Sofia has $4.35 in quarters and nickels in her pocket. She has 3 more nickels than quarters. Write an equation that can be used to determine the number of quarters, x , Sofia has.
Answers
Answer:
Let's say x is the number of quarters. Then the number of nickels is x + 3.
The total value of the quarters is 0.25x, and the total value of the nickels is 0.05(x + 3).
The total value of both types of coins is 4.35:
0.25x + 0.05(x + 3) = 4.35
0.25x + 0.05x + 0.15 = 4.35
0.3x + 0.15 = 4.35
0.3x = 4.2
x = 14
So Sofia has 14 quarters and 17 nickels.
Answer:
.25q + .05(q - 3) = 4.35
Step-by-step explanation:
Let q = the number of quarters
Let n = the number of nickels
.25q + .05n = 4.35
n = q- 3
Substitute q - 3 for n
.25q + .05(q - 3) = 4.35
Related Questions
this portion of a taxpayer’s W-2 form. Assume that the taxpayer’s wages for the year are under the Social Security limit. What entry should be in Box 4?
1. wages, tips, other compensation 2. Federal income tax withheld
3. Social security wages
4. Social security tax withheld
5. Medicare wages and tips
6. Medicare tax withheld
$1346.76
7. Social security tips 8. Allocated tips
9. Advance EIC payment 9. Dependent care benefits
Answers
In this case, since the taxpayer's wages are under the Social Security limit, the entry that should be in Box 4 of the W-2 form is "Social security tax withheld."
The term "social security wages" refers to earnings that are subject to Social Security taxes. These salaries are used by the Social Security Administration in the US to determine a person's eligibility for and the amount of their benefits under several Social Security programmes, including retirement, disability, and survivor benefits.
Social Security wages often include self-employment income as well as some employment-related wages, salaries, and tips. Some forms of income, such investment income and some fringe benefits, may not be regarded as Social Security wages, though. For the Social Security system to calculate an individual's payments and benefits, Social Security wages must be calculated and reported.
Box 4 represents the total amount of Social Security tax that was withheld from the taxpayer's wages throughout the year.
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I need help me this somebody help!
Answers
Answer:
M1=136
m4=180-136
=44////
What is expression is equivalent to 5x + 30
Answers
Hey there!
5x + 30
5(x + 6)
= 5(x) + 5(6)
= 5x + 30
5x + 30 = 5x + 30
Therefore, the answer should be:
5(x + 6)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
can u plz answer this? its for my sister
Answers
Answer:
p= 4y+15
Step-by-step explanation:
Thanks me later
Marks as brainlist if you like my work
HELP ME PLEASE IM STUCK QUICK
Answers
Answer:
TRUE
Step-by-step explanation:
15>2
Answer:
The answer is true
Step-by-step explanation:
The left side 15 is greater than the right side 2 , which means that the given statement is always true. True
A strain of peas has 3 green and one yellow for every four peas. If 12 peas are rendomly selected, what is the probability that exactly 8 peas are green
Answers
The probability that exactly 8 peas are green, from the random selection would be 22. 56 %.
How to find the probability ?This is a binomial probability problem as the probability of an exact likelihood from an event needs to be found.
The relevant formula is:
P ( X = k ) = C ( n , k) x p^ k x q ^( n - k)
Solving for the probability, that exactly 8 peas are green gives:
P ( X = 8 ) = C( 12, 8) x ( 3 / 4 ) ^8 x ( 1 / 4 )^4
P ( X = 8 ) = (12! / ( 8 ! ( 12 - 8 )!) ) x ( 3/4 ) ^8 x ( 1 / 4 ) ^4
P ( X = 8 ) = 0. 2256
P ( X = 8 ) = 22. 56 %
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I WILL GIVE BRAINLIEST AND 30 POINTS
What is the slope of the line on the graph?
Enter your answer in the box.
Answers
Answer:
6
Step-by-step explanation:
(y1-y2)/(x1-x2) = (-1-5)/(0-1) = -6/-1 = 6
hope it helps!
Nelly and her famliy went on vacation to a beach resort. there are 4 large buildings. each building has 8 floors, with 27 rooms on each floor, One of the buildings is getting new carpet, and will not be available. how many rooms are available for Guests?
1) 548
2) 648
3) 448
4) 628
Answers
Answer:
648 floors.
Step-by-step explanation:
Since there are 4 large buildings and 1 would be unavailable, there would be three left. You multiply. 3 x 8 x 27 = 648 !
Enlarge the triangle by the scale factor 1/3 with centre (-5, -4)
Answers
To enlarge the triangle by the scale factor of 1/3 with a center of (-5, -4), we will apply the concept of dilation.
Dilation involves multiplying the coordinates of each vertex by the scale factor and then translating the resulting points based on the center of dilation.
To enlarge the triangle by a scale factor of 1/3 with a center of (-5, -4), follow these steps:
Determine the coordinates of the original triangle's vertices.
Subtract the x-coordinate of the center (-5) from the x-coordinate of each vertex, and subtract the y-coordinate of the center (-4) from the y-coordinate of each vertex.
Multiply the resulting values by the scale factor of 1/3.
Add the x-coordinate of the center (-5) to the scaled x-coordinate, and add the y-coordinate of the center (-4) to the scaled y-coordinate.
These new coordinates represent the enlarged triangle's vertices.
By applying these steps, you can enlarge the triangle by a scale factor of 1/3 with a center of (-5, -4).
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use the reciprocal rule to determine the derivative of the function…
Answers
The function is given as,
\(f(x)=\frac{1}{5-6x}\)Differentiating both sides with respect to 'x',
\(f^{\prime}(x)=\frac{d}{dx}(\frac{1}{5-6x})\)According to the reciprocal rule,
\(\frac{d}{dx}(\frac{1}{g(x)})=\frac{-g^{\prime}(x)}{g(x)^2}\)Comparing with the expression,
\(g(x)=5-6x\)The corresponding derivative is given by,
\(\begin{gathered} g^{\prime}(x)=\frac{d}{dx}(5-6x) \\ g^{\prime}(x)=\frac{d}{dx}(5)-6\cdot\frac{d}{dx}(x) \\ g^{\prime}(x)=0-6(1) \\ g^{\prime}(x)=-6 \end{gathered}\)Substitute the values in the formula,
\(\begin{gathered} \frac{d}{dx}(\frac{1}{5-6x})=\frac{-(-6)}{(5-6x)^2} \\ \frac{d}{dx}(\frac{1}{5-6x})=\frac{6}{(5-6x)^2} \end{gathered}\)So the derivative of the given function becomes,
\(f^{\prime}(x)=\frac{6}{(5-6x)^2}\)Thus, the derivative of the given function is obtained as,
\(f^{\prime}(x)=\frac{6}{(5-6x)^2}\)Is the relationship between volume and moles of gas proportional or inversely proportional?
Answers
The volume of the gas approximately directly proportional to its number of moles of gas when both temperature and pressure are constant.
Explain the Mole-Volume Relationship - Avogadro’s Law?The volume of a gas being directly proportional to the amount of moles of that gas, according to a plot illustrating the relationship between temperature and volume of a gas under constant pressure. Avogadro's law is cited in support of this: When the pressure (P) and temperature (T) are constant, the volume (V) of an ideal gas (n) directly varies depending on the number of moles of the gas (n).V∝ n at constant P and T
V = constant × (n)
Vn = constant
This can be mathematically stated as follows: As before, we can anticipate what will change to the volume of the a sample of gas as we adjust the number of moles using Avogadro's law.
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How many terms are there in the sequence 1, 8, 28, 56, ..., 1 ?
Answers
Answer:
9 terms
Step-by-step explanation:
Given:
1, 8, 28, 56, ..., 1
Required
Determine the number of sequence
To determine the number of sequence, we need to understand how the sequence are generated
The sequence are generated using
\(\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}\)
Where n = 8 and r = 0,1....8
When r = 0
\(\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1\)
When r = 1
\(\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8\)
When r = 2
\(\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8\)
When r = 3
\(\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56\)
When r = 4
\(\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70\)
When r = 5
\(\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56\)
When r = 6
\(\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28\)
When r = 7
\(\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8\)
When r = 8
\(\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1\)
The full sequence is: 1,8,28,56,70,56,28,8,1
And the number of terms is 9
Part BNow that you know the missing side length, is triangle BCD a right triangle? Give your reason.
Answers
Given: The image shown
To Determine: The value of the unknown
Solution
Let us apply the pytahgoras theorem
From the right triangle ABD
\(\begin{gathered} hypothenuse)^2=leg1^2+leg2^2 \\ ?^2=4^2+4^2 \\ ?^2=16+16 \\ ?^2=32 \\ ?=\sqrt{32} \\ ?=4\sqrt{2}inches \end{gathered}\)Hence, the unknown side is 4√2 inches
Describe the method used to integrate sin °x
Choose the correct answer below.
O A. Rewrite sin °> as tan x cos 3x, then use the substitution u = cos x.
O B. Rewrite sin °x as (1 - cos 2x) sinx, then use the substitution u = cos x.
O C. Rewrite sin °x as ( sin ?x) sin x, then use a half-angle formula to rewrite the sin ? term.
O D. Rewrite sin °x as (1 - cos 2x) sinx, then use a half-angle formula to rewrite the cos ^x term.
Answers
The correct answer is option B. Rewrite sin °x as (1 - cos 2x) sinx, then use the substitution u = cos x.
What is sine?
Sine is a trigonometric function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Mathematically, the sine function is denoted as sin(x), where x is the angle. The sine function takes an angle in radians as its input and returns the corresponding sine value.
By using the identity \(sin^2(x) + cos^2(x) = 1\), we can rewrite sin °x as (1 - cos 2x) sinx.
Then, we can make the substitution u = cos x, which allows us to express the integral in terms of u. This substitution simplifies the integral and makes it easier to evaluate.
Therefore, the correct method to integrate sin °x is to rewrite it as (1 - cos 2x) sinx and then use the substitution u = cos x.
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which of the following represents the graph of this equation?
Answers
Help plz.. plz plz lmz
Answers
Answer:
seven hundred and twenty nine
CAN someone PLZ help !?
Answers
no entiendo hingles......pero puedo puedo tener esos 5 puntos
2x - m x= 4 m= 2 can you help me because I wanna know what the answer
Answers
Answer:
6
Step-by-step explanation:
2x-m
When you substitue in the values for x and m:
2(4)-2
Now you can solve the equation:
2(4)-2
8-2
6
So this leads to the answer
2x-m=6 or 2(4)-2=6
So bad at this someone help
Answers
Answer:
Volume of a cylinder : πr^2h
: π = 22/7
: r = 9
: h = 20
: 22/7 × 9^2 × 20
: 5091.4 (corrected to 1.dp )
Answer:
5089.4 cm³
Step-by-step explanation:
You want the volume of a cylinder with radius 9 cm and height 20 cm.
VolumeThe volume of a cylinder is given by the formula ...
V = πr²h
ApplicationFor r = 9 cm and h = 20 cm, the volume is ...
V = π(9 cm)²(20 cm) = 1620π cm³
The value you get for this depends on the value you use for π. The attachment shows the three common choices: "π button", 3.14, 22/7.
Using the "pi button" value provided by a calculator, the volume is ...
5089.4 cm³
<95141404393>
Which of the following points lie in the solution set to the following system of inequalities?
y < −3x + 3
y < x + 2
(1, −5)
(1, 5)
(5, 1)
(−1, 5)
Answers
Answer:
(1, −5)
Step-by-step explanation:
Because in this case it is less than and the -3x would be cancelled out and I had this question and that correct answer was A(1,-5).
Hope this helps:)
Answer:
the answer is (1,-5)
Step-by-step explanation:
plug in the x and y values and see if they are true
y<-3x+3
(-5)<-3(1)+3
-5<-3+3
-5<0 is true
y<x+2
(-5)<(1)+2
-5<1+2
-5< 3 is true also
what is the future value of $800 one year from today if the interest rate is 7 percent?
Answers
Answer:
800(1+7/100)
800(1.7)
1360
Step-by-step explanation:
formula isp(1+r/100)power t
The exponential or the future value with interest is A = $ 856
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the future value be represented as A
To calculate the future value of $800 after one year with an interest rate of 7%, we can use the formula for simple interest:
The future value = present value x (1 + (interest rate x time))
So , the exponential equation is
x ( t ) = x₀ × ( 1 + r )ⁿ
Plugging in the values we have:
The future value = $800 * (1 + (0.07 * 1))
The future value = $800 * 1.07
The future value = $856
Hence , the future value of $800 one year from today with a 7% interest rate would be $ 856
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A quantity m varies jointly with p and r. When p is 2 and r is 4, m is 1. What is the constant of variation? One-eighth One-half 2 8.
Answers
Variation can be direct, inverse or joint
The constant of variation is one-eighth
How to determine the constant of variationThe variation is given as:
\(m \to pr\) --- the joint variation
Rewrite as an equation
\(m = kpr\)
Where k represents the constant of variation
When p is 2 and r is 4, m is 1.
So, we have:
\(1 = k * 2 * 4\)
This gives
\(1 = 8k\)
Solve for k
\(k = \frac 18\)
Hence, the constant of variation is one-eighth
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Answer:
A: 1/8
Step-by-step explanation:
100%
The measure of an exterior angle of a regular polygon is 45 degrees name then shape of the polygon
Answers
Given
Exterior angle of a regular polygon = 45 degree.
Find
Name of the shape of polygon
Explanation
As we know that sum of exterior angle of exterior angle is 360 degree.
given each angle = 45 degree
so,
number of sides of regular polygon =
\(\begin{gathered} \frac{360\degree}{45\degree} \\ \\ 8 \end{gathered}\)number of sides = 8
Final Answer
The shape of the regular polygon = octagon
What is the simplest form of (x^2+5x-6) / (x^2+9x+18)?
a) (x+2) / (x+6)
b) 1/3
c) (x-1) / (x+3)
d) -1/3
Answers
Answer:
a. \(\frac{x+2}{x+6}\)
Step-by-step explanation:
\(\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}\)
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify. 2 is subtracted from the product of 5 and a number. 2 is subtracted from the product of 5 and a number.
Answers
The statement 2 is subtracted from the product of 5 and a number is
5x - 2.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A statement an unknown number 'x' 2 is subtracted from the product of 5 and a number.
∴ 5×x - 2.
= 5x - 2 is the numerical expression.
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Today, Andrew borrowed R200 000 from a bank. The bank charges interest at 5.25%p.a, a compounded quarterly. Andrew will make make payments of R6 000 at the end of 3 months. His first repayment will be made 3 months from now, how long in years will it take for Andrew to settle the loan
Answers
In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.
The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.
We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.
Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.
Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000
We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)
Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0
Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.
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What is that I don’t know it
Answers
Answer:
103⁰
Step-by-step explanation:
180⁰ minus 77⁰ is equal to 103⁰
Answer:
x=103°
Step-by-step explanation:
Since 77° corresponds with the angle below x°, then x° and 77° are supplementary to each other, making x°=180°-77°=103
now is Tuesday. which day of the week will it be after 34^(2022) days?
Answers
Since there are 7 days in a week, the remainder will correspond to a specific day of the week.The day of the week is Thursday. So, after \(34^(2022)\) days, it will be Thursday.
to determine which day of the week it will be after 34*(2022) days, we need to find the remainder when 34*(2022) is divided by 7.
Since there are 7 days in a week, the remainder will correspond to a specific day of the week.
To calculate this remainder, we can use modular arithmetic. The formula for modular arithmetic is a % b = r, where a is the dividend, b is the divisor, and r is the remainder.
In this case, a is 34*(2022) and b is 7.
Now, let's calculate the remainder:
34*(2022) % 7 = 2
Therefore, after 34*(2022) days, it will be 2 days ahead of Tuesday.
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Select the correct answer
Which ratios are equal to each other?
OA
1:16 and 2:8
OB
2:32 and 4:8
1:64 and 4:16
D
1:16 and 4: 64
Reset
Reset
Next
Answers
What is 30 divided by 4? Show your work and explain.
Answers
Answer:
7.5
30
÷
4
__
7.5
4×6=24
4×7= 28
4×8= 32
4×8= X
4×7.5= 30