figures: "1", "0", and "2".
All three digits are considered significant because they convey meaningful information about the value.
Therefore, the significant figures in 0.00102 are "1", "0", and "2".
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Find the measure of the missing angles h,g and m,k
Give the degrees 119 and 121
The missing angles in degrees are-
∠k = 61°∠m = 119°∠g = 29°∠h = 151°What is defined as the vertically opposite angles?Vertically opposite angles are produced by two straight intersecting lines that are exact reverse one another at a specific vertex. Angles that are vertically opposite each other are equal. These are sometimes referred to as vertical angles.In the given figure;
∠g = 29°, as ∠g and ∠29° are vertically opposite to each other. Both will be equal.
Similarly,
∠k = 61°, as ∠k and ∠61° re vertically opposite to each other. Both will be equal.
What is defined as the linear pair?When 2 lines intersect at a single point, a linear set of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is indeed 180°.From the linear pair;
∠h + ∠g = 180
∠h = 180 - 29
∠h = 151°
Similarly,
∠m + ∠k = 180
∠m = 180 - 61
∠h = 119°
Thus, the missing values of the angles are found.
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Help due tomorrow would highly appreciate this.
The value of the part of side of triangle given as x is equal to 11/3 in simplified fraction.
What is fraction?
A fraction is referred to as the part of something a whole in maths. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter (¼). Fractions can make calculations faster and easier through making it easier to distribute and judge different numbers. The depiction of fractions appears easier than when decimal values are used.
As given in the question, in the given triangle DE is parallel to AC,
It implies that the ration of the sides are equal.
i.e. AD/DB = CE/EB
Putting the value from the figure given in the question,
we get,
11/x = 9/3
11/x = 3
x = 11/3
Therefore, The value of the x is 11/3 in the form of simplified fraction.
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the top and bottom margins of a poster are 2 cm and the side margins are each 12 cm. if the area of printed material on the poster is fixed at 778 square centimeters, find the dimensions of the poster with the smallest area.
The dimensions of the poster with the smallest area is (\(12\sqrt{389} +24\)) units width and (\(\sqrt{389} /6+4\)) units height.
It is a measurement of a point or line extended in one direction, according to the notion of dimension. Each shape we see has a few dimensions.
The statement indicating the powers to which the fundamental units are to be increased in order to obtain one unit of a derived quantity is known as the dimensional formula of any quantity. The formulation for any physical quantity Q's dimensional formula is given by,
Dimensional Formula: Q = \(M^{a}L^{b}T^{c}\)
The area of printable area is wh.
wh = 778
Due to margins on both sides, the poster is w + 2*12 wide and h + 2*2 tall.
We want to reduce the poster's size =
(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)
Wh = 778, thus we can replace it with h = 778/w.
Then, A = (w + 24)(778/w + 4)is the poster's size, which we aim to reduce.
(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =
4w + 874 + 18672/w
We minimize this by calculating
the formula dA/dw = 4 - 18672/w2 and setting it to 0
\(4-18672/w^{2} =0\)
\(4w^{2} =18672\)
\(w^{2} =18672/4\)
\(w=\sqrt{4668}=12\sqrt{389}\)
\(h=778/(12\sqrt{389} )=\sqrt{389} /6\\\)
Keep in mind that the margins' ratio matches that of h and w.
In due to the fact that the problem requests the poster's width and height,
Width = \(12\sqrt{389} +24\)
Height = \(\sqrt{389} /6+4\)
Thus, the width is (\(12\sqrt{389} +24\)) units and the height is (\(\sqrt{389} /6+4\)) units.
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The principal of a high school wants to gather opinions from the parents of students at his school. He starts with the 2nd name in the Parents Teacher Association (PTA) phone handbook and then selects every 5th name in the directory. The 2nd, 7th, 12th, … names in the directory are chosen for his sample. This is an example of a/an ___________ sample.
Answer:
It is systematic sampling.
What is the circumference in centimeters the circle is 24 centemeters in diamater
Answer:
75.398 cm to the nearest thousandth.
Step-by-step explanation:
Circumference = π * diemeter
= 24π
= 75.3982 cm
Someone help, AA, SAS, SSS NOT SIMILAR?!!!
Answer:
answer is AA criteria
hope it helps.
Answer:
aa
Step-by-step explanation:
its aa because the tringle degree on top is 50 degrese for both
Find the slope PERPENDICULAR to line AB
HELP QUICK ASAP!!!!!!!!!!!!!!
Answer:
1/3
Step-by-step explanation:
there are 3 ways to draw a black sock. because there are 9 socks in all you put the sock you drew first back the chance is 3/9 or 1/3
In a pack of Skittles, 20% are red. If 13 are red, how many skittles were in the entire bag?
Answer: 65
Step-by-step explanation:
First we need to know what the 13 is 20% of. 13 is 20% of 65.
To make sure we are correct we must take 20% of the 65 which gives us 13 showing that 20% of the 65 skittles (13) are red.
Hope that helped :)
prove that x = 0 is the only solution to ax = 0 if and only if the rank of the p ×q matrix a equals q, the number of unknowns.
The statement that x = 0 is the only solution to ax = 0 if and only if the rank of the p × q matrix a equals q, the number of unknowns, can be proven as follows:
First, assume that x = 0 is the only solution to ax = 0. This means that there are no nonzero solutions to the equation, implying that the null space of the matrix a is trivial (only containing the zero vector). By the rank-nullity theorem, the nullity of a matrix is equal to the dimension of its null space. Since the null space of a is trivial, its nullity is zero.
Next, consider the rank of the matrix a. By the rank-nullity theorem, the rank of a plus its nullity is equal to the number of columns in a, which is q. Therefore, if the nullity is zero, the rank of a must be equal to q.
Conversely, if the rank of the matrix a equals q, it implies that the nullity of a is zero. This means that the only solution to the equation ax = 0 is the zero vector, x = 0.
x = 0 is the only solution to ax = 0 if and only if the rank of the matrix a equals q, the number of unknowns. This result highlights the relationship between the null space and the rank of a matrix, providing insights into the solutions of linear equations and the properties of the matrix.
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What is the solution to this system of equations? 3.2 x 0.5 y = 4.2. negative 1.6 x minus 0.5 y = 3.4. (4.75, 38.8) (4.75, negative 22) no solution infinitely many solutions
The solution to the system of equation is (4.75, -11)
3.2x + 0.5y = 4.2
-1.6x -0.5y = 3.4
How to solve system of equation?
3.2x + 0.5y = 4.2
-1.6x -0.5y = 3.4
add equation(i) to equation(ii)
Therefore,
1.6x = 7.6
divide both sides by 1.6
x = 7.6 / 1.6
x = 4.75
Therefore,
3.2(4.75) + 0.5y = 4.2
0.5y = 4.2 - 15.2
0.5y = -11
y = - 11 / 0.5
y = - 22
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Answer:
The solution is x=4.75 and y = -22
Step-by-step explanation:
To find the solution to the system of equations, we will follow the steps below:
3.2x + 0.5y = 4.2 --------------------------------------------------------------------------(1)
-1.6x -0.5y = 3.4 ----------------------------------------------------------------------------(2)
add equation (1) and equation (2)
1.6x =7.6
Divide both-side of the equation by 1.6 to get the value of x
1.6x /1.6 =7.6/1.6
x =4.75
substitute x = 4.75 into equation (1) and solve for y
3.2(4.75) + 0.5y = 4.2
15.2 + 0.5y = 4.2
subtract 15.2 from both-side of the equation
15.2 - 15.2 + 0.5y = 4.2-15.2
0.5y = -11
Divide both-side of the equation by 0.5
0.5y/0.5 = -11/0.5
y = -22
The solution is x=4.75 and y = -22
For any positive integer n, the sum of the first n positive integers equals n ( n 1 ) 2 . What is the sum of all the even integers between 99 and 301
Answer:
The sum of all the even integers between 99 and 301 is 20200
Step-by-step explanation:
For the sum of all the even integers between 99 and 301, this can be calculated using the formula for Sum of n terms in an Arithmetic Progression (AP)
Sum of n terms in an AP \(S_{n}\)= \(\frac{n }{2}[ 2a + (n - 1)d]\)
Where \(n\) is the number of terms
\(a\) is the first term
and \(d\) is the common difference
The AP for the sum of all the even integers between 99 and 301 will look like
100 + 102 + 104 + ... + 300
\(a\) = 100
\(d\) can be calculated by taking the difference of the first two terms or any two consecutive terms of the AP
Hence, \(d\) = 102 - 100 = 2
\(n\) can be determined from the formula used to calculate the Last term of an AP
\(l = a + (n - 1)d\)
Where \(l\) is the last term
In the AP, the last term, \(l\) = 300
Then
\(300 = 100 + (n - 1)2\\300 - 100 = (n - 1)2\\200 = (n - 1) 2\\(n - 1) = 200 / 2\\n - 1 = 100\\n = 100 + 1\\n = 101\)
Hence, there are 101 terms in the AP
Now, to determine the sum
\(S_{n}\)= \(\frac{n }{2}[ 2a + (n - 1)d]\)
\(S_{n} =\frac{101}{2}[ 2(100) + (101 - 1)2]\\ S_{n}=\frac{101}{2}[ 200 + (100)2]\\ S_{n}=\frac{101}{2}[ 200 + 200]\\S_{n}=\frac{101}{2}[ 400]\\S_{n} = 20200\)
Hence, the sum of all the even integers between 99 and 301 is 20200
25) A father is twice as old as his son. The sum oth of the ages is 99 years. Find their ages.
Answer:
If the son’s age is x, the father’s age is 2x.
If the son’s age is x, the father’s age is 2x.Ten years ago:
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 52
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 52
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 24
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.
Hope this answer helps you..!!.
.
Select this answer as the BRAINLIESTBetween 10 pm and 7:45 am the water level in a swimming pool decreased by 3/16 inches
The rate of change of the level of the swimming pool is -0.019 inches per hour.
How to get the rate of change in the level of the swimming pool?
The rate of change will be given by the quotient between the change in the level of the water (-3/16 inches) and the time in which that change happens.
We know that the change happens between 10 pm and 7:45pm, so the number of hours is:
2 hours + 7 hours + 45 min
Where:
1 hour = 60 min
45 min = 45/60 hours = 0.75 hour
Then the total time is:
2h + 7h + 0.75h = 9.75h
Then the rate of change is:
R = (-3/16 inches)/(9.75 h) = -0.019 inches per hour.
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Guided Practice
Which property justifies the first step in solving this equation ?
\(\frac{x}{5}\)+9=11
\(\frac{x}{5}\)+9−9=11−9
A.
Substitution Property of Equality
B.
Addition Property of Equality
C.
Subtraction Property of Equality
Answer:
a subtraction
Step-by-step explanation:
C.
Subtraction Property of Equality
what is the percentage decrease of $420 being the original price and new price being $280?
Step-by-step explanation:
since$420 is the original price then it's 100%
then to find the %decrease, $420-$280=$140
if, 100%=420
then x%=140
14000/420=x
x=33.3%
can someone please help me, I don’t understand this
Answer:
To find the circumference
diameter x 3.14 = circumference
We can undo the multiplication and divide to get the diameter
37.68 /3.14 = 12
diameter / 2= radius
12 / 2 = 6
the radius is 6
radius x radius x pi = area
6 x 6 x 3.14 = 113.04
113.04 is the answer
Hope this helps
Step-by-step explanation:
Answer:
113.04 square inches.
Step-by-step explanation:
The formula to find the circumference is 2πr. The formula for the area is πr^2. We are trying to find r in order to solve the problem.
It says use 3.14 for π. The circumference is 37.68 inches.
2πr = 37.68
2 * 3.14r = 37.68
3.14r = 18.84
r = 6
Now that we know the radius of the circle, we can find the area!
πr^2 = 3.14 * (6^2) = 3.14 * 36 = 113.04.
Hope this helps!
A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.8 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour.
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 8.75 miles in 7 hours.
No, it is not proportional because 2.5 miles in 2 hours is not equivalent to 7.5 miles in 6 hours.
Option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.
From the data given:
Ratio = distance/time
2.5 / 2 = 1.25 miles per hour
7.5 / 6 = 1.25 miles per hour
8.75 / 7 = 1.25 miles per hour
Thus, option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.
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hey! i’ll give brainliest please help
Answer:
conjunction
Step-by-step explanation:
Answer:
Conjunction is correct answer. (I think)