Answer: 56 minutes
Step-by-step explanation:
7 = 7, 14, 28, 35, 42, 49, 56
8 = 8, 16, 24, 32, 40, 48, 56
7 and 8 have 56 in common so it would take them 56 minutes
During a triathlon, Tasneem swims 1/4 of the total route and cycles 3/5 of the remaining route. She runs the rest of the route. If she runs 3600 m, determine the total distance of the triathlon.
The total distance of the triathlon is 12000 m.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Let the total distance of the triathlon be x.
Tasneem swims 1/4of the total route, therefore, she swims for a distance of S = (1/4)x.
Now the remaining route is,
x - (1/4)x
=3/4x
After swimming, she cycles 3/5 of the remaining route, therefore, she cycles for a distance of C = (3/5)×(3/4)x,
C = (9/20)x
Now, she runs for the rest of the route, therefore, she runs for a distance of R = x - (1/4)x-(9/20)x
Or, R = (20x - 5x - 9x)/20
R = (6x)/20
Given that Tasneem runs 3600 m, therefore, substitute R = 3600 into the above equation,
3600 = (6x)/20
(3600×20)/6 = x
12000 = x
Therefore, the total distance of the triathlon is 12000 m.
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A trust company offers 3-year compund interest GIC earning annual interest of 5.50% compounded monthly or 5.70% compounded semi-annually. Which rate should an investor choose?
As per the given interest rate and types of annual interest , investor should choose compounded monthly as it gives interest more frequently .
As given in the question,
Time period to calculate the compound interest = 3years
Interest rate compounded monthly = 5.50%
Each month interest output is 5.64079
Rate of interest compounded semi- annually = 5.70%
Each month interest output is 5.78123
Compounded monthly gives interest every month and semi-annually gives twice a year.
Monthly is more frequent compare to semi-annually.
Investor should choose monthly.
Therefore, as per the given interest rate and types of annual interest , investor should choose compounded monthly as it is more frequent .
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Consider the two points F(-9,0) and G(9,0) as the foci of an ellipse. The length of the major axis is 36. Give the equation of the ellipse.
well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]
[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]
Check the picture below.
how many different outcomes are possible when flipping a coin and rolling a die
The total possible outcome when a coin is flipped and a die is rolled is 12
What is Probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total possible outcomes.
For example if a coin is flipped, a coin only has two faces, this means that it will have 2 Total possible outcome. When a die is rolled, a die has 6 faces which means that it will Total outcome of 6. When both a coin is flipped and a die is rolled the total possible outcome is 6×2 = 12 outcomes.
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Write the number in two other forms (fraction, decimal, or percent) 355%
Answer:3.55 , 71/20
Step-by-step explanation:
Solve the following 2(x + 3) = x - 4
Answer:
x = - 10
Step-by-step explanation:
2(x + 3) = x - 4
==> distribute the 2
2x + 6 = x - 4
==> subtract 6 from both sides
2x = x - 10
==> subtract x from both sides
x = - 10
what is the product of 9x-4 and 8x+5?
Suppose you have a complete, weighted graph with 8 vertices. How many Hamilton Circuits are there in this graph?
The number of Hamilton Circuits with 8 vertices are 5040.
Given that, a complete, weighted graph with 8 vertices.
What are Hamilton Circuits?A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start and end at the same vertex. A Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex.
For N vertices in a complete graph, there will be (n−1)!=(n−1)(n−2)(n−3)…3⋅2⋅1 routes. Half of these are duplicates in reverse order, so there are (n−1)!/2 unique circuits.
A complete graph with 8 vertices would have = 5040 possible Hamiltonian circuits. Half of the circuits are duplicates of other circuits but in reverse order, leaving 2520 unique routes.
Therefore, the number of Hamilton Circuits with 8 vertices are 5040.
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[tex]\frac{90}{x} - \frac{90}{15-x} = 5[/tex]
Solving for X the value is = 45, 6
What is an equation?A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions.For instance, an équation is defined as having one or more variables in French.Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables.The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfill the equality are known as the equation's solutions. Equations can be categorized as either identities or conditional equations.acc to our question-
90/x=90/x+15+1/2
(15-x)90 - 90x/15x-x^2 = 5
x= 45 or 6
hence, for X the value is = 45, 6
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Choosing the best bank for a new savings account
The major criteria to be considered when going for a bank to have a new savings account registered with them are as follows:
Low interest rates on my savingsFriendly customer serviceOnline banking site usability platform.Why low interest rate makes a criterion for choosing the bank to bank with.As an entrepreneur, finding a good bank to open a savings account with might be much tedious to do. However, I have live to understand that banks with low interest rate are a better catch if I am considering a good saving lifestyles. I cannot stand a banking system that charges me unnecessarily all the time all in the name of fee or the other, which results to reducing my money in their system.
That being said, discovering a bank which has welcoming and helping customer service is also an important factor to be considered when choosing to right banking system.
In conclusion, it can be deduced that a bank with which does not deduct one's money anyhow all in the name of interest is worth having a savings account with.
Complete question:
What are the conditions to be considered in choosing the best bank for a new savings account?
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What is the price of a jacket that originally costs $125 but has a 25%
discount?
Answer:
$93.75
Step-by-step explanation:
$125 × 0.75 = $93.75
PLEASE MARK AS BRAINLIEST!!!Answer:
$93.75
Step-by-step explanation:
125x0.25
31.25
125-31.25
$93.75
Hopes this helps
A metallurgist has one alloy containing 29% aluminum and another containing 51% aluminum. How many pounds of each alloy must he use to make 48 pounds of a third alloy containing 50% aluminum? (Round to two decimal places if necessary.)
The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.
The number of pounds of alloy that must be used.Let
x = pounds of 29% alloyy = pounds of 51% alloyx + y = 48
29x + 51y = 50*48
x + y = 48
29x + 51y = 2400
Solve simultaneously
From (1)
x = 48 - y
Substitute into (2)
29x + 51y = 2400
29(48 - y) + 51y = 2400
1392 - 29y + 51y = 2400
- 29y + 51y = 2400 - 1392
22y = 1008
divide both sides by 22y = 1008/22
y = 45.82 pounds
Substitute y = 45.82 pounds into (1)
x + y = 48
x + 45.82 = 48
x = 48 - 45.82
x = 2.18 pounds
So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.
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lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. Work out how much money Elliot received. Elliot received £
If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.
How to find the amount received?Given data;
Sharing ratio 8:5
Amount Elliot got = 21
In order to determine the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.
Equation
21 × 8 ÷ (8-5)
Hence,
£21 × 8 ÷ (8-5)
£168 ÷ 3
= £56
Therefore Elliot received £56.
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21 washing machines in a laundromat, and 4 broken down. what is the ratio of the broken to all washing machines?
Answer: 17:4
Step-by-step explanation:
21 washing machines
4 broken
21 - 4 = 17
17:4
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WILL MARK BRAINLIEST
Angle x= 45
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to the question-
N + M = 90X + X= 902X=90X=45Hence, Angle x= 45
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need help pleaseeeeeeeeee
The value g(7) of the function g(x) = 7 / 8 x - 1 / 2 is 45 / 8.
How to solve function?A function relates each element of a set with exactly one element of another set (possibly the same set).
In a simpler term, a function relates an input to an output.
Therefore, let's find the value of g(7) for the function below:
g(x) = 7 / 8 x - 1 / 2
Hence,
g(7) = 7 / 8 (7) - 1 / 2
g(7) = 49 / 8 - 1 / 2
g(7) = 49 - 4 / 8
Therefore,
g(7) = 45 / 8
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LoWatts Ltd makes light bulbs that are identical in size
They have regular orders from company A for 120 light bulbs and from Company B for 168 light bulbs.
LoWatts Ltd uses one size of box to supply both company A and company B. Each box used contains the same number of light bulbs and is full.
The number of boxes used is as few as possible
How many light bulbs does each box hold?
Using the greatest common factor, the number of light bulbs in each box is 24.
What is the greatest common factor?The greatest common factor (GCF) is the number that can divide two or more numbers without a remainder.
The GCF is a divisor that divides dividends evenly, leaving only quotients without remainders.
For instance, the greatest common factor of 120, 168, and even 288 is 24.
Using this GCF implies that 24 can divide 120, 168, and 288 without leaving any remainders.
Company A Company B Total
Total orders for light bulbs 120 168 288
Greatest common factor of 24 24 24
Number of boxes delivered 5 7 12
Thus, with the greatest common factor as 24 light bulbs in each box, Company A will be supplied 5 boxes, while Company B will be supplied with 7 boxes.
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Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 19, upper bound is 25.
The point estimate of the population mean is 22 and margin of error for the confidence interval is 3.
How to find the point estimate?1. Point estimate
Point estimate = Upper bound+ Lower bound/2
Point estimate = (25+19) /2
Point estimate = 44/2
Point estimate = 22
2. Margin error
Margin error = Upper bound - Lower bound/2
Margin error = ( 25-19) /2
Margin error = 6 /2
Margin error = 3
Therefore the point estimate is 22.
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Orenda opened a savings account with $4500 that earns 0.6% simple interest
annually. After how many years will the balance of the account be $4635? Round to the nearest tenth, if necessary.
WHAT IS THE ANSWER???
The time required for for the balance to reach $4635 is 5 years.
How to solve simple interest problems?The formula for simple interest can be expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $4500Interest rate r = 0.6%Accrued amount A = $4635Time t = ?First convert the interest rate from percent to decimal
Interest rate = 0.6%
Interest rate = 0.6/100
Interest rate = 0.006
Plug the given values into the above formula and solve for time t.
A = P( 1 + rt )
t = ( 4635/4500 - 1) / 0.006
t = ( 1.03 - 1) / 0.006
t = ( 0.03) / 0.006
t = 5 years.
Therefore, the required time is 5 years.
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A rectangular floor is long and wide. Pablo wants to carpet the floor with carpet titles sold by the square yard. Use the facts to find the area in square yards.
The required area of the flour in the square yard is A =n[ L×W ] where L and W are the length and width of the tiles respectively.
Given that,
A rectangular floor is long and wide. Pablo wants to carpet the floor with carpet titles sold by the square yard.
Surface area is defined as the area of the surface that is uncovered.
here,
Let for a tile the length be L and the width be W,
Assume that the number of tiles required is N,
The area of the N tiles is equal to the area of the rectangular floor,
Area of the floor = N [area of the tile]
Area of the floor (A = N [L× W]
Thus, the required area of the flour in the square yard is A =n[ L×W ] where L and W are the length and width of the tiles respectively.
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Simple random sampling uses a sample size of n from a population of size N to obtain data that can be sued to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?
If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of different random samples of four accounts that are possible is 230,300.
How to find the different random samples?Given data:
Number of population of bank account = 50
Random sample = 4 accounts
Now let find the different random samples of four account that are possible
Different random sample = 50! / (50 -4)! × 4!
Different random sample = 50! / 46! × 4!
Different random sample = 230,300
Therefore the different random samples is 230,300.
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Give two ordered pairs on the line with equation x = 7
(7,0); (7,−5) ;(7,3); (7,10);. (7,y)
Step-by-step explanation:
Answer:
The equation x = 7 forms a vertical line which we refer to as undefined. So any points with a x value of 7 will pass through the line.
Step-by-step explanation:
For example, points like (7, 0) (7, 1) (7, 2) are all points that the line x = 7 passes through.
A point is made up of 2 values. An x-value and and a y-value. You simply plug in 7 for the x and any value for y.
Points that are on the line x = 7 include:
(7, 0)
(7, 1)
(7, 2)
(7, 4)
(7, 5)
(7, 6)
what is the measure of arc XY in the diagram below ?
The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°
What is a secant of a circle?A secant line is a straight-line which has two points of intersection with a circle.
From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°
The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.
Mathematically;
[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]
Where;
The outside angle formed by the secant ZW and ZV, m∠z = 41°
[tex]\widehat{VW}[/tex] = 112°
Which gives;
[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]
2 × 41° = 112° - [tex]\widehat{XY}[/tex]
82° = 112° - [tex]\widehat{XY}[/tex]
[tex]\widehat{XY}[/tex] = 112° - 82° = 30°
[tex]\widehat{XY}[/tex] = 30°
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f: x → 15/x - 5 What number must be excluded from the domain of f?
Answer:
x = 5
Step-by-step explanation:
You want to know what number must be excluded from the domain of f(x) = 15/(x -5).
DomainThe domain of a function is the set of numbers for which it is defined. The function f(x) = 15/(x-5) will be undefined when the denominator is zero:
x -5 = 0
That will be the case when x = 5.
The domain of f must exclude x=5.
The table shows the fraction of the world's surface land area taken up by each continent. In other words, the continent of Africa makes up StartFraction 20 Over 100 EndFraction of the land in the world. How much greater is the fractional part of the continent of North America than the fractional part of the continent of Europe ?
Answer:
[tex]\frac{9}{100}[/tex]
Step-by-step explanation:
According to the map, North America makes up [tex]\frac{16}{100}[/tex] of the world's land surface area, while Europe makes up [tex]\frac{7}{100}[/tex]. Since both fractions already have a common denominator ( [tex]\frac{n}{100}[/tex] ), we can simply subtract the two to find how much greater the fractional part of North America is than the fractional part of Europe:
[tex]\frac{16}{100}-\frac{7}{100}=\frac{9}{100}[/tex]
a regular deck of playing cards is shuffled what would probability of not drawing an ace
Answer:44/52
Step-by-step explanation:There are four aces in a deck of 52 cards, so the probability of not drawing an ace is 44/52 =
Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week.
Which equation can you use to find h, the length of each afternoon practice in hours?
The equation used to find the length of each afternoon practice is given as follows:
4(h + 3) = 20.
What is the system of equations?The variables in this problem are defined as follows:
Variable x: length of each morning practice.Variable h: length of each afternoon practice.During the summer, the team practices 4 days per week, for a total of 20 hours each week, hence the equation is of:
4(x + h) = 20.
The number of hours practiced during the morning is of:
x = 3.
Hence the equation to solve for h is given as follows:
4(3 + h) = 20
Applying the commutative property:
4(h + 3) = 20.
Hence the second option is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week.
Which equation can you use to find h, the length of each afternoon practice in hours?
Summer swim practice is 4 days per week. Each day has 3 hours of morning practice and h hours of afternoon practice. So, the number of hours of practice each day is h+3. Weekly practice is a total of 20 hours. This equation represents the situation.
4 (h+3)
=
20
days of practice per week
hours of practice each day
total hours of practice each week
The equation 4(h+3)=20 can be used to find the length of each afternoon practice in hours. Solve the equation for h.
4(h+3)
= 20
h+3
= 5 Divide both sides by 4
h
= 2 Subtract 3 from both sides
Each afternoon practice is 2 hours.
Find the values of x, y, and z. The diagram is not to scale.
Answer:
x= 68 z= 180 y=38
Step-by-step explanation:
Arianys runs a farm stand that sells grapes
and apples. Each pound of grapes sells for
$3.75 and each pound of apples sells for
$4. Arianys made $251.75 from selling a
total of 64 pounds of grapes and apples.
Determine the number of pounds of
grapes sold and the number of pounds of
apples sold.
The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
According to the question,
We have the following information:
Cost of 1 pound of grapes = $3.75
Cost of 1 pound of apples = $4
Total cost made by selling = $251.75
And the weight of the apples and grapes sold = 64
Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.
So, we have:
x+y = 64
x = 64-y ....(1)
3.75x+4y = 251.75
Putting the value of x in this equation:
3.75(64-y)+4y = 251.75
3.75*64-3.75y+4y = 251.75
240+0.25y = 251.75
0.25y = 251.75-240
0.25y = 11.75
y = 11.75/0.25
y = 47 pounds
Now, putting this value of y in equation 1:
x = 64-y
x = 64-47
x = 17 pounds
Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
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Question 7
Let f (x) = -2x³ + ax² +2. You are told that f (2) = 14, what is the value of a ?
a=9
a=8
a=7
a=6
Answer:
a = 7
Step-by-step explanation:
Substitute x for 2 and f(x) for 14
14 = -2(2³) + a(2²) + 2
14 = -16 + 4a + 2
14 = -14 + 4a
14 + 14 = 4a
28 = 4a
4a = 28
Divide both sides by 4
4a/4 = 28/4
a = 7
Alternative:
Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.