Answer: £225
Step-by-step explanation:
Amount shared = £750
Let Sarah's share = y
Therefore,
Caroline's share = 3y
Bridget's share = 2(3y) = 6y
Mathematically,
y + 3y + 6y = £750
10y = £750
y = £750/10
y = £75
Caroline's share = 3y
Caroline's share = 3 × £75 = £225
Caroline's share is £225
When Anna bought 10 cream puffs and ice creams, at $1.50 per
cream puff and $1.20 per ice cream, the total price was $13.80.
How many cream puffs and ice creams did she buy, respectively?
Answer:
6 cream puff and 4 ice creams
Step-by-step explanation:
i = ice cream
p = cream puff
p+i= 10
1.50p + 1.20 i = 13.80
Multiply the first equation by -1.2
-1.20p -1.20 i = -12.00
Add this to the second equation
1.50p + 1.20 i = 13.80
-1.20p -1.20 i = -12.00
----------------------------------
.3p = 1.80
Divide each side by .3
p =6
Now find i
p+i = 10
6+i= 10
i= 10-6 =4
Carter has 123 songs on a playlist. He's categorized them in the following manner: 11 gospel, 25 country, 21 blues, 6 folk, 16 pop. 14 jazz.
and 30 rock. If Carter begins listening to his playlist on shuffle, what is the probability that the first song played is a gospel song? Express
your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Plsssss help
Answer:
11/123
Step-by-step explanation:
P( gospel) = number of gospel songs/ total
= 11/123
slove for g : 9+3.5g=11-0.5g
Answer:
g= 1/2
Step-by-step explanation:
9+3.5g=11-0.5g
Add .5 g to each side
9+3.5g+.5g=11-0.5g+.5g
9+4g = 11
Subtract 9 from each side
9+4g-9 = 11-9
4g = 2
Divide by 4
4g/4 = 2/4
g= 1/2
What is the answer to this, I need an explanation please ASAP
Answer:
323 ft^2
Step-by-step explanation:
Separate the figure on the left into two figures, a trapezoid and a square
The area of a trapezoid is
A = 1/2 (b1+b2)h
A = 1/2 (12+15)*7
= 1/2 (28)7
98 ft^2
The area of a square is
A = s^2
= 15^2
= 225 ft^2
Add the areas together
A total = 98+225 =323 ft^2
The lengths of two sides of a triangle are 3 inches and 8inches. Find the range possible for lengths for the third side, s.
Answer:
Using triangular inequality:
[tex]0< s\leq 3+8\\\ 0<s\leq 11\\[/tex]
Simplify (x^4y)^3.
x^12y^3
x^4y^3
x^7y^3
=========================================================
Explanation:
Think of x^4y as x^4y^1. When we raise this to the third power, we multiply the outer exponent 3 by each inner exponent
x^4 turns into x^12
y^1 turns into y^3
-----------
This is one way to show your work
(x^4y)^3
(x^4y^1)^3
x^(4*3)*y^(1*3) ... multiplying outer exponent by each inner exponent
x^12y^3
-----------
A more lengthy way to get the answer is to write x^4y out three times multiplying by itself that many times. The outer exponent 3 tells us we will have three copies of x^4y multiplied with itself.
(x^4y)^3 = (x^4y)*(x^4y)*(x^4y)
(x^4y)^3 = (x^4*x^4*x^4)*(y*y*y)
(x^4y)^3 = ( x^(4+4+4) ) * ( y^(1+1+1) )
(x^4y)^3 = x^12y^3
HELP! What is the volume in cubic inches of the solid figure, rounded to the nearest cubic inch?
Answer:
Volume of the solid figure = 1131 cubic inches
Step-by-step explanation:
Volume of solid figure = Volume of half cylindrical prism + Volume of the rectangular prism
Volume of half cylindrical prism = [tex]\frac{1}{2}(\pi r^2h)[/tex]
= [tex](\frac{1}{2})(\pi )(17-11)^2(6)[/tex]
= 339.29 cubic inch.
Volume of the rectangular prism = (length × width × height)
= 11 × 6 × 12
= 792 cubic inches
Volume of the solid figure = 339.29 + 792
= 1131.29
≈ 1131 cubic inches
find the value of trig function indicated, use Pythagorean theorem to find the third side if you need it. Part 4
Answer:
[tex]\fbox{\begin{minipage}{5em}13. 0.830\\14. 0.800\\15. 0.391\\16. 0.750\end{minipage}}[/tex]
Step-by-step explanation:
A right triangle with 3 sides: adjacent side, opposite side and hypotenuse (as shown in attached picture)
According to the trigonometric properties:
[tex]sin(theta) = \frac{opposite}{hypotenuse}[/tex]
[tex]cos(theta) = \frac{adjacent}{hypotenuse}[/tex]
[tex]tan(theta) = \frac{opposite}{adjacent}[/tex]
[tex](adjacent)^{2} + (opposite)^{2} = (hypotenuse)^{2}[/tex]
[tex](adjacent)^{2} = (hypotenuse)^{2} - (opposite)^{2}[/tex]
[tex](opposite)^{2} = (hypotenuse)^{2} - (adjacent)^{2}[/tex]
Use the above formulas with corresponding sides:
[tex]13) cos(theta) = \frac{9}{3\sqrt{13} } = 0.83[/tex]
[tex]14) sin(theta) = \frac{\sqrt{5^{2}-3^{2} } }{5} = \frac{4}{5} = 0.8[/tex]
[tex]15) sin(theta) = \frac{9}{\sqrt{(8\sqrt{7}) ^{2} + 9^{2} } } = 0.391[/tex]
[tex]16) tan(theta) = \frac{3}{4} = 0.75[/tex]
Hope this helps!
:)
8. Solve for a:
p+q=2ab
[tex]\text{Solve for a:}\\\\p+q=2ab\\\\\text{Since we want to solve for a, it needs to be by itself}\\\\\text{To do this, we have to divide both sides by 2b}\\\\\frac{p+q}{2b}=a\\\\\text{Now since A it's by itself, that'll be your answer}\\\\\boxed{\frac{p+q}{2b}=a}[/tex]
Given the equations below what is the value of ab?
10b-9a=6
b-a=1
Answer:
12
Step-by-step explanation:
Adding a to both sides of the second equation we get b = a+1
Substituting this in we get
10a + 10 - 9a=6
a +10 =6
a=-4
Putting this back in to the second one we get b+4=1
B=-3
-4*-3=12
The value of ab = 36.
We have the following equations -
10b - 9a = 6
b - a = 1
We have to determine the value of ab.
If [tex]a^{2} -b^{2} = \pi[/tex] and [tex]a + b = 4\pi[/tex] then the value of (a - b) will be ?We have - [tex]a^{2} -b^{2} = \pi[/tex]
(a + b) (a - b) = [tex]\pi[/tex]
a - b = [tex]$\frac{\pi }{4\pi }[/tex] = 1/4
According to question, we have -
10b - 9a = 6
b - a = 1
Now -
b - a = 1
a = b
Therefore -
10b - 9a = 6
10b - 9b = 6
b = 6 = a
ab = 6 x 6 = 36
Hence, the value of ab = 36.
To solve more questions on finding unknowns, visit the link below -
https://brainly.com/question/14728313
#SPJ2
For one month Siera calculated her home town's average high temperature in degrees Fahrenheit. She wants to convert
that temperature from degrees Fahrenheit to degrees Celsius using the function co-32) What does C(F)
represent?
Answer:
the temperature of f degrees Fahrenheit converted to degrees Celsius.
Step-by-step explanation:
If 28 g of cashew nuts contains 14 g of fats.
How many grams of fat are there in 42g of cashew nuts?
Answer:
21 g
Step-by-step explanation:
Use ration method
28:14 = 42:x
To find x,
(14 x 42) divided by 28, which equals 21g
HELP ME OUT! A student dissolves 1 gram of sugar in 10 grams of water. She then determines the mass of the solution. What is the mass of the dissolved sugar and water?
Answer:
The mass of the dissolved sugar and water is 11 g.
Step-by-step explanation:
When a substance is dissolved in another, they are mixed together forming a new one, therefore the new substance's mass must be the same as the sum of the individual mass of each substance mixed, because there are no leaks. In this case, there are two substances being mixed, the water which have a mass of 10 grams and the sugar which have a mass of 1 gram, therefore the final solution's mass must be equal to 11 g.
It’s the math question please help
Answer:
-22, 4, -27, 2
Step-by-step explanation:
-10 + (-12) = -10 - 12 = -22
-3 + 7 = 4
-11 - 16 = -27
-13 - (-15) = -13 + 15 = 2
Answer:
-22 4 -27 2
Step-by-step explanation:
-10 + (-12) = -22
-3 + 7 = 4
-11 - 16 = -27
-13 -(-15) = 2
I have 2 questions, What is 1/4 x 9 =? then 2/5 x 12 ( Multiplying fractions by whole numbers using tape diagrams)
Answer:
What is 1/4*9=2.25 then 2/5*12=4.8
Step-by-step explanation:
The area of a triangle garden can
be no more than 120 square
feet. The base of a triangle
is 16 feet in
lenght What
inequalitie describes the
possible heights, h, of the
triangular garden?
Answer:
0< h ≤ 15
Step-by-step explanation:
A = 1/2 * base * height = 1/2*16*h = 8h
A no more is ≤.
A ≤ 120
8h ≤ 120
h ≤ 15
0< h ≤ 15
Height should be more than 0 feet and no more than 15 feet.
please but this equation in function form, 15+3y=-24x and what is funciton form?
Answer:
y = -8x - 5 ; function form is y = mx+b
Step-by-step explanation:
15 + 3y = -24x
3y + -24x - 15
y = -8x - 5
if i have 85 lessons and only 42 days to complete them how many lessons would i have to do a day to finish on time?
Answer:
At least 3 per day
Step-by-step explanation:
All you gotta do is divide 85 by 42. You get 2.024 but you can't do .024 parts of a class, i mean you probably can but its finna be hard to do it exact so just do 3 per day and you'll even finish before. By the way, if this is an actual scenario, you gotta remember that they be adding lessons everyday so good luck!
Which expression is equivalent to 81^1/3?
33/3
3133
9313
273/3
Answer: 3 3√3
Step-by-step explanation:
81^1/3
=3√81
= 3 3√3
Solve for x 3x - 5 = 2x + 6.
01
O-1
O 11
0-11
Answer:
X= 11
Step-by-step explanation:
Move constant to the right side and change its sign
Mitchell's family is slow cooking 2 3/4 pounds of meat. The recipe says to cook the meat 1 1/2 nours per pound,
How long should Mitchell's family cook the meat?
A 1 5/6
B. 2 3/8
C 4 1/ 8
D. 4 1/4
Answer:
C
Step-by-step explanation:
Multiply the 1.5 hours per pound by 2.75 pounds and we get 4.125 hours or 4 1/8
Answer:
C: 4 1/8
Step-by-step explanation:
i took the quiz
match the expressions 21/25 60% 13/20 84% 2/5 75% 65% 3/4 3/5
Answer:
21/25 ---> 84%
13/20 ---> 65%
3/5 ---> 60%
3/4 --->75%
2/5 ---> 40%
Which graph shows a system with no solutions?
Answer:
A Graph b
Step-by-step explanation:
Since the two lines are parellel, they will never intersect and there will be no solutions
URGENT!!! A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points) A: No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 B: No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 C: Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 D: Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answer:
A: No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Step-by-step explanation:
c for child
a for adult
4c+ 6a ≤ 120 for build
4c +4a ≤ 100 for test
We want 20 child and 6 adult
4(20)+ 6*6 ≤ 120
80+36 ≤ 120
116 ≤ 120 true for build
4*20 +4*6 ≤ 100
80+24 ≤ 100
104 ≤ 100
False for test
Answer:
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Step-by-step explanation:
Which arcs are congruent? Check all that apply. Arc B C ≅ Arc M P Arc B C ≅ Arc M O Arc C F ≅ Arc K P Arc E G ≅ Arc K L Arc L O ≅ Arc M P
Answer:
Step-by-step explanation:
The arcs that are congruent are:
Arc B C ≅ Arc M P. Arc E G ≅ Arc K L. Arc L O ≅ Arc M P.What congruent angles in math?
Two geometric figures can be described as congruent if on can be superpose on the other.
Conclusively, congruent' is said to be a word that connote 'exactly equal' when looking at the shape and size of the angles. The options chosen above are congruent because they have the sides to be equal.
Learn more about congruent from
https://brainly.com/question/2938476
why is x^2-8x+20 always positive?
Answer:
cause it is
Step-by-step explanation:
it just is, sorry i can't help. maybe bc there are more positive functions then negative ones?
If angle P= 50 then angle R=
Answer:
it matters what the whole angles is.
Step-by-step explanation:
for example if it's a 180 degree angle P=50 then R would equal to 130 degrees
second example if P=50 and it's a 90 degree angle R=40
For anyone on OW, it's 130.
The following data shows prices of meal options at Bob's Burgers. Bob
wants to construct a histogram from this graph. Prices of Meal Options at
Bob's Burgers: $6, $7, $7, $8,$9,$10, $10, $11, $11, $12,$12, $13, $13, $13,
$13,$14, $14, $14, $15, $15, $15, $15, $16, $16, $17. How many meals could
belong in the interval $10.99 - $13.99? *
Answer:
Step-by-step explanation:
The number of meals that could
belong in the interval $10.99 - $13.99 is represents the frequency of that interval. The interval is also called the class width. Since there are no decimals, the meals must be greater than or equal to $11 and lesser than $14. Looking at the data, the meals that fall within the interval are
$11, $11, $12,$12, $13, $13, $13,$13
The frequency is 8
Therefore, 8 meals could
belong in the interval $10.99 - $13.99
In right triangle XYZ, ∠Z is a right angle, m∠Y=16∘, and XZ=7. sin16∘≈0.276 cos16∘≈0.961 tan16∘≈0.287. What is the measurement of YZ?
Answer: 24.4
Step-by-step explanation:
So lets review a bit about sine, cosine, and tangent.
Look at attachment below
Okay so we have the opposite side of the triangle and are trying to find the length of the adjacent side. The only trig expression that contains both opposite and adjacent is tangent. The equation goes
tanX = opposite(XZ)/adjacent (YZ)
we know what X is X = 16
and we know what opposite is opposite = 7
so now the equation looks like
tan16 = 7/adjacent
and in the question it says that tan16 = 0.287 so lets plug that in
0.287 = 7/adjacent
0.287adjacent = 7
adjacent = 7/0.287
adjacent = 24.4
YZ = 24.4
Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-fifth x minus four-fifths? f Superscript negative 1 Baseline (x) = negative one-fifth x + four-fifths
Answer:
The inverse of the function is [tex]g (x)=-5x-4[/tex].
Step-by-step explanation:
The function provided is:
[tex]f^{-1}(x)=-\frac{1}{5}\ x-\frac{4}{5}[/tex]
Let us assume that:
[tex]y=f^{-1}(x)[/tex]
Then the equation will be:
[tex]y=\frac{-x-4}{5}[/tex]
To compute the inverse of the function substitute x as y and y as x.
[tex]x=\frac{-y-4}{5}[/tex]
Now solve for y as follows:
[tex]x=\frac{-y-4}{5}[/tex]
[tex]5x=-y-4[/tex]
[tex]y=-5x-4[/tex]
Thus, the inverse of the function is [tex]g (x)=-5x-4[/tex].
Answer:
The answer is "-5x-4"
Step-by-step explanation:
Given:
[tex]\bold{f^{-1} (x)=(-\frac{1x}{5}-\frac{4}{5})}[/tex]
solve the above equation:
[tex]\to f^{-1}(x)= \frac{-x-4}{5}\\\\\to f^{-1}(x)= -\frac{x+4}{5}\\[/tex]
Let
[tex]y= f^{-1} x= -(\frac{x+4}{5})\\\\[/tex]
inverse the above function:
[tex]\to x= -(\frac{y+4}{5})\\\\\to 5x= -(y+4)\\\\\to 5x= -y-4\\\\\to\boxed {y=-5x-4}\\\\[/tex]
