Anne, Becky and Charlotte had sums of money in the ratio 7:6:5. One of them gave £9 to one of the others and this changed the ratio (in the same order of names) to 6:5:4. The total sum of money remained the same; what was it?
Answer:
The total sum of money is £810
Step-by-step explanation:
The parameters given are;
The ratio of the sum Anne, Becky and Charlotte had = 7:6:5
One of them gave one of the others £9 and the new ratio becomes 6:5:4
The total sum of money remains the same = M
The initial fraction amount of the total sum of money each had is given as follows;
Anne = 7/(7 + 6 + 5)×M = 7/18·M = 0.389·M
Becky = 6/18·m = 1/3·M
Charlotte = 5/18·M = 0.278·M
After one of them gave £9 to one of the others, the fraction amount of the total sum of money each had became;
Anne = 6/(6 + 5 + 4)×M = 6/15·M = 0.4·M
Becky = 5/15·m = 1/3·M
Charlotte = 4/15·M = 0.267·M
Therefore, given that Anne's fraction of the total sum of money increased while Charlotte's fraction of the total sum of money decreased, it was Charlotte that gave Anne £9
Therefore, the fraction of the total sum of money equivalent to £9 is found s follows;
5/18·M - 4/15·M = 1/90·M = £9
Therefore;
M = 90 × £9 = £810
The total sum of money = £810.
What are the dimensions of the poster at 1/3 its current size?
Answer:2 in. by 3 in
Step-by-step explanation:
only my best guess
A certain arithmetic sequence has this explicit formula for the nth term:
an = 11 + (n - 1)(4)
The same sequence has this recursive formula:
an = an-1 +__
What number belongs in the blank space in the recursive formula?
Answer:
4
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
[tex]a_{n}[/tex] = 11 +(n - 1)4 , then
d = 4
The recursive formula allows a term in the sequence to be found by adding d to the previous term, thus
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 4
Answer:
The answer is 4
Step-by-step explanation:
An appliance store reduced the price of a refrigerator by 20% and then raised the prices by 10% from the lower price. What was the original price of the refrigerator, if the price was $70.49 ?
Answer: $80
Step-by-step explanation:
Let the original price of the refrigerator be represented by y.
We are told that an appliance store reduced the price of a refrigerator by 20%. This will be:
= y - (20% of y)
= y - (20/100 × y)
= y - (0.2 × y)
= y - 0.2y
= 0.8y
We are then told that the store then raised the prices by 10% from the lower price. This will be:
= 0.8y + (10% of 0.8y)
= 0.8y + (0.1 × 0.8y)
= 0.8y + 0.08y
= 0.88y
Since we told that now the price was $70.49, this means that we have to find the value of y using the above expression. This will be:
0.88y = $70.49
y = $70.49/0.88
y = $80.10
y = $80 approximately
The original price of the refrigerator is $80.
p inversely as( m + 1 ). when p = 4, m = 8 . (a)Find a equation connecting P and ( m + 1 ). (b)calculate the value of p when m = 11
Answer:
a. p= 36/(m + 1)
b. p = 3
Step-by-step explanation:
If p varies inversely as (m + 1)
then p = k × 1/(m + 1). {Where k is the constant}
when p = 4, m = 8, that means 4 = k/(8 + 1)
4 × 9 = k and k = 36
a. Therefore the equation is p= 36/(m + 1)
b. When m = 11,
p = 36/(11 + 1)
p = 36/12
p = 3
405 increased by 8.3
Answer:
413.03
Step-by-step explanation:
405 increased by 8.3 is 405+8.3.
[tex]405+8.3=\\405+8.0+0.3=\\413+0.3=\\413.03[/tex]
Answer:
413.3 if ADD, 437.5215 if add by percent
Step-by-step explanation:
If it's increaced by 8.3%, then it is 405 + 32.5215 = 437.5215
If it's add 8.3, then it's 413.3.
Model the situation with the sum of polynomials. Then simplify the sum.
4. The width of a rectangle is represented by 4x, and its length is
represented by (3x + 2). Write a polynomial for the perimeter of the
rectangle
3x + 2
4x
O
Answer:
[tex]perimeter= 14\,x\,+ \,4[/tex]
Step-by-step explanation:
Recall the formula for the perimeter rectangle (the addition of all rectangle\s sides): That is: twice the width ( 4x) plus twice the length (3x+2);
[tex]perimeter=2\,*\,width \,+\,2\,*\,length\\perimeter = 2\,(4\,x)+2\,(3\,x+2)\\perimeter= 8\,x+6\,x+4\\perimeter= 14\,x\,+ \,4[/tex]
Please help urgently!
Answer:
[tex]a=-6\quad and \quad b=8[/tex]
Step-by-step explanation:
[tex]\frac{8-\sqrt{18}}{\sqrt{2}}=\frac{\sqrt{2}}{\sqrt{2}}\times \frac{8-\sqrt{18}}{\sqrt{2}}\\\\=8\sqrt{2}-\sqrt{2}\cdot \sqrt{18}\\\\=8\sqrt{2}-\sqrt{36}\\\\=-6+8\sqrt2[/tex]
By comparing the last expression with [tex]a+b\sqrt{2}[/tex], we get:
[tex]a=-6\quad and \quad b=8[/tex]
Best Regards!
The 3 by 3 grid below shows nine 1 cm × 1 cm 1 cm×1 cm squares and uses 24 cm 24 cm of wire. What length of wire is required for a similar 20 by 20 grid?
Answer:
Length of wire is required = 840 cm
Step-by-step explanation:
Given:
20 by 20 grid
Find:
Length of wire is required.
Computation:
We know that 20-20 grid required 21 lines.
20 cm vertical and horizontal.
⇒ Length of wire is required = (21 + 21)20 cm
⇒ Length of wire is required = (42)20 cm
⇒ Length of wire is required = 840 cm
In each figure below, find m∠1 and m∠2 if a||b. Show your work with statements.
Answer:
m < 1 = 80
m < 2 = 70
Step-by-step explanation:
As we can see in the figure that
[tex]a || b[/tex]
Plus line s and t are considered to be transversals
That results into
m < 1 and 80
i.e alternate angles
And as we know that alternative angles are equal to each other
So,
m < 1 = 80
Moreover,
m < 2 = 70
As corresponding angles are equal to each other
Therefore the m < 1 = 80 m < 2 = 70 could be computed easily by applying the above things
At a school carnival you pick a ball from two different containers. Each container has red balls and green balls. How many possible outcomes are there?
Answer:
4
Step-by-step explanation:
2^2
Answer:
4
Step-by-step explanation:
Raphael graphed the function g(x)=x+2 and f(x)=x-1. How many units below the y intercept of g(x) is the y intercept of f(x)
Answer:
3
Step-by-step explanation:
If you take the y-intercept of x+2 and the y-intercept of x-1 and graph them, count the number of units in between them and you should see that your answer is 3
Answer:
D) 3 units
Step-by-step explanation:
Help!!! ASAP!! :3 Will Givve BRAINLIEST!!
Answer:
V = 672 cm³ (Option 3)
Step-by-step explanation:
Volume of Rectangular Prism = [tex]Length * Width * Height[/tex]
Where L = 14 cm, W = 6 cm and H = 8 cm
V = 14 * 6 * 8
V = 672 cm³
please help me please :(
Answer:
18
Step-by-step explanation:
There is a string that is 3 yards long that is divided into pieces that are 1/6 of yard long. Divide the total length by the length it was divided into to find the number of pieces.
When dividing with fractions, the second number will be inverted and multiplied by the first number.
3 ÷ (1/6) = 3 × 6 = 18
You will have 18 pieces
A car travels 0.75 miles every minute explain how you could use proportional reasoning to find how far the car travels in one hour
Answer:
A car can travel 45 miles every hour, because I multiply 3/4 (0.75) by 60. Because of this, 60 minutes is an hour.
Step-by-step explanation:
in Germany, VAT is at 19 % Jeremy buys a calculator for 58.31 German money this price contains VAT find the amount of VAT paid by jeremy
Answer:
9.31?
Step-by-step explanation:
Match the information on the left with the appropriate equation on the right.
Answer:
See attachment below
Step-by-step explanation:
For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,
y = - 2 / 3x + 3,
y + 2 / 3x = 3,
2x + 3y = 9 - Option C
_______________________________________________________
Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.
- 1 = ( - 3 / 2 )( 4 ) + b,
b = 5,
Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,
y = - 3 / 2x + 5,
2y = - 3x + 10,
- 2y = 3x - 10 - Option A
_______________________________________________________
( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,
Slope = 3 - 1 / 6 - 3 = 2 / 3
Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,
3 = ( 2 / 3 )( 6 ) + b,
b = - 1,
y = 2 / 3x - 1 = Option D
Take a look at the attachment below for further help;
what is as a percentage and decimal
[tex] \frac{11}{20} [/tex]
Answer:
Percentage: 55%
Decimal: 0.55
Step-by-step explanation:
11÷20=
0.55
[tex]\frac{11}{20}=\frac{55}{100}[/tex]
or 55%
David, Malachy and Paul share some sweets in the ratio 4:3:3. David gets 24 sweets. How many did Paul get?
If David, Malachy and Paul share some sweets in the ratio 4:3:3 then Paul get 7.2 number of sweets
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that David, Malachy and Paul share some sweets in the ratio 4:3:3
All three shared 24 sweets together.
Let x be the number of sweets
4x+3x+3x=24
Add the like terms
10x=24
Divide both sides by 10
x=2.4
Now paul has 3x sweets so 3×2.4=7.2
Hence, Paul get 7.2 number of sweets
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What type of number is -2343 a)whole number b)integer c)rational d)irrational
Answer: B and C
Step-by-step explanation:
-2343 is an integer and also a rational number since it can be expressed as a fraction.
An integer is whole number and its opposite so -2343 is an integer because its opposite is 2343.
Five minutes after midnight of 25 April 2016 there was a heavy rain in Adelaide. 144 hours later, what is the probability that it would be sunny over there? Justify your answer.
Answer:
0
Step-by-step explanation:
144 h = 6 days
Six days later would be midnight on May 1.
That's autumn in Australia, so sunset was probably around 8 pm. By midnight it would be completely dark.
The probability of Adelaide being sunny at midnight is zero.
What is the value of X that makes A parallel to B? WILL GIVE BRAINLIEST!
Answer:
20
Step-by-step explanation:
To make these parallel, 2 and 5 would have to be corresponding angles, meaning that they have equal angle measure:
3x-20=x+20
3x=x+40
2x=40
x=20
Hope this helps!
Answer:
x= 20
Step-by-step explanation:
To make the lines parallel, angle 2 would equal angle 5
3x-20 = x+20
Subtract x from each side
2x -20 = 20
Add 20 to each side
2x-20 +20 = 20+20
2x = 40
Divide by 2
2x/2 = 40/2
x = 20
find the area of triangle two sides of which are 8cm and 11cm and the perimeter is 32cm with Herons formula
Answer:
8√30
Step-by-step explanation:
The length of the third side is 32 - 8 - 11 = 13. s (which is half of the perimeter) is 32 / 2 = 16 so the answer is:
√s(s-a)(s-b)(s-c) = √16 * (16 - 8) * (16 - 11) * (16 - 13) = √16 * 8 * 5 * 3 = √1920 = 8√30
Who wants to help I really really need it ❤️
Answer:
4^8
Step-by-step explanation:
4^5 * 4^3
We know that a^b* a^c = a^(b+c)
4^(5+3)
4^8
Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was 160 meters away. After 3 seconds of driving, she was 85 meters away from the safe zone. Let D represent the distance (in meters) from the safe zone after t seconds. Complete the equation for the relationship between the distance and number of seconds. D=
Answer:
The answer is D(t) = 160 - 25t
Step-by-step explanation:
well khan academy said it lol
For which equations is 8 a solution? Check all that apply.
Ox+6=2
X+2 - 10
ox-4-4
Ox-2-10
0 2x=4
3x - 24
OŠ - 16
Answer:
3x-24
Step-by-step explanation:
because 3x-24 divide both side by co efficient of x which is 3 so 24/3=8
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. (A) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
Answer:
See below
Step-by-step explanation:
When you roll an 8-sided die twice, the sample space is the set of all possible pairs (x,y) where x is the first outcome and y is the second outcome.
The sample space is:
[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]
The sample space of the product xy of each outcome forms the required possibility diagram.
This is given as:
[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]
Which of the following is the result of the equation below after completing the square and factoring?
Answer:
D) [tex](x + \frac{5}{2})^{2} = \frac{9}{4}[/tex]
Step-by-step explanation:
Step(i):-
Given equation
x² + 5 x + 8 = 4
⇒ [tex]x^{2} + 2 X \frac{5}{2} x + (\frac{5}{2} )^{2} - (\frac{5}{2} )^{2}+ 8 = 4[/tex]
Step(ii):-
By using (a + b)² = a² + 2 a b + b²
⇒ [tex](x + \frac{5}{2})^{2} - (\frac{5}{2} )^{2}+ 8 = 4[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = 4 + (\frac{5}{2} )^{2} -8[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = (\frac{25}{4} ) -4[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = (\frac{25-16}{4} )[/tex]
⇒ [tex](x + \frac{5}{2})^{2} = \frac{9}{4}[/tex]
Final answer:-
[tex](x + \frac{5}{2})^{2} = \frac{9}{4}[/tex]
The mapping diagram shows a functional relationship.
Domain
Range
Complete the statements
f(4) is
f(x) = 4 when x is
4
8
2
3
11
3
NI-
Intro
Done
Answer:f(4)=1/2
f(x)=4 when x is 8
The complete statements would be as:
⇒ function f(4) is 1/2 and function f(x) = 4 when domain x is 8.
What are the domain and range?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
We have been given that the mapping diagram shows a functional relationship.
To determine the value of f(4)
As per the given functional relationship,
If the value of the domain is 4 then the value of the respective range would be 1/2.
Therefore, the function f(4) would be 1/2.
To determine the value of x, when f(x) = 4
As per the given functional relationship,
If the value of the range is 4 then the value of the respective domain would be 8.
Therefore, x would be 8 if function f(x) = 4 .
Hence, the complete statements would be as:
f(4) is 1/2 and f(x) = 4 when x is 8.
Learn more about the domain and the range here:
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Edward has 30 sweets.
The ratio of red sweets to yellow sweets is 2:3
How many red sweets does Ed have? *
Answer:
20 red sweets
Step-by-step explanation:
do two thirds of 30 and the part that cane out is the red sweets
Answer:
12
Step-by-step explanation:
Sum the parts of the ratio, 2 + 3 = 5 parts
Divide the number of sweets by 5 to find the value of one part of the ratio
30 ÷ 5 = 6 sweets ← value of 1 part of the ratio, thus
2 × 6 = 12 ← number of red sweets