By using arithmetic progression, it can be calculated that
i) Distance she ran on 21 days = 37 km
ii) Total distance she ran in 21 days = 525 km
What is arithmetic progression?
Arithmetic progression consist of a sequence of numbers in which the difference between the consequent terms of the sequence are same.
This problem is based on arithmetic progression
Distance an athlete ran on first day = 13 km
She increases the distance she runs each day by 1.2km
So this is an arithmetic progression with first term 13 km and common difference 1.2 km
i) Distance she ran on 21 days = 13 + (21 - 1) [tex]\times[/tex] 1.2
= 37 km
ii) Total distance she ran in 21 days = [tex]\frac{21}{2}(13 + 37)[/tex] = 525 km
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Kiera's lemon cookie recipe calls for 5 cups of sugar. How much sugar would Kiera use to make 3 5/8 batches of cookies?
Answer:18 1/8
Step-by-step explanation:
5x3=15
5x5/8=25/8=3 1/8
15+3 1/8=18 1/8
x = [?]
4x-2 3x + 14
Enter the value of n so that the expression (-y + 3) + (2y - 4) is equivalent to (ny - 1).
Answer:
n=1
Step-by-step explanation:
(-y + 3) + (2y - 4) = (ny - 1)
-y + 3 + 2y - 4 = ny - 1
-y + 2y + 3 - 4 = ny - 1 -> combine like terms on the left side of the equation
y - 1 = ny - 1 ==> simplify
y - 1 + 1 = ny - 1 + 1
y = ny ==> solve for n
y/y = ny/y
1 = n ==> n=1
Two angles form complements. One angle measure is eight more than twice the other. Find both angles measures.
Answer:
41° and 49°
Step-by-step explanation:
Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:
2x + 8 = 90
Solving for x, we get:
2x = 82
x = 41
Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.
Therefore, the two angles have measures of 41 and 49 degrees.
A college student is deciding how many hours to work at a part time job(x) and how many hours to work at an internship (y). The job pays $24 and hour, and the internship pays $12 an hour. The student needs to work less than 15 hours a week but needs to earn at least $240 a week to pay expenses. Write 2 systems of inequalities to represent all the combinations of number of hours the student can work at the job and internship
Answer:
x + y < 152x + y ≥ 20-------------------------------
Total hours worked is x + y.
Earning from the part time job is 24x, from the internship is 12y.
Inequality for the number of hours:
x + y < 15Inequality for the earning:
24x + 12y ≥ 240This can be simplified by dividing all terms by 12:
2x + y ≥ 20Answer:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
Step-by-step explanation:
Part-time job
Let x be the number of hours worked.$24 = pay per hour.Internship
Let y be the number of hours worked.$12 = pay per hour.The student needs to work less than 15 hours a week:
[tex]\implies x+y < 15[/tex]
The student needs to earn at least $240 a week:
[tex]\implies 24x+12y \geq 240[/tex]
Therefore, the system of inequalities is:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
The second inequality can be simplified by dividing each term by 12:
[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]
[tex]\implies 2x+y \geq 20[/tex]
Therefore, a second system of inequalities is:
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
To solve the system of equalities, graph both inequalities and shade the overlapping region.
Any (x, y) point in the overlapping region is a solution to the system of inequalities.
One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.
Look at the triangles shown below.
5
Which statement is TRUE?
Answer: B
Step-by-step explanation:
vertical angles are =
Write a cosine function that has a midline of 3, an amplitude of 5 and a period of 2.
Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
What is a Cosine Function?A crucial periodic function in trigonometry is the cosine function.
Utilizing the unit circle will make understanding the cosine function the simplest.
Draw a unit circle on the coordinate plane, center the angle at the origin, and label one side as the positive x-axis for the supplied angle measure.
The point where the other side of the angle intersects the circle has an x-coordinate of cos(), and a y-coordinate of sin().
According to our answer-
B = 2pi/T, where T is the period and T = 1/f is the frequency; T is the period
Determines horizontal phase shift by using
C =determines vertical shift.
When solving the given issue, D = midline = 5
A = amplitude = 2.
B = 2pi/T = 2pi/(2/3) = 3pi since frequency = 3/2 means that the period is T = 2/3, which is the reciprocal of the frequency.
C = 0.
The result of adding everything up is A = 2, B = 3pi, C = 0, and D = 5.
so,
A*cos(B(x-C)) + D = y
y = 2*cos(3pi(x-0)), plus 5.
y = cos(3pi*x) * 2 * + 5
Hence, Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
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Which one. Multiple choice.
In the given relation, 1 is not a domain.
What is domain?The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.
All the values that go into a function. The output values are called the range.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.
Given that, a function,
{(5, 1), (4, -3), (3, -1)}
We know, a domain is the set of all "x" values.
Therefore, domain of the function are, 5, 4 and 3
But, if we see, 1 is one of the values of y.
Hence, 1 is not a domain.
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Witch expression is equivalent to (-10/9t+1/8)-(-6/18t+3/4) (I NEED THIS FAST!)
Answer: ( -56 - 45t ) / 72t
Step-by-step explanation:
attached a picture for explaination.
hope that helps...
Given: segment BD bisects angle ABC and segment BD bisects angle ADC. Prove: segment AD is congruent to segment CD
If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.
What is bisector of an angle?
In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..
Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.
Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.
AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.
Consider △ABD and △DBC:
∠ABD = ∠DBC
∠ADB = ∠BDC
Therefore, △ABD ≅ △DBC
According to CPCT, AD ≅ CD.
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These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
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The library at your school has MP3 players pre-loaded with audio and digital books
to check out. When the librarian starts downloading new books at 11:00 am, there
are 15 already loaded. When she checks at noon, there are 25 books completely
loaded. Assuming that the computer downloads books at a consistent rate, how
many complete books will have downloaded at 2:45 pm?
Write a function of books downloaded, y, based on time passed, x (in hours), as well
as the total number of books that will be completed by 2:45 pm.
The total number of books completed by 2:45 pm will be 42.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that when the librarian starts downloading new books at 11:00 am, there are 15 already loaded. When she checks at noon, there are 25 books completely loaded.
The number of books loaded in 1 hour is calculated as,
N = 25 - 15
N = 10 books
Now from 12 noon to 2:45 pm, the time in hours will be,
T = 165 minutes or 165 / 60 = 2.75 hours
The equation for the number of books loaded will be written as,
y = 15 + 10T
y = 15 + ( 10 x 2.75)
y = 15 + 27.5
y = 42.5 or 42
The completely loaded books are 42 in number.
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Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it she paused it for 16 minutes what time did the movie end?
Answer:
The movie ended at 7:39 a.m.
Step-by-step explanation:
She started at 6:30. 53 minutes added to that would be 7:23. Another 16 minutes added to that would be 7:39.
The movie will end at 20:39.
What is time conversion?Conversion Time means a time which falls after the Calculation Time and is the time at which the admission of the Ordinary Shares arising on Conversion to the Official List becomes effective.
Given that, Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it, she paused it for 16 minutes
The total time taken = 1 hour + 53 minutes + 16 minutes = 1 hours + 69 minutes
= 1 hour + 60 minutes + 9 minutes
= 1 hours + 1 hours + 9 minutes
= 2 hours + 9 minutes
Therefore, total time she took for movie is 2 hr 9 min
Since, the movie started at 18:30,
Therefore, 18:30 + 2 hour 9 minute
= 20 hours + 39 minutes
Hence, The movie will end at 20:39
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The expression - 270 +18.3y represents a submarine that began at a depth of 270 feet below sea level and ascended at a rate of 18.3 féet par minute. What was the depth
of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The submarine ___ was feet below sea level after 8 minutes.
(Type an integer or a decimal:)
B. The submarine will have reached sea level after 8 minutes.
The depth of the submarine after 8 minutes is -123.6 feet below sea level.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Depth of the submarine after y minutes.
= -270 + 18.3y
The depth of the submarine after 8 minutes.
= -270 + 18.3 x 8
= -270 + 146.4
= -123.6
Thus,
The submarine is at -123.6 feet below sea level.
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in a certain town, 60 families own tv sets, 85 own scooters, 70 own refrigerators, and 95 own radio sets. 130 families own exactly one of these items. what is the maximum possible number of families in that town? assume that every family owns at least one of the items.
Therefore ,the solution to this equation question is option C) 220 .
Describe equation.In an equation, it is said that the values of two mathematical expressions are equal. The equality of two variables is established via a mathematical formula. It is denoted by the equal ('=') sign. For example, the formula is 8+2=12-2. The aforementioned equation indicates that the left and right sides of the equation are equal. In light of this, an equation is a claim that "this equals that."
Here,
S is the total families
thus,
S = 60 + 85 + 70 + 95 = 310.
I + II + III + IV = X
S = I + 2 II + 3 III + 4 IV
S - I = 2 II + 3 III + 4 IV
310 - 130 = 180 = 2 II + 3 III + 4 IV
Make III & IV = 0 to increase X.
2 II therefore equals 1800. II = 90
X max = 130+90 = 220
Therefore ,the solution to this equation question is option C) 220 .
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PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!!!
Answer:
x=-1 3/8
Step-by-step explanation:
-2.25 + 0.4x = -2.8
-2.25 + 2.25 + 0.4x = -2.8 + 2.25 ==> add 2.25 on both sides to isolate x
0.4x = -0.55
(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals
8x = -11
x=-11/8
x=-(3+8)/8 ==> turn x into a mixed number
x=-3/8 - 8/8
x=-3/8 - 1 ==> simplify
x=-1 - 3/8
x=-(1 + 3/8)
x=-1 3/8
1,000 individuals total: 900 are fully susceptible (fs) to methicillin, meaning they die early in the course of treatment. 90 are somewhat susceptible (ss) to methicillin, meaning they have some resistance to methilicillin. 10 are killed only by a full treatment with methicillin (ft), meaning they have the greatest degree of resistance. what is the percentage of each type of s. aureus?
The percentage of each types of s. aureus
Fully susceptible (fs) to methicillin = 90% Somewhat susceptible (ss) to methicillin = 9% Killed only by a full treatment with methicillin = 1%Total number of individuals = 1000
Number of individuals susceptible (fs) to methicillin = 900
The percentage = (Number of individuals susceptible (fs) to methicillin / Total number of individuals) × 100
= (900/1000) × 100
= 90%
90 are somewhat susceptible (ss) to methicillin
The percentage = (90 /1000) × 100
= 9%
10 are killed only by a full treatment with methicillin (ft)
The percentage = (10/1000) × 100
= 1%
Therefore, the percentage of each types of s. aureus are 90%, 9% and 1%
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Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
She invested $2300 at 2% and $1400 at 6% interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P₁ = $2300, P₂ = $1400, t₁ = t₂ = 1 and r₂ = r₁ + 4.
The sum of the simple interests from both these accounts is $130.
Therefore, (2300×r₁×1)/100 + (1400×(r₁ + 4)×1)/100 = 130
2300r₁/100 + 1400r₁/100 + 5600/100 = 130.
2300r₁ + 1400r₁ + 5600 = 13000.
3700r₁ = 7400.
37r₁ = 74.
r₁ = 2% and hence r₂ = 6%.
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Geometry is hard help
Mr.green Is putting lights around 8 windows; each window is 3 and 1/2 feet wide and 5 feet long. How many feet of light does he need?
Answer:
The answer is 140
Step-by-step explanation:
The first step is simple L x W which will give us.
L being 5 and W being 3.5 The equation is 5 × 3.5 = 17.5.
With that being said I just need to multiply that answer by 8 which gives us 140.
This means that he will need 140 ft of light in order to put light around each window.
Hope this helped :)
Which of these triangle pairs can be mapped to each other using a single translation?
O
E
D
$
What is the slope of y = − 5 + 4x
You recently joined a gym. You had to pay a joining fee of $40, and you will pay $20 per month to maintain the membership.
What is the one-time charge? What does it represent in slope-intercept form?
What is the recurring charge? What does it represent in slope-intercept form?
What does x represent?
What does y represent?
The number 40 represents the one-time charge which is the y-intercept. And the number 20 presents the fee for gym per month. The x-intercept represents that you need to pay 14 monthly fees for a year.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' represents the number of months and 'y' be the total cost. Then the equation is given as,
y = 20x + 40
The number 40 addresses the one-time charge which is the y-capture. Also, number 20 presents the charge for the exercise center each month. The x-block addresses that you really want to pay 14 month-to-month charges for a year.
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A school requires 2 iPads for every 5 students. How many iPads are needed for 145 students?
Answer:
58 iPads
Step-by-step explanation:
To calculate how many iPads are needed for 145 students, we can use the given ratio of 2 iPads for every 5 students.
First, find out how many groups of 5 students are in 145 students by dividing 145 by 5:
[tex]\sf \dfrac{145\; students}{5\; students/group} = 29\;groups\; of \;5 \;students[/tex]
Now, for each group of 5 students, we need 2 iPads. So, multiply the number of groups of 5 students by 2 to find the total number of iPads needed:
[tex]\sf 29 \;groups \times2\; iPads/group = 58\; iPads[/tex]
Therefore, 58 iPads are needed for 145 students.
a car manufacturer wants to learn more about the brand preferences of electric car owners. there are millions of electric car owners in the world. who should the company survey? 1 point the entire population of electric car owners a sample of car owners who have owned more than one electric car a sample of all electric car owners a sample of car owners who most recently bought an electric car
A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.
What is Survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.
As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.
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Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f(x)=x^2-5x+1 . Write a rule for g .
Answer:We may rewrite f(x) = (x-1)^2
We stretch by having 3(x-1)^2
We reflect about the y axis by changing x to -x: 3(-x-1)^2 = 3(x+1)^2
We move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2
Step-by-step explanation:A way to verify this: Consider y = x^2 to be the unit parabola. f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1; moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2
We may write g(x) = 3x^2 + 18x + 27, also.
one of the 4 choices
The translation from the parent function is defined according to the following option:
A translation of 5 units to the right.
How to define the translation?The four possible translations are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is defined as follows:
f(x) = x².
The translated function is given as follows:
g(x) = (x - 5)².
Meaning that the translated function can be written as follows:
g(x) = f(x - 5).
Thus the transformation to the parent function is given as follows:
x -> x - 5.
Thus it was a translation right of five units, and the third option is the correct option.
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Work out:
(1.2 × 10′²) × (2 × 10ª)/3 x 10-5
Give your answer in standard
form.
The standard form of the expression is [tex]0.000286 \times 10^a[/tex].
What is a standard form?
A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.
The given expression is
[tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]
Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].
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What is the name given to the exponent to which 3 must be raised to obtain 11?
The number which can be raised by 3 to give the value of 11 is 2.224.
What are exponential functions?The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.
Given:
The exponent to which 3 must be raised to obtain 11,
Assume the number is x then, According to the statement,
x³ = 11
x = ∛11
x = 2.224
Thus, the number is 2.224.
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