Brian has £63 Initially, by using the ratio and proportion method.
What are Ratio and Proportion?
In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.
An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".
In the question, It is given that:
The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.
Let 7x denotes the amount in Brian's wallet and 2x denote the amount in Colin's wallet on that day.
we know that:
Brian spent £39 that day.
Amount left in Brian's wallet = 7x- 39
Brian now had £4 less than Colin.
⇒ 2x -4= 7x- 39
⇒ 7x-2x=4+39
⇒ 5x=35
⇒ x=7 [Divide both sides by 5 ]
So , The initial amount in Brian's wallet = 7(7)= £49
The initial amount in Colin's wallet = 2(7)= £14
The amount they had together = £49+£14 = £63
So, They had £63 altogether initially.
Therefore, Brian has £63 Initially.
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Answer: £14
Step-by-step explanation: Because Hegarty Maths says it is when I got this same Question Wrong :(A cat’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat′s heart beat per second?
Work Shown:
45 beats = 15 seconds
45/15 beats = 15/15 seconds
3 beats = 1 second
To convert to beats per minute (bpm), multiply by 60.
48) in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people, if a) the bride must be in the picture?
The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
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Write an equivalent ratio for each ratio
Answer:2/5=4/10 and 1/4=2/8
Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.
2. Write 420 as a product of prime numbers.
Answer:
As a product of prime numbers:
420 = 2 × 2 × 3 × 5 × 7
Two complementary angles have measures of x and y. If y is 9 less than twice x, write a system of linear equations that can be used to determine the measure of each angle. Find the measure of each angle.
Using system of linear equation, the complementary angles (x, y) are 27 and 63 degrees respectively.
Complementary AnglesWhen the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles. However, when the sum of the two angles is equal to 180 degrees, the angles are supplementary angles
In this case, we have two angles x, y which are complimentary to one another.
We can represent this with system of equations;
x + y = 90 ...eq(i)y - 9 = 2x ... eq(ii)solving equation (i) and (ii)
The value of x and y are 27 and 63
The complementary angles are 27 and 63
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Can anyone state the vertex of the graph?
There is no vertex in the graph and the transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
In this case, there is no maximum or minimum in the graph
This means that that there is no vertex in the graph
The transformationHere, we have:
We can see that:
The graph is 4 units to the left of the origin and 2 units below the origin
This means that the function has been shifted down and shifted to the left
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2x+y=4 1x-y=11 adding subtracting equations to solve systems.
By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
What is meant by an equation?An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.
An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.
Given,
2x+y=4
x-y=1
By solving above two equations we get,
2x+y=4
x-y=1
3x=5
x=5/3
y=-1+x
y=(5/3)-1
y=2/3
Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
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A rectangular book measures 3*5. What is the length of its diagonal to the nearest tenth?
The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
Area of rectangle = length × width.
The angle between any two consecutive sides will be 90 degrees.
As per the given rectangle with dimensions 3 × 5.
The rectangle has been attached below,
The length of the diagonal using Pythagoras' theorem is,
x = √(3² + 5²)
x = √34 = 5.8
Hence "The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8".
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The graph below plots the values of y for different values of x:
plot the ordered pairs 1, 8 and 2, 3 and 3, 0 and 4, 1 and 5, 2 and 6, 1
What does a correlation coefficient of −0.2 say about this graph?
x and y have a strong, positive correlation
x and y have a weak, positive correlation
x and y have a strong, negative correlation
x and y have a weak, negative correlation
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation
What is a correlation coefficient?
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.
As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].
So,
[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]
As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.
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Graph the function f(x) = -5(x - 8)² - 2.
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can
erase your parabola by selecting the second point and placing it on top of the first.
The vertex is at (8, -2).The point (10, -22) is also on the parabola.
Step-by-step explanation:
Here is the graph of the function:
The vertex is at (8, -2).
To plot another point on the parabola, we can choose any x-value and plug it into the equation to solve for y.
For example, if we choose x = 10, then we have:
f(x) = -5(x - 8)² - 2
f(10) = -5(10 - 8)² - 2
f(10) = -5(2)² - 2
f(10) = -5(4) - 2
f(10) = -20 - 2
f(10) = -22
So, the point (10, -22) is also on the parabola.
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There are 39 students in the bike club.
All but 8 of them participated in a race.
What is the total cost if each student who entered the race paid $6?
Answer:
Total Cost = $186
Step-by-step explanation:
All but 8 means that All of them participated except for 8 of them
Since there is 39 Students in the Club
Then the Number of Students participated = 39 - 8 = 31 Students
Total Cost = (Cost per Student ) * ( Number of Students )
=$6 * 31 = $186
Glad to Help
1. Name a plane parallel to plane WXT
2. Name two segments parallel to VU.
3. Name two segments parallel to SW.
4. Name two segments skew to XY.
5. Name two segments skew to VZ.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
What are parallel lines ?Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given : The quadrilateral prism
Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
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it is claimed that the mean age of bus drivers in chicago is 50.2 years. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
The null hypothesis is a statement which describe the claim of 'no difference'.
Let μ be the population mean.
Given claim : The mean age of bus drivers in Chicago is 50.2 years.
i.e. μ = 50.2
Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.
Then, the null hypothesis for the given situation is
Ηο : μ = 50.2
If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
71°
(2x+5)
62⁰
Answer:
x=21
Step-by-step explanation:
The angles of a triangle always add up to 180°
71+62+(2x+5)=180
First add 71 and 62
133+(2x+5)=180
Then you subtract 133
2x+5=47
Subtract 5 too
2x=42
Then divide by 2
x=21
We can check our answer by adding all the angles
71+62+(2*21+5)
71+62+(42+5)
71+62+47=180
suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime x (in weeks) has a gamma distribution with mean 24 weeks and standard deviation 12 weeks. (a) what is the probability that a transistor will last between 12 and 24 weeks? (b) what is the probability that a transistor will last at most 24 weeks? (c) is the median of the lifetime distribution less than 24? why or why not?
The probability that the transistor will last between 12 and 24 weeks is 0.424
the probability that a transistor will last at most 24 weeks is 0.567
The median of the lifetime distribution is less than 24
X= lifetime of the transistor in weeks E(X)= 24 weeks
O,= 12 weeks
The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.
a) X~gamma([tex]\alpha , \beta[/tex])
E(X)= [tex]\alpha \beta[/tex] [tex]\beta[/tex] =[tex]12^{2}/24[/tex] =6 weeks
V(x)=[tex]\alpha \beta ^{2}[/tex] [tex]\alpha[/tex]=24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X,[tex]\alpha[/tex] ,[tex]\beta[/tex] , False)
P([tex]12\leq X\leq 24[/tex])
P([tex]12/6 \leq X\leq 24/6[/tex])
P([tex]2\leq X\leq 4[/tex])
P= 0.424
Therefore, the probability that the transistor will last between 12 and 24 weeks is 0.424
b) For this case we want this probability:
[tex]P(X\geq 24)=1-P(X\leq 24)[/tex]
In order to find this probability we can use excel with the following code:
=1-GAMMA.DIST(24,4,6,TRUE)
And we got:
[tex]P(X\geq 24)=P(1-X\leq 24)= 0.567[/tex]
c) For this case the median of the lifetime distribution is less than 24
[tex]P(X\leq \alpha )[/tex] = 0.5 (by definition) So [tex]\alpha[/tex]< 24 because P([tex]X\leq 24[/tex])=0.567 which is greater than 0.5
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a scout group has a raffle to rasie money for charity there is 1 prize to be won in the raffle
laura buys 12 raffle tickets a total of 350 raffle tickets are sold
find the probability that laura does not win the prize
The probability that Laura does not win the prize is 119 / 175.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
Total number of raffle rickets to be sold is 350.
The number of tickets bought by Laura is 12.
Since, the probability of an event is defined as the ratio of favorable outcome to the total outcomes, the probability of winning the prize is,
P = 12 / 350
Thus, the probability of not winning the prize is,
1 - 12 / 350
= 338 / 350
= 119 / 175
Hence, the probability of not winning a prize is 119 / 175.
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g(a)=3a+2; find g(-3) HELP PLEASE!!
The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.
What is the output value of g( -3 ) in the given function?A function is simply a relationship that maps one input to one output. For relation to qualify as a function, each x-value can only have one y-value.
Given the data in the question;
g( a ) = 3a + 2g( -3 ) = ?To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.
g( a ) = 3a + 2
g( -3 ) = 3( -3 ) + 2
Multiply 3 and -3
g( -3 ) = -9 + 2
Add -9 and 2
g( -3 ) = -7
Therefore, the output value is -7, this forms an ordered pair of (-3,-7).
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Find the slope and the y-Intercept of the line.
-5x + 4y = -3
Write
your answers in simplest form.
Answer:
slope=5/4 y intercept=-3/4
Step-by-step explanation:
put it into slope intercept form y=5/4x-3/4
pull out 5/4 as slope and -3/4 as y intercept
Find the slope of the line. Write your answer in simplest form.
HELP ME PLEASEEEEEEEEEEEEEEEEEEEEE
Answer:
0,3
Step-by-step explanation:
it between the 2 and it is negative and positive cases in the -2
There are 1,459 children registered for camp. There is enough room for 18 campers to sleep in
each cabin. What is the least number of cabins needed for all the registered campers?
Answer:
82 rooms
Step-by-step explanation:
1459/18=81.05
so 82 rooms
Please mark as brainliest
Answer:
82
Step-by-step explanation:
1459/18
[tex]1459 \div 18[/tex]
for each cabin there 18 And there are 1459
81.05 \times 48=159
since you can't have a half a cabinet the answer is 82
Which of the following statements are true?
Corresponding angles of congruent figures are the same.
Corresponding angles of similar figures are the same.
Corresponding sides of congruent figures are the same.
Corresponding sides of similar figures are the same.
The statements that are true are:
Corresponding angles of congruent figures are the same.Corresponding sides of congruent figures are the same.What is Corresponding angles of congruent figures ?It should be noted that the two figures can be regrdedas as one that are similar in the case whereby their corresponding angles are congruent ,also their ratios of the lengths with respect to their corresponding sides would also be equal.
In conclusion, when two figures are similar then it can be concluded that their corresponding angles are congruent .
Hence, the second and third options are correct.
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Answer:
Corresponding angles of congruent figures are the same.
The corresponding sides of congruent figures are the same.
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no
more than $465 to spend on parking and admission. Parking is $12.50,
and tickets cost $33 per person, including tax. Which inequality can be
used to determine p, the maximum number of people who can go to
the amusement park?
14 people can go to the amusement park. Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.
How to calculate No. of people?Inequality: 33p + $12.50 ≤ $465
14 people can go to the amusement park
Inequality:
$465= Amount of money they have
$12.50= Parking Cost
$33= Cost of tickets per person
Because they only have $465, they can't spend more than that amount.
Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (aka x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:
33p+ $12.50 ≤ $465
$465- $12.50 = $452.5 (452.5 is how much is left for tickets after subtracting the parking cost)
$33 x1 4 = $462 (14 tickets can be bought for the price of $33)
$462 - $452.5 = $9.5 (9.5 isn't enough for another person)
So, the solution to the inequality is 14 people can go to the amusement park.
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Answer: 45.5p is less than or equal to 465
A parabola can be drawn given a focus of (−3,−3) and a directrix of x=5. Write the equation of the parabola in any form.
Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
As given in the question,
Focus of the parabola is equal to (-3, -3)
Directrix of the parabola is given by x = 5
Let (x, y) be the point on the parabola.
Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5
⇒√(x +3)² + (y +3)² = | x -5|
⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²
⇒x² +6x +y² +6y +18 = x² -10x +25
⇒y² +6y -7 = -16x
⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.
Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
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four vehicles are traversing a 1-km segment of a highway and the following observations are made: vehicle a: 1.2 min vehicle b: 1.5 min vehicle c: 1.7 min vehicle d: 1.4 min what is the space-mean speed?
Using the concept of average speed we conclude that the space-mean speed of the vehicles is 0.69 km/min.
What is space-mean speed?The average speed of a vehicle traveling a given segment of a highway in a specific time period is called space-mean speed, i.e.
Average mean speed = total distance traveled / average time travel
Given for vehicles are traversing a 1 km segment of highway. Hence total distance is 4km.
Average time = (1.2 + 1.5 + 1.7 + 1.4)/4
= 5.8/4
= 1.45 min
Now Average mean speed = 1/1.45
=0.689
=0.69 km/min
Hence the space-mean speed of the vehicles is 0.69 km/min
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Dominic needs a new bike mirror. His old mirror was a square with a side length of 9 cm. He wants the new mirror to have an area as close as possible to his old bike mirror.
The new mirror must have at least 81 cm² of the area.
What is the area of the square?The area of the square is defined as the product of the length and width.
As per the given question, we have
Dominic requires a new bicycle mirror. His old mirror was a square with a 9-cm side length.
He wants the replacement mirror to have an area that is as near to his previous bike mirror as feasible.
We have to determine the area of the previous bike mirror.
The area of the previous bike mirror = (side length)²
The area of the previous bike mirror = (9)² = 9 x 9
The area of the previous bike mirror = 81 cm²
So the new mirror must have greater than 81 cm² of area.
Thus, the new mirror must have at least 81 cm² of the area.
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Answer:
5 cm
Step-by-step explanation:
hope this helps
A parallelogram has a base of 20 millimeters and a height that is 6 mm less than the base. Create an equation that
can be used to find the area, A, of the parallelogram in square millimeters.
Move the correct answer to each box. Not all answers will be used.
Answer the following answer
As per given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.
As given in the question,
Minimum height require to ride in amusement park = at least 48 inches
Present height of Michael is 42 inches tall
Increase in height every month 1/2 inch.
Let 'm' months taken by Michael to ride in amusement park.
Required equation is:
48 = 42 + (1/2)m
⇒(1/2)m = 48 -42
⇒ m = 6×2
⇒ m =12 months
Therefore, for the given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.
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justin went to the track at bobcat stadium and performed the 1.5-mile run test to estimate his vo2max. he completed 1.5 miles in 11 minutes and 25 seconds. what is his estimated vo2max? round your answer to the first decimal place.
3Justin's estimated Vo2 max is 25.8(mL*kg*min)
What is Vo2 max ?
The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.
Here using vo2 max fomula 1.5 miles ,
=> VO2 max = 3.5+483/Time
Here Time= 11 min 25 sec = 25/60 = 0.41 min
Then time=11.42 mins. Now,
=> VO2 max = 3.5+ 483/11.41
=> VO2 max = 3.5+42.3
=>VO2 max = 25.8(mL*kg*min)
Hence His estimated Vo2 max is 25.8(mL*kg*min)
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2– 1 8 y=11+ 7 8 y solve the y
Answer:
y=-3/32
Step-by-step explanation:
2-18y=11+78y
-18y-78y=11-2
-96y=9
y=-3/32
- is slightly variable - and follows a nearly normal distribution - with a mean of 25 square feet - and a standard deviation of 3 square feet. (a) what is the probability that - the area covered by a can of spray paint - is more than 27 square feet?
The probability that the area covered by a can of spray paint is 0.251
The variable of interest is:
X: are objects that can be painted with a single can of spray paint.
This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.
Symbolically:
P(X≥27)
To calculate the probability, use the standard normal distribution, so first standardize the value of X using:
Z= (X-μ)/σ
P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)
Now, because the Z-table contains cumulative probability information:
P(Zα≤Z₀)=1-α
you must perform the following conversion to calculate the requested probability:
1 - P(Z<0.67)= 1 - 0.749= 0.251
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