$9.10 in all nickels is how many nickels
9.10 / 0.05
how many 5 cent pieces add up to that
182 nickels
a penny is one cent
just move the decimal place over twice
9.10
910.0
910 pennies
Hope this helps
- Jeron :- )
A school set up a new sports club. In the first week, 8 girls and 7 boys went to the club. In the second week, another 2 girls and some more boys joined the club. The number of boys in the club was now double the number of girls. How many boys joined the club in the second week?
I Need Help ASAP!!!!!!!!!!
The difference in simple interest at 13% and 12% p.a. of a sum in one year is $ 110. Then the sum is (a) $11,000 (b) $13,000 (c) $15000 (d) 12000
Based on the information provided, it can be concluded the sum is $11,000.
How to know what is the sum?To know what is the sum, let's calculate the difference in the interest rate:
13% - 12% = 1%
This means the difference between the two interest rates presented is 1%. Based on this, let's calculate the 1% of the sums given:
11,000 x 0.01 = 11013,000 x 0.01 = 13015,000 x 0.01 = 15012,000 x 0.01 = 120Based on the above, the correct sum is $11,000 because only in this one 1% is equivalent to $110.
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please help asap, show your work then choose an answer
Note that where the figure below contains two semi-circles that are tangent to each Other at point B and ray DE is tangent to both semicircles at points E and F, it is correct to state that ED = 6√2 (Option A).
What is a Semi Circle?A semicircle is a one-dimensional point collection that forms half of a circle in mathematics. It is a circular arc with a circumference of 180°. It just has one symmetry line.
Solving the ED, we have:
ΔDEM ~ ΔDFP
This means that MD/PD = EM/FP
MD/(MD + 9) = 3/6
6MD = 3MD + 27 (Collect like terms over the equation)
3MD = 27
MD = 9 (If both sides are divided by 9)
Note that
ED = √[MD²-EM²]
ED = √9²-3²]
ED = 6√2
Thus, it is correct to state that ED = 6√2
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Given parallelogram A B C D below, DE = 31 If EB = x-7, solve for x.
The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.
Given parallelogram A B C D below, DE = 31 If EB = x - 7.
By the definition, then the equation is given as,
EB = DE
x - 7 = 31
Simplify the equation, then we have
x - 7 = 31
x = 31 + 7
x = 38
The value of the variable 'x' is 38.
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Mark is planning a birthday party at the local skating rink.The table shows the rates that are charged for parties at the skating rink.Is the number of guests proportional to the cost?If so, what is the constant of proportionality, and what does it mean in this situation? Is the graph a straight line?
The constant of proportionality is, 12
Yes, The graph of equation is a straight line.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Mark is planning a birthday party at the local skating rink.
And, The table shows the rates that are charged for parties at the skating rink.
Let two points on table are (5, 60) and (10, 120)
Now, The equation of line is,
⇒ y - 60 = (120 - 60) / (10 - 5) (x - 5)
⇒ y - 60 = 60/5 (x - 5)
⇒ y - 60 = 12(x - 5)
⇒ y - 60 = 12x - 60
⇒ y = 12x
Thus, The number of guests proportional to the cost.
And, Constant of proportionality = 12
And, The graph of y = 12x is a straight line.
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Complete question is shown in figure.
Norachai and Rain each improved their yards by planting rose bushes and grass. They bought their supplies from the same store. Norachai spent $209 on 11 rose bushes and 11 bunches of grass. Rain spent $40 on 3 rose bushes and 2 bunches of grass. What is the cost of one rose bush and the cost of one bunch of grass?
The cost of one rose bush is $2 and the cost of one bunch of grass is $17.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, Norachai and Rain each improved their yards by planting rose bushes and grass.
Let the cost of rose bushes be x and the cost of bunches of grass be y.
Norachai spent $209 on 11 rose bushes and 11 bunches of grass.
Now, 11x+11y=209
x+y=19 --------(i)
Rain spent $40 on 3 rose bushes and 2 bunches of grass.
3x+2y=40 --------(ii)
Substitute x=19-y in equation (ii), we get
3(19-y)+2y=40
57-3y+2y=40
57-40=y
y=17
Substitute y=17 in equation (i), we get
x=2
Therefore, the cost of one rose bush is $2 and the cost of one bunch of grass is $17.
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Evaluate:
[tex]4^{log_{2}(9) }[/tex]
Show your work.
The value of the equation is A = 81
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 4 ^ ( log₂ ( 9 ) ) be equation (1)
On simplifying the equation , we get
log₂ ( 9 ) = 2 log₂ ( 3 )
So , on further simplification , we get
A = 2² ^ ( 2 log₂ ( 3 ) )
A = ( 2⁴ )^log₂ ( 3 )
From the logarithmic rule , a^logₐ ( b ) = b
Substituting the values in the equation , we get
A = 2 ^ ( log₂(3) )4
A = 3⁴
A = 81
Hence , the equation is A = 81
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Write a system of equations or inequalities to represent each
situation. Write the systems in standard form and line up
the variables.
1. The middle school has a total of 456 students. There are 54 more
seventh graders than eighth graders.
Answer:
201 eighth graders and 201 + 54 = 255 seventh graders at the middle school.
Step-by-step explanation:
The system of equations representing the situation is:
x + 54 = 456 - x
2x + 54 = 456
2x = 402
x = 201
where x represents the number of eighth graders. So, there are 201 eighth graders and 201 + 54 = 255 seventh graders at the middle school.
Which figure would best model the sandbox to help determine the amount of sand needed?
You need to buy 80 cubic feet of sand to fill the sandbox.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The sandbox is a rectangular prism.
Length is 10 feet.
Width is 8 feet
Height is 1 feet.
Volume of prism=Length×Width×Height
=10×8×1
=80 cubic feet.
Hence, you need to buy 80 cubic feet of sand to fill the sandbox.
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The complete question is given in the attachment.
Let the functions f : R → R, g : R → R and h : R → R be defined by
f (x) = 1/(x - 5) , g (x) = 3 x + 6, h (x) = cos (x + 1).
Find
(a) The domain and range of f.
(b) The composite functions (fog)(x), (foh)(x) and (gof)(x).
(c) g^(-1) (x)
(d) The domain of (f + g)(x):
The definition of the f, h, and g functions, indicates the possible damains, range and composite functions are as follows;
(a) The domain of f is the set of real numbers except x = 5
The range is the set of all real numbers except f(x) = 0
(b) (f○g)(x) = 1/(3·x + 1)
(f○h)(x) = 1/(cos(x + 1) - 5)
(g○f)(x) = (6·x - 27)/(x - 5)
(c) g⁻¹(x) = (x - 6)/3
(d) The domain is; x ∈ R, and x ≠ 5
What is the domain of a function?The domain of a function is the set of the possible input values of the function.
The specified functions are;
f(x) = 1/(x - 5), g(x) = 3·x + 6, h(x) = cos(x + 1)
(a) The domain of f is the set of numbers such that the rational polynomial, 1/(x - 5) is defined
The polynomial, f(x) = 1/(x - 5) is defined when x - 5 ≠ 0, therefore;
x - 5 + 5 ≠ 0 + 5 = 5
x - 0 ≠ 5
x ≠ 5
The polynomial, f(x) = 1/(x - 5) is difined where x ≠ 5
The domain is the set of all real numbers, such that x ≠ 5
The range of the function, is the set of the possible output values, such that as (x - 5) ≠ 0, f(x) ≠ 0
The range is therefore; -∞ < f(x) < ∞, f(x) ≠ 0
(b) The composite functions (f○g)(x) = f(g(x))
Therefore; (f○g)(x) = f(g(x)) = f(3·x + 6)
Plugging in x = (3·x + 6) in the function, f(x) = 1/(x - 5), we get;
f(g(x) = 1/((3·x + 6) - 5) = 1/(3·x + 1)
f(g(x) = 1/(3·x + 1)
(f○g)(x) = 1/(3·x + 1)(f○h)(x) = f(h(x))
h(x) = cos(x + 1), therefore; (f○h)(x) = f(cos(x + 1))
Plugging in x = cos(x + 1) in f(x) = 1/(x - 5), we get;
(f○h)(x) = f(cos(x + 1)) = 1/((cos(x + 1)) - 5)
(f○h)(x) = 1/((cos(x + 1)) - 5)(g○f)(x) = g(f(x))
g(f(x)) = g(1/(x - 5)) = 3/(x - 5) + 6 = (6·x - 27)/(x - 5)
(g○f)(x) = (6·x - 27)/(x - 5)(c) g⁻¹(x)
g⁻¹(x) is the inverse of the function, g(x), which can be foiund as follows;
Plugging in; y = g(x) = 3·x + 6
y = 3·x + 6
y - 6 = 3·x
x = (y - 6)/3
Therefore;
g⁻¹(x) = (x - 6)/3(d) (f + g)(x) = f(x) + g(x)
f(x) + g(x) = 1/(x - 5) + 3·x + 6
The use of a graphing calculator indicates that we get;
1/(x - 5) + 3·x + 6 = (3·x² - 9·x - 29)/(x - 5)
Therefore; (f + g)(x) = (3·x² - 9·x - 29)/(x - 5)
The domain is therefore, the possible values of x at which the denominator is not zero, that is x ≠ 5
The domain is the set real numbers except x = 5, which is; x ∈ R, x ≠ 5
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if x,y,z are different and =mod x x^2 1+x^3
y y^2 1+y^3 = 0 then show than 1+xyz=0
z z^2 1+z^3
Given that x, y, z are different and satisfy the equations:
x^3 + x^2 - x = 0
y^3 + y^2 - y = 0
z^3 + z^2 - z = 0
We can multiply the first equation by y, the second by z, and the third by x to obtain:
x^3y + x^2y - xy = 0
y^3z + y^2z - yz = 0
z^3x + z^2x - zx = 0
Adding these three equations together, we get:
x^3y + x^2y - xy + y^3z + y^2z - yz + z^3x + z^2x - zx = 0
Expanding and simplifying, we find that:
x^2y + xy^2 + y^2z + yz^2 + z^2x + zx^2 - xy - yz - zx = 0
Now, we use the fact that x, y, and z are roots of the equations given above to simplify the expression further:
x^2 - x + y^2 - y + z^2 - z = 0
We can also write this as:
(x - 1)(x + 1) + (y - 1)(y + 1) + (z - 1)(z + 1) = 0
This expression can be factorized as:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
Since x, y, and z are all different, we have that:
(x - 1)(x + 1) ≠ 0
(y - 1)(y + 1) ≠ 0
(z - 1)(z + 1) ≠ 0
Therefore, we have:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = (x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
So, we can conclude that:
xyz = -1
And,
1 + xyz = 0
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The population of a certain animal species decreases at a rate of 12.5% per year. In 2021, at the beginning of the study, you counted 97 of the animal species you are studying in their natural habitat. Write a function that models the change in the animal population.
P should stand for the population in a certain year. P = 97*(0.875) is the function to model the population change (year-2021).
P should stand for the population in a certain year. To simulate how the animal population changes over time, we can utilise a function. The 12.5% annual reduction rate will be considered by the function. This can be stated mathematically as P = 97*(0.875), which is how it will appear in the equation (year-2021). In this equation, the number 97 stands in for the population in 2021, and the number 0.875 denotes the 12.5% annual decline rate. The exponent (year 2021) represents the number of years that have passed since 2021, allowing the equation to take the population decline over a number of years into consideration. As a result, the equation can be used to determine the animal species' population at the start of a particular year.
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Moore's Law predicts that the number of transistors that can be fit on a microchip will
increase by 40% every year. If microchips from a given year could hold about 922,200
transistors, how many transistors could fit on a microchip 19 years later?
Answer:
Moore's Law states that the number of transistors on a microchip will double approximately every two years. So, if a microchip in a given year could hold 922,200 transistors, 19 years later, it could hold approximately 922,200 * 2^(19/2) = 922,200 * 2^9.5 = 922,200 * 15,564,224 = 14,225,067,008,000 transistors.
Solve the inequality.
X/10 >5
Answer:
x > 50
Step-by-step explanation:
[tex]\frac{x}{10}[/tex] > 5 ( multiply both sides by 10 to clear the fraction )
x > 50
Two families attend a performance of the Circus Mage. The cost of a ticket for adult is
1.5 times higher than that of a child ticket. Clothilde buys a ticket for her, for her
husband and for her 2 children. She pays $90 in all, taxes included. Her friend Naomie
buys tickets for her 4 children and herself. Clothilde thinks that going to the circus
costs her less than Naomie. Is she right?
Answer: NO
Step-by-step explanation:
Adult tickets cost $27
Child tickets cost $18
$18 x 4 child tickets = $72 + $27 adult ticket = $99
Need help with this question.
Not sure if it’s: 2x + y =3
The options are:
x=1
-x + y = 2
X - y = 2
2x + y = 3
Thanks
Answer:
-x + y = 2
Step-by-step explanation:
Graphing a shape means all the points in the shape will give you a true answer when you put the x and y back in the equation used to graph that shape.
Let's pick a point (0,2)
x = 1
0 = 1
This is not true, so the first option is wrong.
-x + y = 2
0 + 2 = 2
2 = 2
The second option is true.
x - y = 2
0 - 2 = 2
-2 = 2
This is not true, so the thrid option is wrong.
2x + y = 3
2(0) + 2 = 3
2 = 3
This is no true, so the fourth option is wrong.
Evaluate the expression 52 × (7.2 + 16) − 8.
The evaluation of the expression is 1198.4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Expression; 52 × (7.2 + 16) − 8
Now,
=52*23.2-8
=1206.4-8
=1198.4
Therefore, the algebra will give 1198.4.
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the dencity of apple juice is
Answer:
density of apple juice
1.034-1.051g.cm‐³
Archive invested an amount of money in a savings account that pays compound interest at a rate of 6% per annum. After 11 years there is £13,288.09 in the savings account (rounded to the nearest 1p). How much did Archive initially invest?
Answer: 7000 (4 s.f)
Step-by-step explanation:
[tex]x[/tex] x [tex]1.06^{11} = 13,288.09[/tex]
[tex]x = \frac{13,288.09}{1.06^{11} }[/tex]
[tex]x = 7000[/tex] (4 s.f)
This is a question where you make the equation by yourself using compound interest. If you have any further questions, feel free to ask me :)
how far from the base of a building must a 15-ft ladder be placed so that it reaches 12 ft up the wall?
The base of the ladder must be placed 3 ft from the base of the building. The total length of the ladder is 15 ft.
1. The ladder must reach 12 ft up the wall, so we need to calculate the distance from the base of the building to 12 ft.
2. The total length of the ladder is 15 ft.
3. Subtract the length of the ladder (15 ft) fromthe desired height (12 ft) to get the distance from the base of the building.
4. 12 ft - 15 ft = -3 ft
5. Since the distance cannot be negative, the base of the ladder must be placed 3 ft away from the base of the building.
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Reena is completing a 30 km run. So far she had run one sixth of the distance . How far has she run
So Reena has ran a distance of 5 kilometers while only covering one-sixth of the distance.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
If Reena has completed one sixth of the 30 km run,
30 km / 6 = 5 km.
So, Reena has run a distance of 5 km so far when she had run one sixth of the distance.
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The Tour de France is not a 3500 km race, it is a 3500 km cycling race. The diameter of the bike wheels used in the race must be between 55 cm and 75 cm. To find the minimum number of rotations
The minimum number of rotations required for a 3500 km race is 52,800 rotations.
This is calculated by dividing the total distance of the race, 3500 km, by the circumference of the wheel, which is 2πr, where r is the radius of the wheel. The radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm). So, the minimum number of rotations is given by 3500/(23.14r), where r is the minimum radius of the wheel. Substituting in r = 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
To arrive at this result, we must first calculate the circumference of the wheel, which is given by 2πr, where r is the radius of the wheel. Since the diameter of the wheel must be between 55 cm and 75 cm, the radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm).
We then divide the total distance of the race, 3500 km, by the circumference of the wheel, which is given by 2πr. Substituting in the minimum radius of the wheel, 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
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Help me with this one pls
4x + 7g - 2g - 8x
Answer:
-4x + 5g
Step-by-step explanation:
4x + 7g - 2g - 8x
Combine the variable g with variable g and variable x with variable x
-4x + 5g
Choose the best method for solving and solve. Show your work.
y = -x-6
x + 3y = -18
The final solution to the given simultaneous equation is (0, -6)
Solving simultaneous equationsA finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
Given the set of equations below:
y = -x-6
x + 3y = -18
Using the substitution method;
Substitute equation 1 into 2 to have:
x + 3(-x - 6) = -18
x - 3x - 18 =-18
-2x = 0
x = 0
Since y = -x- 6
y = -0 - 6
y = -6
Hence the solution to the system of equation is (0, -6)
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Consider quadrilateral EFGH on the coordinate grid.
b
In quadrilateral EFGH, sides FG and EH are
because they
Sides EF and GH
are
v . The area of quadrilateral EFGH is closest to
v square units.
The area of quadrilateral EFGH is closest to 29 square units.
How to calculate the areaThe area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.
Based on the values or the sides, and the slopes given, the area will be:
= 1 + 4 + 8 + 8 + 2 + 4 + 2
= 29 units.
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Lindsay invests $2200 in one account and $1000 in an account paying 4 % higher interest. At the end of one year she had earned $168 in interest. At what rates did she invest?
Answer:
4% and 8%
Step-by-step explanation:
You want to know the interest rates that yield $168 on investments of $2200 at one rate and $1000 at a rate 4% higher.
SetupLet r represent the lower interest rate. Then x+0.04 is the higher rate, and the total interest earned is ...
2200r +1000(r +0.04) = 168
SolutionSimplifying the equation, we have ...
3200r +40 = 168
3200r = 128 . . . . . . . . subtract 40
r = 128/3200 = 0.04 = 4% . . . . . divide by the coefficient of r
The rates of interest on Lindays's investments were 4% and 8%.
the patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add 7 1/4% tax to the cost of the meal. Mr patterson was very happy with the food and service so he gave a 20% tip to the waitress. How much does the lunch cost, including tax and tip?
the lunch cost, including tax and tip 67.31$.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, the Patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add a 7 1/4% tax to the cost of the meal.
total cost after the tax = 52.30*(1 + 7 1/4)%
total cost after the tax = 52.30* 7.25/100 + 52.30
total cost after the tax = 3.79 + 52.30
total cost after the tax = 56.09
Since,
Mr Patterson was very happy with the food and service so he gave a 20% tip to the waitress.
Thus,
Total cost after the tip = 56.09(1 +20/100)
Total cost after the tip = 56.09 * 1.2
Total cost after the tip = 67.308
Therefore, the lunch cost, including tax and tip 67.31$.
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ayudaa
la tarea es sobre intercalos numéricos en la recta numérica
x=2xER/2_>x<7(
Los intervalos numéricos en la recta numérica para x=2, en donde x ∈R y x>2 y x<7, son: (2, 7).
En la recta numérica, los intervalos se definen utilizando dos números, uno inferior y uno superior. Por ejemplo, el intervalo (2, 7) representa todos los números entre 2 y 7, incluyéndolos. Esto significa que el intervalo (2, 7) incluiría 2, 3, 4, 5, 6 y 7. Además, los intervalos numéricos pueden incluir o excluir los números de los extremos. Por ejemplo, el intervalo (2, 7) representa todos los números entre 2 y 7, incluyéndolos, mientras que el intervalo (2, 7] sólo incluiría 3, 4, 5, 6 y 7.
English Version:The number intervals on the number line for x=2, where x ∈R and x>2 and x<7, are: (2, 7).
On the number line, intervals are defined using two numbers, one lower and one upper. For example, the interval (2, 7) represents all numbers between 2 and 7, including them. This means that the interval (2, 7) would include 2, 3, 4, 5, 6 and 7. In addition, numerical intervals can include or exclude the numbers at the ends. For example, the interval (2, 7) represents all numbers between 2 and 7, including them, while the interval (2, 7] would only include 3, 4, 5, 5, 6 and 7.
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2. Decide whether ∆ABC and ∆DEF are similar, not similar, or cannot be determined for the given information. Include your reason.
Answer:
By AA similarity Triangle ABC and DEF are similar.
What is Similarity?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given:
First in Triangle ABC
using Angle Sum Property
<C= 180 - <A - <B
<C = 180 - 77 - 48
<C = 55 degree
and, In Triangle DEF
using Angle Sum Property
ND= 180- <E- <F
<D = 180- 55 - 48
<D = 77
As, In both Triangle ABC and DEF all angles triangles are Equal.
<A = <D= 77
<B = <E = 48
<C = <F= 55
So, by AA similarity Triangle ABC and DEF are similar.
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numbers that summarize a sample of data are called and numbers that summarize populations are called
Numbers that summarize a sample of data are called "sample statistics," and numbers that summarize populations are called "population parameters."
A sample statistic is a single value that describes a characteristic of a sample, such as the mean, median, or standard deviation. Sample statistics are used to make inferences about the population from which the sample was drawn.
A population parameter, on the other hand, is a single value that describes a characteristic of an entire population, such as the population mean, population standard deviation, or population proportion. Population parameters are usually not known and must be estimated from a sample.
For example, if you have a sample of 100 students' heights, the mean height of the sample (a sample statistic) can be calculated and used to make inferences about the mean height of the population of all students.
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