Start off with %70 of 150
0.7 • 150 = 105
To find their total donation amount,
105 • £1 = £105
Then we know the rest of the parents account for the last %30 of the attendees
We can find this out by either,
150 - 105
or
0.3 • 150
Either way we end up with 45
45 • £2 = £90
%70 (105) of the parents donated £105
%30 (45) of the parents donated £90
The parents, in total, donated £195
For which values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2)?
The values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2) are ( 0, B, 2B)
In the above question, a horizontal line is given whose equation is Ax + By = C which passes through a point (-4, 2)
We can make two observations from the given information of horizontal line passes through point (-4,2) which are as follows:
1. The slope of a horizontal line will be parallel to the x-axis whose slope will be, m=0.
2. The given point and the line meet at (-4,2).
Now as the point (-4,2) lie on the line it will satisfy the equation of the horizontal line
We get,
A(-4) + B(2) = C
-4A + 2B = C ..... eqn 1
Also, we can write the given equation in the slope-intercept form which is
y = mx + c
By = -Ax + C
y = [tex]\frac{-A}{C}[/tex]x + [tex]\frac{C}{B}[/tex]
So, we can imply that m = [tex]\frac{-A}{C}[/tex] = 0
A = 0
Putting this in eqn 1 we get,
-4A + 2B = C
0 + 2B = C
C = 2B
Hence, we conclude that values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2) are ( 0, B, 2B)
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ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Answer:
y = - x + 8
Step-by-step explanation:
y = - x + 8
What are Co-Interior angles
Answer: angels that lie between two lines and are intersected by a transversal.
Step-by-step explanation:
A recipe for oatmeal cookies calls for 2 cups of flour and 2.5 cups of oats. For each cup of flour, he must also add 1.5 teaspoons of baking powder. If a baker uses 15 cups of oats how many teaspoons of baking powder must he use?
He will use 18 teaspoons of baking powder for the oatmeal recipe
How to calculate the amount of baking flour ?A recipe requires 2 cups of flour and 2.5 cups of oats
For each cup he must add 1.5 teaspoons of baking powder
He uses 15 cups of oats
Each recipe uses 2 cups of flour, the teaspoons of baking powder used in one recipe is
1.5 × 2 = 3
2.5 cups of oats is used for one recipe, he uses 15 cups of oats, this means that the number of recipes is 6 (15/2.5)
Since the number of recipes is 6 and 3 teaspoon of baking powder is used for one recipe, then the number of teaspoons used is
= 6 × 3
= 18
Hence he used 18 teaspoons of baking powder
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7-3+5x(6-2)=
A 16
B 24
C 0
D 36
find R=x^2/y when
y=3.8x10^5
x=5.9x10^4
The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
How to evaluate the expression?The expression is given as
R = x^2/y
Where
y = 3.8 x 10^5
x = 5.9 x 10^4
Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y
So, we have
R = (5.9 x 10^4)^2/3.8 x 10^5
Evaluate the exponent
So, we have
R = 34.81 x 10^8/3.8 x 10^5
Evaluate the quotient
So, we have
R = 9.16052631579 x 10^3
Approximate the above expression
So, we have
R = 9.2 x 10^3
Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
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Simplify each expression.
ln e²/2
[tex]\frac{ln(e^2)}{2}[/tex] = 1, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Given: [tex]\frac{ln(e^2)}{2}[/tex]
Now,
By property of logarithm, [tex]log_b(a)^m=m(log_b(a))[/tex],=> [tex]\frac{ln(e^2)}{2}[/tex] = [tex]\frac{2 (ln(e))}{2}[/tex]
=> [tex]\frac{ln(e^2)}{2}[/tex] = ln (e)
AS we know that ln (e) = 1 (by properties of logarithm),=> [tex]\frac{ln(e^2)}{2}[/tex] = 1
Hence, [tex]\frac{ln(e^2)}{2}[/tex] = 1, by properties of logarithm.
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sue wants 1 2 of a rectangular pan of cornbread. dena wants 1 3 of the same pan of cornbread. how should you cut the cornbread so that each girl gets the size portion she wants? solve this problem any way you choose.
Finding LCM for the problem, you should cut the cornbread into 6 parts, Sue will get 3 parts and Dena will get 2 parts.
LCM is referred to as the least common multiple for a set of numbers that can be divided by the same whole number as a result.
At first, we have to find LCM of 2 and 3, which is the denominator of 1/2 and 1/3, and its 6 and we will cut it into 6 pieces.
So, Sue will get 3 pieces from the cornbread ( 3/6 = 1/2 ) and Dena will get 2 pieces from the cornbread ( 2/6 = 1/3 ).
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The Leapin Lizards Center sells entrance tickets for $10.00 per child on Saturday nights. At capacity, the center can only hold 50 children during the 5:00-6:00pm time slot. The function L(c)=10c represents the amount of money Leapin Lizards makes on Saturday nights during the time slot.
Which statement best represents the range of the function in this context?
The statement that best represents the range of the function in this context is 0 <= L(c) <= 500
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine which statement best represents the range of the function in this context?The function is given as
L(c) = 10c
From the question, we understand that:
Maximum number of children = 50
This means that
c =50
So, we have
L(50) = 10 * 50
Evaluate
L(50) = 500
Hence, the statement that best represents the range of the function in this context is 0 <= L(c) <= 500
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Let f(x)=x-4 and g(x)=x²-16 . Perform each function operation and then find the domain. g(x)-f(x)
The domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
We are given the two functions as:
f (x) = x - 4
g (x) = x² - 16
Now, first, we need to subtract f (x) from g (x).
So, we get that:
g (x) - f (x) = x² - 16 - (x - 4)
g (x) - f (x) = x² - 16 - x + 4
g (x) - f (x) = x² - x - 12
Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.
Therefore, we get that the domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
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nth term for 6,21,46,81
can someone explain how to answer this type of quadratic sequence step by step please
A sequence of events or things is a number of events or things that come one after another in a particular order. The nth term of
for 6,21,46,81 is 5n²+1.
What is sequence?A sequence of events or things is a number of events or things that come one after another in a particular order.
Write down the nth term of this quadratic number sequence.
6,21,46,81...
number sequence has nth term = an² + bn + c.
Confirm the sequence is quadratic. This is done by finding the second difference.
Sequence =6,21,46,81
1st difference = 15,25,35
2nd difference = 10,10
If you divide the second difference by 2, you will get the value of a.
10/2=5
So the first term of the nth term is 5n².
ext, substitute the number 1 to 4 into 5n².
n=1,2,3,4
5n²=5,20,45,80
Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.
5n²+1=6,21,46,81.
Therefore nth term for 6,21,46,81 is 5n²+1.
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Order the numbers from least to greatest.
Which expression is equivalent to (5x−5y3)−2? −25x10y6 negative quantity 25 times x raised to the tenth power end quantity over y raised to the sixth power x raised to the tenth power over quantity 25 times y raised to the sixth power end quantity 1 over quantity 25 times x raised to the tenth power times y raised to the sixth power end quantity
Using the rules of exponents, the expression (5 x^−5 y^3)^−2 is equivalent to x^10 / (25 y^6) or "x raised to the tenth power over quantity 25 times y raised to the sixth power end quantity".
Given: (5 x^−5 y^3)^−2
1. Distribute the power of two using the Power of a Power Rule. "When a power is raised to another power, multiply the exponents."
5^−2 x^(−5)(−2) y^(3)(−2) = 5^−2 x^10 y^-6
2. Use Negative Rule of Exponent. "A number with a negative exponent should be put to the denominator, and vice versa."
5^−2 x^10 y^-6 = (x^10) / (5^2 y^6)
3. Simplify the constant term.
(x^10) / (5^2 y^6) = x^10 / 25 y^6
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2. Matthew earns $35.00 on Saturday for mowing lawns and deposits it into his
savings account. He then withdraws $27.00 to buy a video game.
What is the overall increase or decrease in Matthew's savings account balance?
A. - $9.00
B. + $6.00
C. + $8.00
D. - $7.00
Step-by-step explanation:
Technically none of these are the right answer. The decrease in his account would be -27.
But out of the given choices, I'll go with option C because he has $8 left in his savings
Which multiple choice response is true?
O Decreasing on (-*, 0); increasing on (0, *)
O Increasing on (-x, ∞)
O , Increasing on (-*, 0); decreasing on (0, *)
O Decreasing on (-∞, ∞)
True response is that the function represented by the graph is Increasing on (-∞, 0) and decreasing on (0, ∞)
A function is said to be increasing in its domains if the value of its range is increasing in that domain.
Similarly, if the function is decreasing in its domain then it's range must be decreasing with the domain.
When the value of x(domain) is increasing on the left side. The value of y(range) is increasing constantly. But when the value of x increases further after 0, then the value of y is decreasing constantly.
So we can say, the following function represented on the graph is increasing in the interval of ( -∞,0) and decreasing in (0,∞).
As per the situation described in the graph the option third which say increasing on (×,0) and decreasing on (0,×).
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Age
Pete is ten years older than his brother Jeff.
In five years, Pete will be twice as old as
Jeff. How old will Pete be in five years.
Answer:
20 years
Step-by-step explanation:
jeff's age = x
pete's age = x+10
in 5 years time
2(x+5) = x+10+5
thus x=5 therefore
pete's age in 5 years will be 20
Lisa’s square garden has an area of 64 square feet . Lisa increase each side of her square garden by 5 feet . What is the total area of the garden
Answer:
the total area of the enlarged garden is 324 square feet
Step-by-step explanation:
Lisa square garden has an area of 64 square feet. The formula for determining the area of a square is expressed as
Area = Length²
Length = √Area
Therefore, Length of each side of Lisa's garden is
√64 = 8 feet.
Lisa increases each side of her square garden by 5 feet. It means that the length of each side of the enlarged garden is 8 + 5 + 5 = 18 feet
Therefore, the total area of the enlarged garden would be
18² = 324 square feet
f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
c. The inverse of f₁(x)=b x-h is not equivalent to a vertical stretch or compression of g .
The inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g: TRUE
What accurately do we mean by Logarithmic Functions?The logarithmic function is the inverse of the exponential function.A logarithm to the base b is the power to which b must be increased in order to obtain a specific number.For example, log28 is the power to which 2 must be raised to generate eight. Clearly, 23 = 8, so log28=3.So,
Given inverse function: f₁(x)=b^(x-h)
First, find out the inverse of this function.
So, let f₁(x) = yThen, y=b^(x-h)Switch the variables x & y as follows;
x=b^(y-h)Solve for y as shown below and take logarithm both sides:
log(x) = (y-h)log(b)y=h+ log(x)/log(b)So,
f₁^(-1)(x)= h+log(x)/log(b)f₁^(-1)(x)= h+logb(x)f₁^(-1) (x)= g(x)+hFrom the first equation we get the inverse of as f₁ follows:
f₁^(-1) (x)= g(x)+hTherefore, the statement "the inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g" is TRUE.
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Carlos has 20 coins in his pocket. He has only quarters and dimes. The
number of quarters is 1 less than half the number of dimes. How many dimes
and quarters does Carlos have?
By resolution of systems of linear equations, Carlos has 6 quarters and 14 dimes in his pocket.
How many quarters and dimes does Carlos have in his pocket?
A dime is equivalent to 0.10 dollars and a quarter is equivalent to 0.05 dollars. In accordance with the statement, Carlos has 20 coins between dimes and quarters, whose algebraic equations are described below:
q + d = 20 (1)
q = 0.5 · d - 1 (2)
Where:
q - Number of quarters.d - Number of dimes.By (2) in (1):
(0.5 · d - 1) + d = 20
1.5 · d - 1 = 20
1.5 · d = 21
d = 14
By (2):
q = 0.5 · d - 1
q = 0.5 · 14 - 1
q = 7 - 1
q = 6
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Please help me part 2
Answer: 45 76 82
Step-by-step explanation: for 8
who can help please i need this for my maths score
Answer:
196 degrees, reflex.
Step-by-step explanation:
The angles fit around a point, therefore, they add up to 360 degrees.
Let [tex]x[/tex] be the size of the third angle.
[tex]x + 113 + 51 = 360 \\x + 164 = 360 \text{ / Subtract 164 on both sides} \\x + 164 - 164 = 360 - 164} \\x = 196[/tex]
The angle is larger than 180 degrees and smaller than 360 degrees, therefore, its a reflex angle.
Answer:
196 degrees, reflex.
Step-by-step explanation:
Simplify each expression. 16¹/₃. 4t/₃
The simplified form is [tex]4 ^{\frac{2+t}{3} }[/tex].
Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.
The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.
Converting mixed numbers to an improper fraction,
[tex]16^{1/3} . 4^{t/3} \\4^{2/3} .4^{t/3} \\4^{\frac{2+t}{3} }[/tex]
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x = 4, work out the value of 2x² + 7
Answer:
39
Step-by-step explanation:
2×4²+7
2×16+7
32+7=39
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Colin has three rabbits called Fluffy, Mr Flopsy and Hoppy.
Fluffy's weight is 42% of Mr Flopsy's weight and 56% of Hoppy's weight.
If Mr Flopsy weighs 2500 g, how much does Hoppy weigh?
In linear equation, 1875 does Hoppy weight .
What are instances of linear equations?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.A = 42b = 56c
a : b : c = 42 : 100 : 75
total Mr Flopsy weights = 2500
then Hoppy weight = 75 = 2400/100 * 75
= 1875
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PLEASE HELP!!!!!
Yolanda is 4 years younger than 3 times her daughter's age. The sum of their ages is 88 What is Yolanda's daughter's age?
The table below shows the percentage of the U.S. labor force in unions for selected years between 1955 and 2005 .
Year
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
%
33.2
31.4
28.4
27.3
25.5
21.9
18.0
16.1
14.9
13.5
12.5
b. Make a scatter plot of the data. Which kind of polynomial model seems to be most appropriate?
Error while snipping
Answer: 1955 and 2005 .
Year
1955
1960
1965
1970
1975
1980
1985
1990
1995
see if i help u now ?
Step-by-step explanation:
Simplify each number. 8²/₃
Express 8 as a product of its prime factors. Write it in index form and apply the power rule: (a^m)^n = a^mn
8 = 2x2x2 = 2^3
(2^3)^2/3 = 2 ^ 3x2/3 = 2^2
=4
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I need help with this!!
Answer:
m<1=159 degree
m<2=21 degree
m<4=21 degree
Mitchell owes his mom $18. He's been helping
around the house a lot, so his mom decided to
forgive $12 of his debt. How much does he owe
now?
Answer:
Mitchell owes his mom =$18. sum of money his mom reduced =$12.
Step-by-step explanation:
SO IT 6 DOLLARS
Answer: $6
Explanation: $18-$12=$6
Hope this helps!!! have a nice day!
In which direction does the electric field point at a position directly east of a
negative charge?
The electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.
The correct option is D.
Briefing:A negative point charge has an electric field focused at it. Thus, the electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.
Electric field describe as:The electric field is defined as that of the electric force per unit of charge. The direction of the field is assumed to represent the direction of the force it would impose on a positive test charge. The electric field radiates outward from the a positive charge and inward from a negative point charge.
What are the characteristics of an electric field?The field lines never cross. The field lines lie parallel to the charge's surface. The quantity of charge and indeed the number of field lines are proportionate.
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I understand that the question you are looking for is:
What is the direction of the electric field directly to the east of an isolated negative point charge?
A. north
B. south
C. east
D. West