The number of Quarter coins that she has is 8 and the number of Dimes is 16.
It is given in the question that the woman has twice as many Dimes as the quarters in her purse.
We know that the value of Dimes is 0.10$ and the value of Quarters is
0.25 $
Let the number of Quarter coins is y and the number of Dimes coin be u.
According to the question above,
u = 2y equation (i)
The total value z = 0.25y + 0.10u
Putting here the value of u from equation (i) we have,
z = 0.25y + 0.10(2y)
⇒ z = 0.25y + 0.20y
⇒ z = 0.45y equation (ii)
Now it has been mentioned that if the Dimes were Quarters and the Quarters were the Dimes, she would have $ 1.20 greater than she has now.
So we have,
z + 1.2 = 0.25u + 0.10y
Putting the value of u from above eqation (i),
z + 1.2 = 0.25(2y) + 0.10y
⇒ z + 1.2 = 0.50y + 0.10 y
⇒ z + 1.2 = 0.60y
Putting the value of z from equation (ii)
⇒ 0.45y + 1.2 = 0.60y
⇒ 0.45y - 0.60y = - 1.2
⇒ -0.15y = - 1.2
⇒ y = [tex]\frac{-1.2}{-0.15}[/tex]
⇒ y = 8
Therefore u = 2y
⇒ u = 2 x 8 = 16
Hence the number of Quarter coins is 8 and the number of Dimes is 16
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16 dimes, 8 quarters
I checked RSM it's correct
Write the equation for g(x)
The equation of the graph of g is represented by y - 6 = (x-2)²
The very first step in balancing a variable equation is to correctly identify the specific values of the variables that lead to equality.
The equation's solutions are the specific values of the unknown variables that perfectly satisfy the equality, which are often referred to as the variables for which the particular equation must be solved. Identity equations and conditional equations are the two types of equations. The variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match. The equals sign is an important symbol that is used in mathematical formulas to denote the equality of two expressions.The graph of the function is f is y = x²
Now we can see that the graph of g is translated to 2 units to the right and 6 units up.
We know from the properties of translation that when the graph moves 2 units to the right we get the equation as y = (x-2)²
Again when the graph moves 6 units up wards the graph changes by
y - 6 = (x-2)²
Therefore the equation of g is y - 6 = (x-2)²
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The single inequality y > |x + 2| is equivalent to which of the following systems?
Answers:
1.y > x + 2
y > –x + 2
2.y > x + 2
y > –x – 2
3.y > x + 2
y < –x + 2
4.y > x + 2
y < –x – 2
The single inequality:
y > |x + 2|
Can be rewritten into:
y > x + 2
y > -x - 2
So the second option is the correct one.
How to decompose the inequality into two ones?
Remember that an absolute value equation like:
|x + a| = b
Can be rewritten as:
x + a = b
x + a = -b
So the inequality:
y > |x + 2|
Also can be rewritten into two equations, which are:
y > x + 2
-y < x + 2
The direction of the sign changes in the second one because the sign of the variable in the left changes.
Then if we multiply both sides by -1 of the second inequality, we get:
y > -x - 2
Then the two inequalities are:
y > x + 2
y > -x - 2
So the correct option is the second one.
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I need help please ! I'm struggling
The graph of the quadratic equation:
y = x^2 -8x + 16
Can be seen in the image at the end.
How to graph the functions?First, we have a quadratic function:
y = x^2 -8x + 16
To graph this we need to find some points on the parabola, to do that, we will evaluate it in some values of x.
if x = 0
y = 0^2 - 8*0 + 16 = 16
So we have the point (0, 16)
if x = 1
y = 1^2 - 8*1 + 16 = 9
So we have the point (1, 9)
if x = -1 we have:
y = (-1)^2 - 8*-1 + 16 = 23
So we have the point (-1, 23)
And so on, once you have enough points, you can graph them in a coordinate axis and then draw a parabola that connects them, the graph of the quadratic equation can be seen in the image below.
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each individual in a random sample of high school and college students was cross-classified with respect to both political views and marijuana usage. does the data support the hypothesis that political views and marijuana usage level are independent within the population?
Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.
The alternative hypothesis states that political beliefs and marijuana use depend on one another within the population, contrary to the null hypothesis that asserts these two variables are independent.
H₀ : Pij = Pi · Pj ; i = 1, 2, 3 ; j = 1, 2, 3
Ha : at least one Pij ≠ Pi · Pj
We want to test whether there is a relationship between political views and marijuana usage levels. The results of a random sample of size n = 1353 are derived from the following formula;
e = (Row total) x (Column total) /Total sample size
We are told to use the 0.01 level of significance to test the null hypothesis. Thus, α = 0.01. The table has r = 3 rows and c = 3 columns. An r × c table has degrees of freedom df = (r - 1) x (c - 1). So, a 3×3 table has degrees of freedom df = (3 - 1) x (3 - 1) = 4. From formula the df = 4 and α = 0.01, χ²₀.₀₁ = 13.277. Reject the null hypothesis if X² ≥ 13.277 where
x² =Σ(a - e)²/e
Substituting the observed and expected frequencies summarized in the table above into the formula for x², we get
X² = 68.732
Rejection Region → X² ≥ 13.277
Test statistic → X² = 68.732
Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.
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at the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of 3 2 centimeters per second. find the rate at which the area of the circle is changing at that instant. indicate units of measure.
The area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.
What is termed as the Rate of Change?The derivative can be thought of as a change rate. If two variables are related, the derivative of the initial variable to respect to the second variable can be used to calculate the rate of change of one of the variation with respect to the other variable.For the given question;
Express the circle's area as a function of the its radius.
A = πr²
Determine the area's derivative with respect towards its radius.
dA/dr = 2πr
Using the chain rule, calculate the derivative of a area with respect to time.
dA/dt = dA/dr . dr/dt
dA/dt = 2πr(9)
dA/dt = 18πr
When the radius is 32 cm, find the derivative of a area with respect to time.
dA/dt = 18π(32)
dA/dt = 576π
As a result, the area of a circle is changing at a rate of 576π cm²/sec when the radius of the circle is 32 cm.
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An engineer is designing a parking lot for a local grocery store. The parking spaces are marked with lines where
The value of x and y in the angles are 15.6 and 10.5 respectively.
How to find the variable x and y in the angles?When parallel lines are cut by a transversal lines, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, line XD, TZ, YF and LP are parallel to each other.
WC is the transversal line.
Hence,
m∠CNL = 6x - 17.6
m∠FBH = 12y - 22
m∠THR = 3x + 29.2
Hence,
180 - (12y - 22) = 6x - 17.6(corresponding angles)
Corresponding angles are congruent
180 - 12y + 22 = 6x - 17.6
6x + 12y = 180 + 22 + 17.6
6x + 12y = 219.6
Therefore,
180 - (3x + 29.2) = 12y - 22 (alternate angles)
Alternate angles are congruent .
180 - 3x - 29.2 = 12y - 22
180 + 22 - 29.2 = 12y + 3x
172.8 = 3x + 12y
combine the equation
6x + 12y = 219.6
3x + 12y = 172.8
subtract equation(ii) from equation(i)
3x = 46.8
x = 46.8 / 3
x = 15.6
12y = 219.6 - 6(15.6)
12y = 219.6 - 93.6
12y = 126
y = 126 / 12
y = 10.5
Therefore,
x = 15.6
y = 10.5
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suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. when graphed, the function gives a line with a slope of 5.9. see the figure below. with 53 gallons of fuel in its tank, the airplane has a weight of 2212.7 pounds. what is the weight of the plane with 20 gallons of fuel in its tank?
The weight of the plane with 20 gallons of fuel in its tank 2218 pounds. using a linear function.
what is linear function?
A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one.
Let y be the weight of the airplane and x be the amount of fuel
And we know that the general form of a linear
function is
(1) And given that the slope of the line is
y = mx + c
m = 5.9
Then (1) becomes
y = 5.9x + c
And given that for x = 53 , y = 2212.7
Then from (2), we have
2212.7 = 5.9 (53) + c
⇒ 2212.7 = 312.7 + c
c = 2212.7 - 312.7
c = 1900
Thus, (2) becomes
y = 5.9x + 1900
Then for x=22, from (3) y = 118 + 2100
= w = 2218
The weight of the plane with 20 gallons in its fuel tank is 2218 pounds
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Johnny found a sick abandoned kitten in his yard. It was very malnourished and he decided to nurse it back to health. He started feeding the kitten enough food to help it gain weight. On average the kitten was gaining 4 ounces per day. After 6 days in Johnny's care, the cat weighed 73 ounces. Determine how many days until the kitten will weighs 105 ounces.
Answer:9 days
Step-by-step explanation:A lot of division is required, but because 8.75 probably isn't an answer, I rounded up to 9.
Find x of the triangle.
Answer:
x = 130°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle , then
x = 50° + 80° = 130°
Answer: 130
Step-by-step explanation:
180 = y + 50 + 80
y = 50
180 - y = x
x = 130
A circle has a circumference of 320 cm.
What is its radius?
A. 80 cm
B. 160 cm
C. 320 cm
D. 320 cm!
If a circle has a circumference of 320 cm, then its radius can be calculated as 50.92 cm according to the formula of circumference of a circle.
What is circumference?In geometry, the circumference can be defined as the perimeter of a circle or an ellipse. It can also be said as the linear distance present around it.
To better describe it, you can imagine that if a circle is opened out and placed as a straight line, then the total length of that straight line can be described as the circumference of the circle.
It is synonymous to perimeter, but the terminology can only be used with circled and ellipses. It is the curved length of the object. In this case, the object is mostly 2 dimensional but sometimes 3 dimensional objects can also be placed to take out their circumference with other methods.
In this particular question,
2[tex]\pi[/tex]r = 320
⇒ r = 320/2[tex]\pi[/tex]
⇒ r = 50.92
⇒ r ≈ 51 cm
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Please Help me immediately. this is due at 11:59pm
Priya bought these items at the grocery store. Find each unit price.
10 apples for $3.50. How much is the cost per apple?
Answer for prompt 1 10 apples for $3.50. How much is the cost per apple?
12 eggs for $3. How much is the cost per egg?
Answer for prompt 2 12 eggs for $3. How much is the cost per egg?
3 pounds of peanuts for $7.50. How much is the cost per pound?
Answer for prompt 3 3 pounds of peanuts for $7.50. How much is the cost per pound?
4 rolls of toilet paper for $2. How much is the cost per roll?
Answer for prompt 4 4 rolls of toilet paper for $2. How much is the cost per roll?
What is the standard form of y=4/9x-3
Answer: 4x-9y=27 is this equation in standard form.
You open up a bank account with $5000. You leave it there, and the bank informs you they will add 5% annually in interest. How much money will you have earned in interest in 7 years?
A. $1850
B.$175
C.1750
D.185
Answer:
Assuming that this is referring to simple interest, your answer is C) 1,750.
Step-by-step explanation:
[tex]5000[/tex] x [tex]0.05[/tex] = [tex]250[/tex]
[tex]250[/tex] x [tex]7[/tex] = [tex]1750[/tex]
Find a quadratic model for each set of values. (1, -2), (2, -2), (3, -4)
Answer:
f(x) = ax^2 + bx + c
I) f(1) = a + b + c = -2
II) f(2) = 4a + 2b + c = -2
III) f(3) = 9a + 3b + c = -4
II - I
IV) 3a + b = 0
III - I
V) 8a + 2b = -2
V - 2IV
2a = -2 --> a = -1
3(-1) + b = 0 --> b = 3
(-1) + (3) + c = -2 --> c = -4
f(x) = -x^2 + 3x - 4
a playground is rectangular with a length of 7/8 miles. If the area of the play ground is 8/20 miles what is the width.
Answer: Width = 8/20 ÷ 7/8 = 8/20 x 8/7 = 16/35 Therefore, the width will be 16/35 miles. Hope you do great :) !
Someone help quickly!
Look at the picture!
A company produces air-filled world globes in the shape of a sphere as shown. What is the volume of a globe with a radius of 10 centimeters? Leave your answer in terms of π.A. 40π cubic centimetersB. 133π cubic centimetersC. 750π cubic centimetersD. 1333π cubic centimeters
The formula for getting the volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r = radius of the sphere.
Let's plug into the formula the given radius of the sphere in the question.
[tex]V=\frac{4}{3}\pi(10cm)^3[/tex]Then solve.
Multiply 10 cm by itself three times.
[tex]V=\frac{4}{3}\pi(10cm\times10cm\times10cm)[/tex][tex]V=\frac{4}{3}\pi(1000cm^3)[/tex]Multiply 1000 by 4, then divide by 3.
[tex]V=\frac{4000}{3}\pi cm^3[/tex][tex]V=1333.33\pi cm^3[/tex]Rounding the calculated volume to the nearest whole number, the volume of the sphere is 1,333π cm³ (Option D or 4)
Answer:
The volume of the sphere is 1,333π cm³ (Option D or 4)
Arithmetic Sequences
CAN SOMEONE PLEASE HELP ME IM BEGGING :’(
Hellow what grade of math is this?
A. No, because one x-value corresponds to two different y-values.
B. Yes, because there are two x-values that are the same.
C. No, because two of the y-values are the same.
D. Yes, because every x-value corresponds to exactly one y-value.
Answer:
its A
Step-by-step explanation:
:)
In circle Q with the measure of arc ⌢=118∘PR⌢ =118 ∘ , find m∠PQRm∠PQ
Explanation
We are given the measure of arc PR = 118°.
We are required to find m∠PQR.
We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:
[tex]\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ obtuse\text{ }m\angle PQR+reflex\text{ }m\angle PQR=360\degree\text{ }\lbrace angles\text{ }at\text{ }a\text{ }point\rbrace \\ reflex\text{ }m\angle PQR=360\degree-obtuse\text{ }m\angle PQR \\ reflex\text{ }m\angle PQR=360\degree-118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}[/tex]But since Q is the measure of the angle, then the final answer is 118°.
Caitlin purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Caitlin paid
The equation for the purchase of n number of notebooks by Caitlin is
4n = c , where c is representing the cost that Caitlin paid.
What is unitary method ?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.
Calculationthe price for one notebook was = $4 each
n number of notebooks were purchased by caitlin
therefore the cost price of 4 notebooks will be = 4 * n
as per given in the question cost price = c
therefore the equation formed will be
4n = c
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at a delicatessen, ham costs $2.49 per pound and swiss cheese costs $3.79 per pound. The customer has $9.50 to spend on 2 pounds of ham and some cheese. how much cheese can she purchase? write an equation and solve it.
The customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).
How much cheese can she purchase?We are given with the cost of ham is $2.49 per pound and
Cost of swiss cheese is $3.79 per pound.
So, the cost of 2 pounds of ham will be given as-
= 2× $2.49
= $4.98
Since, the customer has a total of $9.50 to spend on 2 pounds of ham and some cheese,
∴ Let the number of pounds of cheese she can purchase be x.
Then the equation will be this:
2.49*2 + 3.79*x = 9.50
4.98 + 3.79x = 9.50
Subtracting 4.98 from each side we get-
4.98 -4.98 + 3.79x = 9.50-4.98
3.79x = 4.54
x [tex]=\frac{4.54}{3.79}[/tex]
x = 1.19788 pounds of cheese (approximately 1.2 pounds).
Hence, the customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).
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Find the gradient of = x+3y=13
Answer:
[tex]\textsf{Gradient\;$=-\dfrac{1}{3}$}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope (gradient). \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]x+3y=13[/tex]
Rearrange the equation to make y the subject.
Subtract x from both sides of the equation:
[tex]\implies x+3y-x=13-x[/tex]
[tex]\implies 3y=-x+13[/tex]
Divide both sides of the equation by 3:
[tex]\implies \dfrac{3y}{3}=\dfrac{-x}{3}+\dfrac{13}{3}[/tex]
[tex]\implies y=-\dfrac{1}{3}x+\dfrac{13}{3}[/tex]
Compare the rearranged equation with the slope-intercept form.
Therefore, the gradient (slope) of the given equation is -¹/₃.
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Answer:
Step-by-step explanation:
y = mx + b
The gradient is slope "m" (coefficient by "x")
~~~~~~~~~~~~~~~~~
x + 3y = 13
Solve for "y" :
3y = - x + 13
[tex]\frac{3y}{3}[/tex] = - [tex]\frac{x}{3}[/tex] + [tex]\frac{13}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{13}{3}[/tex]
The gradient is ( - [tex]\frac{1}{3}[/tex] )
What is the image point of (-8, 9) after a translation right 3 units and
down 1 unit?
Answer: (-5, 8)
Step-by-step explanation:
The x-coordinate is responsible for left and right, and the y-coordinate is responsible for up and down translations. Coordinate points are written as (x, y).
(-8, 9) ➜ (-8 + 3, 9 - 1) ➜ (-5, 8)
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Canon needs to produce 1000 milliliters of 36% alcohol solution. At his disposal he has 40% alcohol solution and 20% alcohol solution. How much of each does he need in order to produce his desired solution?
x = milliliters of 40% alcohol
y = milliliters of 20% alcohol
so just alcohol alone in each quantity will just be "x" * (40/100) = 0.4x and "y" * (20/100) = 0.2y, whilst trying to get 1000 mL of 36% alcohol only.
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ \textit{40\% solution}&x&0.4&0.4x\\ \textit{20\% solution}&y&0.2&0.2y\\ \cline{2-4}&\\ mixture&1000&0.36&360 \end{array}~\hfill \begin{cases} x+y=1000\\\\ 0.4x+0.2y=360 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=1000\implies }x=1000-y ~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.4(1000-y)+0.2y=360} \\\\\\ 400-0.4y+0.2y=360\implies 40-0.4y+0.2y=0\implies 40-0.2y=0 \\\\\\ 40=0.2y\implies \cfrac{40}{0.2}=y\implies \boxed{\stackrel{mL}{200}=y} ~\hfill \boxed{\underset{mL}{\stackrel{1000~~ - ~~200}{x=800}}}[/tex]
Factor this trinomial x^2+8x+12
Reason:
We look for two values that
a) multiply to 12b) add to 8Using trial and error, you should find those two values are 2 and 6
2 times 6 = 122 plus 6 = 8This is how we arrive at (x+2)(x+6)
Use the FOIL rule to expand that out and you should get x^2+8x+12 to confirm the answer.
Write and solve an equation to
find how much greater this year's 3-month snowfall was
than last year's
In the graph, which compares the snowfall for the same three months last year and this year, you can see that the total snowfall for last year was 36.4 inches. how much more snow fell over the course of three months this year than did so last year: 5.45
what is the explanation?
The first step is to calculate the amount of snowfall from the previous year, which are:
12.6+6+9.2
=27.8
The next stage is to calculate how much snow has fallen this year, which includes:
10+15.75+7.5
=33.25
Now let's compare the snowfall over the first three months of current year to that of last year.
33.25-27.8
=5.45
In conclusion Graph showing snowfall during the same three months last year and this year, if the total snowfall for last year was 36.4
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If 4a- 3 =13, then find the value of 102 - 5a+6
Answer:
86
Step-by-step explanation:
I'll assume the expression is meant to be 10^2 - 5a +6
4a- 3 =13
4a = 16
a = 4
10^2 - 5a +6
10^2 - 5(4) +6
10^2 - 20 +6
100 - 14 = 86
I need help on this 3rd grade homework
Pls help
The correct option or equation that applies to the given situation is 7*6 = (4*6) + (3*6).
According to the question,
We have the following information:
Akela drew smaller arrays to find the product of a larger array.
Now, we have two figures where one has 6*3 boxes (6 horizontal boxes and 3 horizontal boxes) and in the second figure we have 6*4 boxes (6 horizontal boxes and 4 vertical boxes).
Now, to find the correct option, we will look for these two in options:
So, the option that has both of them is 7*6 = (4*6) + (3*6).
Now, we can verify whether the sides of the equation given are correct or not.
We have:
7*6 = 42
On right hand side, we have:
(4*6) + (3*6)
24+18
42
Hence, the correct option is 4th one.
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A school talent show is featuring 12 acts.
In how many ways can the first 5 acts be ordered?
By the concept of basic arithmetic solo acts are 5 minutes long and ensemble acts are 15 minutes long
What are basic arithmetic?Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.
The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.
Here we are discussing the four basic rules of arithmetic operations for all real numbers.
Addition (sum; ‘+’)Subtraction (difference; ‘-’)Multiplication (product; ‘×’ )Division (÷)12 × x + 2 × y = 90
6 × x + 2 × y = 60
To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.
B. Here we can multiply second equation with negative 1 and add it to first equation.
6x = 30
x = 5
Now we replace x in any of 2 equations to get y.
30 + 2y = 60
2y = 30
y=15
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