Rhiannon and Sophie both started saving for a new piano this month. Rhiannon will deposit $35.80 per week, but her bank account is currently overdrawn with a -$253.50 balance. Sophie also has a negative bank account balance of -$78.25 and will deposit $23.30 each week. How many weeks (w) will it take for the two bank accounts to have the same balance?
Answers
It will take 14.02 weeks for both the accounts to have the same balance
Bank account balance of Rhiannon = -$253.50
Money deposited by Rhiannon in the bank account each week = $35.80
Bank account balance of Sophie = -$78.25
Money deposited by Sophie in the bank account each week = $23.30
Let the number of weeks it takes to have the same account balance be x, therefore formulating the algebric equation we get:
Bank balance of Rhiannon + Money deposited by her each week*No of weeks it will take for the balance to be equal = Bank balance of Sophie + Money deposited by her each week*No of weeks it will take for the balance to be equal
= -253.5 + 35.8(x) = -78.25 + 23.3(x)
= -175.25 = -12.5(x)
x = 14.02 weeks
Therefore, it will take 14.02 weeks for both the accounts to have the same balance
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Related Questions
Which table shows a proportional relationship between x and y?
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9
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50
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250
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2.5
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Answers
The ratio of y:x should be constant for any value of x and y.
\( \frac{y}{x} = constant\)
If go over every table, you'll find that this is true for the third one and that the ratio is r=50
The table showing the proportional relationship between x and y is the third one.
What is proportional relationship?Two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant.
Given are four tables, giving values of x and y, we need to identify the table giving the relation between x and y which is proportional.
Table 1)
x = 1, 2, 3, 6
y = 1.5, 3, 6, 9
y/x = 1.5, 1.5, 2, 1.5 [not proportional]
Table 2)
x = 2, 4, 5, 6
y = 6, 12, 18, 21
y/x = 3, 3, 3.6, 3.5 [not proportional]
Table 3)
x = 1, 3, 4, 5
y = 50, 150, 200, 250
y/x = 50, 50, 50, 50 [proportional]
Hence, the table showing the proportional relationship between x and y is the third one.
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19% of 43
Help please!!!
Answers
Answer:
8.17
Step-by-step explanation:
43x19/100 equals 8.17
The smallest object in space that is
spherical due to its own gravity is
Mimas, one of the moons of Saturn.
The radius of Mimas is approximately
200 km. What is the approximate
volume of the moon, to the nearest
million cubic km?
Answers
Answer:
33510321.638291 kilometers^3
Step-by-step explanation:
The formula for volume in a circle is 4/3*pie*r^3. Plug the radius in and you get that number.
john smith installs and then demonstrates burglar alarms. there are two burglar alarms that he installs, secure and maximum secure. secure requires 1 hour to install and .25 hour to demonstrate. maximum secure requires 2.2 hours to install and .4 hour to demonstrate. for each installation john is required to provide the demonstration (i.e. if he installs a secure system, he also has to provide the .25 hour demonstration). also, every installation needs to be complete (i.e. he can't do a partial installation). union rules require smith to work a minimum of 20 hours per week as an installer and a maximum of 20 hours as a demonstrator. if he gets paid $3 per hour for installing and $2 per hour for demonstrating, how many alarms of each type should smith install and demonstrate each week to maximize his earnings if john plans to work no more than 40 hours per week?
Answers
To maximize his earnings, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms.
Let's first consider the time constraints. Since John cannot work more than 40 hours per week, we have the following inequality:
1h(install Secure) x + 2.2h(install Maximum Secure) y + 0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 40
where x and y are the number of Secure and Maximum Secure alarms John installs, respectively.
John is required to work a minimum of 20 hours per week as an installer and a maximum of 20 hours as a demonstrator. So we have the following constraints:
1h(install Secure) x + 2.2h(install Maximum Secure) y >= 20 (minimum hours as installer)
0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 20 (maximum hours as demonstrator)
Now, we can set up the objective function to maximize John's earnings:
E(x,y) = 3(install Secure) x + 3(install Maximum Secure) y + 2(demo Secure) x + 2(demo Maximum Secure) y
= 5x + 5.6y
Using linear programming techniques, we can solve for the optimal values of x and y that maximize the objective function and satisfy the constraints. The optimal values turn out to be x=5 and y=5 for installing alarms, and x=5 and y=2 for demonstrating alarms. Therefore, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms, to maximize his earnings.
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5(8 - 8x^2) = 8
solve it
Answers
Answer:
the answer is 2√2.
Step-by-step explanation:
5(8-8x^2)=8
or,40-40x^2=8
or,40-8=40x^2
or,32=40x^2
or,32/40=x^2
or,4/5=x^2
or,√4/5= x
therefore.x=√4/5
Consider any conic section and discuss an application of the conic that you find
most interesting. Include an example of a mathematical equation that models
the application. Also, describe why you think this application is relevant and
beneficial to society.
PLEASE HELP ME COME UP WITH AN EQUATION USING A CONIC SECTION! Just one that I could put into a calculator.
Answers
Conic sections are shapes that are formed when the surface of a cone intersects with a plane shape
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and divis
Now, Types of conic section are,
The types include
1) Hyperbola
2) Parabola
3) Ellipse
Here, Application of conic section (Parabola) is,
The parabola can be applied in solving quadratic equations, functions and graph.
Hence, The general equation of a parabola is: y = a(x - h)² +k
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Determine which equation has the same solutions as the given equation.
x – 10k- 11=0
O A. (x-10)2 = 36
B. (x - 10)2 = 21
OC. (x - 5)2 = 21
OD. (x - 5)2 = 36
Answers
Answer:
D
Step-by-step explanation:
The figure is a parallelogram. m
Answers
Answer:
10
Step-by-step explanation:
a 4 side polygon has 360° interior angle
120 +120=240
360-240=120
120÷2=60
60÷6=10
A second story window is 20feet about the ground and the ladder is at a 70° angle. How long must the ladder be?
Answers
The ladder must be 21.26 feet long.
We can use trigonometry to solve this problem. Let's call the length of the ladder "L". We can use the sine function, which relates the opposite side of a right triangle to its hypotenuse, to find the length of the ladder:
sin(70°) = opposite / hypotenuse
sin(70°) = 20 / L
To solve for L, we can rearrange the equation:
L = 20 / sin(70°)
Using a calculator, we can find that sin(70°) is approximately 0.9397. Plugging this value into the equation, we get:
L = 20 / 0.9397
L = 21.26 feet (rounded to two decimal places)
Therefore, the ladder must be about 21.26 feet long to reach the second story window that is 20 feet above the ground at a 70° angle.
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1. What would you think "11 more than a number" would look like if you wrote it as a function ( don't use spaces in answer and use x for variable)
Answers
Answer:
11+x
Step-by-step explanation:
Let the number be x
11 more than the more will be
11+x
i am thinking of a number. I multiply it by 12 and add 16. I get the same number if I multiply it by 5 and subtract 142
Answers
The number you are thinking of can be either -16/11 or 71/2.
Let's represent the number you are thinking of as 'x'. According to the given information, we can set up the following equations based on the operations performed on the number:
Equation 1: 12x + 16 = x
Equation 2: 5x - 142 = x
To solve Equation 1, we can start by isolating the variable 'x'. Subtracting 'x' from both sides gives:
12x - x + 16 = 0
11x + 16 = 0
11x = -16
x = -16/11
To solve Equation 2, we'll again isolate the variable 'x'. Subtracting 'x' from both sides, we have:
5x - x - 142 = 0
4x - 142 = 0
4x = 142
x = 142/4
x = 71/2
Therefore, based on the given equations, we have two possible solutions for 'x': x = -16/11 and x = 71/2.
Thus, the number you are thinking of can be either -16/11 or 71/2, depending on the context or additional information provided in the problem.
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if v²=u²+2gs, find te value of s when v = 25 , u = 12 and g = 10
Answers
The value of s for the given value is 24.05.
Given is an equation v² = u²+2gs, we need to find the value of s if v = 25, u = 12 and g = 10,
So,
25² = 12² + 2(10)s
625 = 144 + 20s
20s = 481
s = 24.05
Hence the value of s for the given value is 24.05.
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find the first five terms for each of these recurrence relations, with the corresponding initial conditions: (a) (2 points) an = −an−1, a0 = 5
Answers
The first five terms for this recurrence relation are: 5, -5, 5, -5, and 5.
The recurrence relation given is an = -an-1, with initial condition a0 = 5. To find the first five terms of this sequence, we can use the relation repeatedly.
a0 = 5
a1 = -a0 = -5
a2 = -a1 = 5
a3 = -a2 = -5
a4 = -a3 = 5
So the first five terms of the sequence are 5, -5, 5, -5, 5. This sequence oscillates between 5 and -5, with each term being the opposite sign of the previous term.
To find the first five terms of the recurrence relation an = -an-1 with the initial condition a0 = 5, follow these steps:
1. Start with the initial condition: a0 = 5.
2. Apply the recurrence relation formula for the next terms:
a1 = -a0 = -5
a2 = -a1 = -(-5) = 5
a3 = -a2 = -5
a4 = -a3 = -(-5) = 5
The first five terms for this recurrence relation are: 5, -5, 5, -5, and 5.
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food inspectors inspect samples of food products to see if they are safe. this can be thought of as a hypothesis test with the following hypotheses. h0: the food is safe. ha: the food is not safe based on the hypotheses above, is the following statement a type i or type ii error? the sample suggests that the food is safe, but it actually is not safe.
Answers
A Type II error occurs when the null hypothesis (in this case, that the food is safe) is not rejected, even though it is false (in this case, the food is actually not safe). In other words, the inspector has failed to identify a problem with the food when there actually is one.
On the other hand, a Type I error would occur if the inspector falsely concludes that the food is not safe when it actually is safe, i.e. rejecting the null hypothesis when it is true.
Each of the following events result in a tax payment. Which is an example of a direct tax?
A. Charles sells a 25-acre lot, which includes a barn.
B. Sammy stops to pump gas on a cross-country road trip.
C. Ingrid's cable bill contains extra fees that weren't listed in the plan.
D. Javier owes money to the federal government based on job earnings.
Answers
Each of the following events result in a tax payment, an example of a direct tax is D. Javier owes money to the federal government based on job earnings.
How Do Direct Taxes Work?A direct tax is one that is paid by an individual or group of individuals directly to the body that levied it. Taxes on assets, real estate, personal property, and income are a few examples that are all paid by an individual taxpayer directly to the government.
Direct taxes are those that you pay to the government directly. You have paid a direct tax, for instance, if you pay income tax, property tax, or capital gains tax. On the other side, an indirect tax is when you make a purchase and someone else subsequently pays the tax on your behalf through a sales tax.
Therefore, option D is correct.
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Find when and .Both values are .Both values are . and and
Answers
from the question;
we to find |x| when x = 15 and when x = -15
by definition of absolute value we have
\(\lvert x\rvert\text{ = x}\)Thats for every value of x, the absolute value is always positive
Hence,
\(\begin{gathered} \text{when x = 15} \\ \lvert15\rvert=\text{ 15} \end{gathered}\)Also
\(\begin{gathered} \text{when x = - 15} \\ \lvert-15\rvert\text{ = 15} \end{gathered}\)Therefore the correct answer is
Both values are 15
option B
Veronica wants to check her work after evaluating -108 divided by (-6). What steps can she follow to verify her answer? A. Divide her answer by –6 and see if the result is –108. B. Divide her answer by –108 and see if the result is –6. C. Multiply her answer by –6 and see if the result is –108. D. Multiply her answer by –108 and see if the result is –6.
Answers
Answer:
C. Multiply her answer by –6 and see if the result is –108.
Step-by-step explanation:
Answer:
The answer is c
Step-by-step explanation:
hope this helps c:
which equation represents the area,y, of the trapezoid
Answers
Answer:
C. y = x^2 + 4x.
Step-by-step explanation:
Area of a trapezoid = (h/2)(a + b) where h is the altitude and a and b are the lengths of the parallel sides.
So here
Area y = (x/2)(8 + 2x)
= 8x/2 + 2x^2/2
= 4x + x^2.
to what decimal place should each answer be rounded? how many significant figures does the rounded answer have?
Answers
The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
Rounding a number is important when providing an answer to a calculation or question. The number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required.
To calculate the number of decimal places and significant figures the answer should be rounded to, the general rule is to round to one more decimal place than the least accurate measurement. For example, if the least accurate measurement used in the calculation is rounded to two decimal places, the answer should be rounded to three decimal places.
The significant figures of the rounded answer can be determined by counting the number of digits in the number, excluding the decimal point. For example, the number 6,782 would have four significant figures, as there are four digits in the number.
In conclusion, the number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required. The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
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you are ordering shirts for a club at your school. the function f(x)=8x+12 represents the cost of ordered x shirts how much would it cost to buy 32 shirts
Answers
The cost of ordering shirts for a club is 268 units.
Define Function.
A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.
This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).
The statement that f is a function from X to Y using the function notation f: X→Y
The function that represents the cost of the shirts(x) is f(x) = 8x+12
Now, for x = 32
f(x) = 8x+12
f(32) = 8(32) + 12
= 256 +12
f(32) = 268 units
.
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Why does everyone need to follow the order of operations when evaluating expressions?
Answers
Answer:
They make sure everyone gets to the same answer. Many people memorize the order of operations as PEMDAS (parentheses, exponents, multiplication/division, and addition/subtraction). The order of operations are one set of agreements for how to evaluate expressions. They make sure everyone gets to the same value.
Step-by-step explanation:
Solve for xxx. Enter the solutions from least to greatest. Round to two decimal places. (x + 8)^2 - 2 = 0
Answers
Answer:
55
Step-by-step explanation:
The values of the x are -6.59, and -9.42 if the quadratic equation is (x + 8)² - 2 = 0.
What is a quadratic equation?Any equation of the form \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)
The complete question is:
Solve for x.
Enter the solutions from least to greatest. Round to two decimal places.
(x + 8)² - 2 = 0
It is given:
(x + 8)² - 2 = 0
Using (a + b)² = a² + 2ab + b²
x² + 16x + 64 - 2 = 0
x² + 16x + 62 = 0
Compare with the standard form of the equation:
a = 1
b = 16
c = 62
Plug the above values in the formula:
\(\rm x = \dfrac{-16 \pm\sqrt{16^2-4(1)(62)}}{2(1)}\)
x = [-16 ±√8]/2
x = [-16 ±2.83]/2
Take + sign:
x = [-16 + 2.83]/2
x = -6.59
Take - sign:
x = [-16 - 2.83]/2
x = -9.42
Thus, the values of the x are -9.42, and -6.59 if the quadratic equation is (x + 8)² - 2 = 0.
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Express 6^1/3 in simplest radical form.
Answers
Greetings from Brasil
From radiciation properties:
\(\large{A^{\frac{P}{Q}}=\sqrt[Q]{A^P}}\)
bringing to our problem
\(\large{6^{\frac{1}{3}}=\sqrt[3]{6^1}}\)
∛6The requried radical form of the given expression is ∛6.
What is radical form?Radical form is mathematical expression that represents the value under the nth roots.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Following the rule \(\sqrt[n]{x} = x^{1/n}\)
Similarly,
\(6^{1/3} = \sqrt[3]{6}\)
Thus, the requried radical form of the given expression is ∛6.
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What is the equation in slope-intercept form of the line that passes through the point (6, 3) and is parallel to the graph of y = −2 3 - 2 3 x + 12?
Answers
The line passing through the coordinates (6, 3) and parallel to the y=-23-23x+12 graph. The equation of the slope intercept form of the line is 23x+y-141=0.
Given that,
We have to find what is the slope-intercept equation for the line passing through the coordinates (6, 3) and parallel to the y = -2 3 - 2 3 x + 12 graph.
The coordinates are (6,3).
y=-23-23x+12
y=-23x-11
The above equation is in the form of equation of the line that is y=mx+b
m value is -23.
Now,
The formula for the equation of line's slope intercept is
y-y₁=m(x-x₁)
y-3=-23(x-6)
y-3=-23x+138
23x+y-3-138=0
23x+y-141=0
Therefore, the equation of the slope intercept form of the line is
23x+y-141=0.
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Let A be a diagonalizable matrix whose eigen values satisfy that A2 = A + 1. Then A satisfies A) A² = A +1 B) A² = A + 2 C) A² = A D) A² = A + 1
Answers
D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.
Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.
We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:
(PDP^(-1))^2 = PDP^(-1) + 1.
Expanding the square and applying the matrix multiplication rules, we get:
PD^2P^(-1) = PDP^(-1) + 1.
Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:
P(D^2)P^(-1) = PDP^(-1) + 1.
Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:
D^2 = D + 1.
This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.
Therefore, the correct answer is D) A^2 = A + 1.
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Find the area of the shaded region. 3 x=y²-2² -1 -3 y -2 y = 1 1 y = -1 X=e2 3 4 X
Answers
To find the area of the shaded region, we need to integrate the given function with respect to x over the given limits.
The shaded region is bounded by the curves y = x^2 - 2x - 3 and y = -2y + 1, and the limits of integration are x = 2 and x = 4. To find the area, we need to calculate the integral of the difference between the upper and lower curves over the given interval:
\(Area = ∫[2, 4] [(x^2 - 2x - 3) - (-2x + 1)] dx\)
Simplifying the expression inside the integral, we get:
\(Area = ∫[2, 4] (x^2 + 2x - 4) dx\)
By evaluating this definite integral, we can find the exact area of the shaded region. However, without the specific value of the integral or access to a symbolic calculator, we cannot provide an exact numerical answer.
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on the south side of the building, the first quartile is 43cm, the median is 46cm, and the third quartile is 48cm. if she goes to the south side and randomly selects three daffodils, what is the probability that none of them are between 46cm and 48cm?
Answers
Around 50% to 75% of the daffodils on the south side of the building are not between 46cm and 48cm.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
This question asks for the probability that none of the three daffodils selected from the south side of the building are between 46cm and 48cm.
Since the median of the data is 46cm
the third quartile is 48cm,
this means that about 50% to 75% of the daffodils on the south side of the building are between 46cm and 48cm.
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23. the difference between the number of customers in line at the express checkout and the number in line at the super-express checkout in exercise 3 is x1 2 x2. calculate the expected difference.
Answers
The expected difference is 0.17
What is super express market?A supermarket is a self-service store with various food, drink, and household goods options divided into categories. While this type of store is bigger and has a wider variety of products than older grocery stores, it is smaller and offers a smaller selection of goods than a hypermarket or big-box market. Fresh meat, produce, dairy, deli foods, baked goods, etc. may usually be found in the store.
Additionally, shelf space is set aside for canned and packaged goods as well as a variety of non-food items like pet supplies, cleaning supplies, cookware, and household cleansers.
The table is: 0 1 2 3
x1 0 0.08 0.06 0.04 0.00
1 0.05 0.18 0.05 0.03
2 0.05 0.04 0.10 0.06
3 0.00 0.03 0.04 0.07
4 0.00 0.01 0.05 0.06
Expected difference =
+(0.08*(0-0)) +(0.06*(0-1)) +(0.04*(0-2)) +(0.00*(0-3)) +(0.05*(1-0)) +(0.18*(1-1)) +(0.05*(1-2)) +(0.03*(1-3)) +(0.05*(2-0)) +(0.04*(2-1)) +(0.10*(2-2)) +(0.06*(2-3)) +(0.00*(3-0)) +(0.03*(3-1)) +(0.04*(3-2)) +(0.07*(3-3)) +(0.00*(4-0)) +(0.01*(4-1)) +(0.05*(4-2)) +(0.06*(4-3))
= 0.17
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f(x) = 2x + 2; Find f(10)
Answers
Answer:
22
Step-by-step explanation:
f(10)=2(10)+2
20+2
22
Find the Value of x.
Answers
Answer:
x = 91
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
x + 89 = 180
x = 91