According to the given information, your share of the groceries was $39.95, your other roommate's share was $42.05, and Sarah's share was $0.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Let's call the amount of money Sarah spent on groceries "S".
Let's call the amount of money you spent on groceries "Y".
Let's call the amount of money your other roommate spent on groceries "O".
We know that:
S + Y + O = 82 (the total bill was $82)
Y = (S/2) - 0.05 (your groceries were $0.05 cheaper than half of Sarah's groceries)
O = Y + 2.10 (your other roommate's groceries were $2.10 more than your groceries)
We can use the second equation to substitute Y in the third equation:
O = Y + 2.10
O = (S/2) - 0.05 + 2.10
O = (S/2) + 2.05
We can now substitute both equations into the first equation:
S + Y + O = 82
S + ((S/2) - 0.05) + ((S/2) + 2.05) = 82
2S + 4 = 164
2S = 160
S = 80
Now that we know S, we can substitute it into the other equations to find Y and O:
Y = (S/2) - 0.05 = (80/2) - 0.05 = 39.95
O = Y + 2.10 = 39.95 + 2.10 = 42.05
So your share of the groceries was $39.95, your other roommate's share was $42.05, and Sarah's share was $80 - ($39.95 + $42.05) = $82 - $82 = $0.
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What is the x and the y Intercept?
For the given function the intercepts are:
x-intercept: x = -4
y-intercept: y = 12.
How to find the intercepts for the given function?Here we have a table that defines a function, and we want to find the intercepts of said function.
We can assume it is linear, then the slope of the function will be given by:
a = (9 - 3)/(-1 + 3) = 6/2 = 3
The linear function is like:
y = 3x + b
To find the value of b we can replace the values of the last point on the table, x = 2 and y = 18.
18 = 3*2 + b
18 = 6 + b
18 - 6 = b = 12
The linear function is:
y = 3x + 12
The x-intercept is the value of x when y = 0
0 = 3*x + 12
-12 = 3x
-12/3 = x = -4
And the y-intercept is the value of y when x = 0.
y = 3*0 + 12
y = 12
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what is the area of the circle below?
The area of the circle shown above is equal to: A. 1,520.5 cm².
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using the following mathematical expression:
Area of a circle, A = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of a circle, A = πr²
Area of a circle, A = 3.14 × 22²
Area of a circle, A = 1,520.5 cm².
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Jenelle bought a home for $470,000, paying 18% as a down payment, and financing the rest at 5.4% interest
for 30 years. Round your answers to the nearest cent.
How much money did Jenelle pay as a down payment? $
What was the original amount financed? $
What is her monthly payment? $
If Jenelle makes these payments every month for thirty years, determine the total amount of money she
will spend on this home. Include the down payment in your answer. $
1- 58000
2- 232000
3- 1245.43
4- 506354.8
Which answer shows shows the equation below written in different forms 9-3=6
The equatiοn 9 -3 = 6 can be written in different fοrms, but the correct one is 9 = 3 + 6.
Are expressiοns cοnsidered equatiοns?Every cοmbinatiοn οf a number, a variables, and οperatiοn symbοls is cοnsidered an expressiοn. An equatiοn is created by cοmbining twο expressiοns and jοining them with the equal sign.
Cοnditiοns οn the parameters are fοund in simple equatiοns. It is clear frοm an equatiοn that the answer οn the left and right are equivalent. The expressiοn tο the left οf the symbοl "=" is the LHS, while the expressiοn tο the right is the RHS. With the fοrm y = "sοme expressiοn invοlving x," a sοlutiοn invοlving x and y can be expressed, such as y = f. ( x). This final statement, which may be interpreted as "y equals f οf x," denοtes that y is a cοefficient οf x.
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Complete question:
Which answer shows the equation 9-3=6 below written in different forms?
6 + 3 = 9, 9 = 3 + 6, 9 - 6 = 3, 3 = 9 - 6PLEASE HURRY!!! I WILL GIVE THE BRAINLIEST!!!
Which answer shows the correct steps to solve the equation
a
Subtract 4 from both sides,, multiply by 12 on both sides, subtract 10 from both sides, and divide both sides by 5 to get x=2/5
b
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
c
Subtract 10 from both sides, multiply by 15 on both sides, and divide by 5 to get x=(-18)
d
Subtract 5x from both sides, subtract 10/15 from both sides, and divide both sides by 5 to get x=10
Answer:
Answer is B
Step-by-step explanation:
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
Which of the following statements is MOST LIKELY TRUE?
A-The lower half of Sample A's data is closer to the value 5 than the lower half of Sample B's data.
B-Both of the data sets range from 1 to 10 on the number line.
CThe upper half of Sample A's data is closer to the value 10 than the upper half of Sample B's data.
D-The data in Sample B is clustered around the center where Sample A is more spread out
Explain
Answer:
Step-by-step explanation:
ntroduction to standard deviation
Standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.
For example, the blue distribution on bottom has a greater standard deviation (SD) than the green distribution on top:
Please help asap! Need the answer quickly!
The time needed for the sample size to double is given as follows:
26.3 hours.
How to obtain the time needed for the sample size to double?The exponential function that models the sample size after t hours is given as follows:
y(t) = y(0)e^(0.0264t).
The parameter y(0) represents the initial population, hence when the population is doubled, we have that:
y(t) = 2y(0).
Then we must solve the exponential function for the variable t, applying the natural logarithm, which is the inverse of the exponential, as follows:
2y(0) = y(0)e^(0.0264t).
e^(0.0264t) = 2
0.0264t = ln(2)
t = ln(2)/0.0264
t = 26.3 hours.
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Professor Yi, M.A. is an expert on mindfulness meditation, and completed a study on how this practice can reduce stress. In the untreated population of Ionia, stress levels as measured by the HRSI (higher values indicate higher levels of stress) the mean stress level is μ = 30 and σ = 12. Professor Yi obtained a sample of n = 16 students to teach mindfulness meditation to for two months. After the two months of lessons the students show average HRSI stress scores of M = 24. Yi decided in advance he was going to run a two-tailed hypothesis test at an α = .05.
What is the null hypothesis for this study?
The null hypothesis for this study is that there is no significant difference in stress levels between the untreated population and the sample of students who were taught mindfulness meditation.
How to find the null hypothesis ?The null hypothesis states that the mindfulness meditation has no effect on the stress levels of the students.
In terms of the mean stress level (μ), the null hypothesis can be expressed as:
H₀: μ = 30
This means that under the null hypothesis, the mean stress level of the students who were taught mindfulness meditation is equal to the mean stress level of the untreated population (μ = 30).
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The difference between two numbers is 2. When each number is rounded to nearest hundred, the difference between them is 100. What could the numbers be?
[tex]101 - 99 = 2[/tex]
each number is rounded to nearest hundred101 → 200
99 → 100
the difference between them is 100:[tex]200 - 100 = 100[/tex]
⇒ the numbers could be: 99 and 101
other pairs of numbers: (199,201), (299,301) ...
In track and field, the 440-yd. race was replaced with the 400-m race when Canada changed from the imperial system to the SI system. Which race is longer and by how much? Use the exact conversion: 1 yd. = 0.9144 m
Answer:
The 440-yd race is longer than the 400-m race by 2.336 meters.
Step-by-step explanation:
We can convert the distance of the 440-yd race to meters using the conversion factor 1 yd = 0.9144 m:
440 yd = 440 x 0.9144 m/yd = 402.336 m
Therefore, the 440-yd race is 402.336 meters long.
On the other hand, the 400-m race is already in meters.
Comparing the two distances, we can see that the 440-yd race is longer than the 400-m race.
To find out by how much longer, we can subtract the length of the 400-m race from the length of the 440-yd race:
402.336 m - 400 m = 2.336 m
Therefore, the 440-yd race is longer than the 400-m race by 2.336 meters.
PLEASE HELP FAST!!
Determine the number of solutions to the system of linear equations shown on the graph.
A: No solution
B: Infinitely many solutions
C: One solution at (-3,2)
D:One solution at (2,-3)
Answer:
the answer is D
both lines intersect at (2, -3)
hope this helps <3
Pearl earns $34,000 per year, and she is considering buying a $130,000 house by
making a down payment of 10% of the purchase price and taking out a 30-year
fixed-rate mortgage with a 6.3% interest rate. She would pay $1280 annually in
property taxes, and for the first 2 years of the mortgage, she would pay $608.40
annually for PMI. Use this information to answer the following six questions.
1.
How much would Pearl's
mortgage be?
Pearl's mortgage payment would be $678.47 per month.
What is mortgage?A mortgage is a type of loan that is used to finance the purchase of real estate, such as a house or a piece of land. When a person takes out a mortgage, they borrow money from a lender (usually a bank or other financial institution) to buy the property, and they agree to pay back the loan over a set period of time, typically 15 to 30 years.
In the given question,
To calculate Pearl's mortgage, we need to first determine the amount of her down payment.
Down payment = 10% x $130,000
Down payment = $13,000
The amount that Pearl needs to finance with her mortgage is:
$130,000 - $13,000 = $117,000
To calculate the mortgage payment, we can use the formula for a fixed-rate mortgage:
Mortgage Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal (amount borrowed)
r = Monthly interest rate (annual rate divided by 12)
n = Number of monthly payments (30 years x 12 months per year)
Monthly interest rate = 6.3% / 12 = 0.00525
Number of monthly payments = 30 years x 12 months = 360
Using these values, we can calculate the monthly mortgage payment:
Mortgage Payment = $117,000 * 0.00525 * (1 + 0.00525)^360 / ((1 + 0.00525)^360 - 1)
Mortgage Payment = $678.47 (rounded to the nearest cent)
Therefore, Pearl's mortgage payment would be $678.47 per month.
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√(×2₂ − ×₁)² + (Y₂ − ¥₁)²
11. Using the distance formula
, find the distance from the
center of your habitat to the point (x, y). Write this equation. Your answer will
contain x- and y-terms. (1 point)
So the equation for the distance from the center of the habitat to the point (x, y) is: Distance = √[(x - x1)² + (y - y1)²].
What is coordinate?A coordinate is a number that indicates the position of a point in a space or plane. In mathematics, we often use a coordinate system to represent points and their positions. A coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the position of a point or an object in a space or plane. The most common coordinate system is the Cartesian coordinate system, which is named after the mathematician René Descartes. In the Cartesian coordinate system, each point is represented by an ordered pair of numbers (x, y), where x is the horizontal coordinate or abscissa, and y is the vertical coordinate or ordinate. The point (0, 0) is called the origin, and it represents the point where the x and y axes intersect. Coordinates can also be expressed in three or more dimensions, using three or more numbers. In three-dimensional space, the coordinates of a point are represented by an ordered triple (x, y, z), where x, y, and z are the horizontal, vertical, and depth coordinates, respectively.
Here,
The distance formula is used to find the distance between two points in a coordinate plane. In this case, we are finding the distance from the center of the habitat (x1, y1) to the point (x2, y2), so the formula becomes:
=√[(x2 - x1)² + (y2 - y1)²]
Substituting the coordinates of the given point (x, y), we get:
=√[(x - x1)² + (y - y1)²]
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Solve For The Radius:
a. r = 9.7 m
b. r = 7 m
c. r = 123.5 m
d. r = 19.4 m
Answer:
a) r = 9.7 m
Step-by-step explanation:
CD = CE + ED
= 9 + r +r
= 9 + 2r
If a tangent and a secant are drawn from a common point outside the circle, then
CE * CD = CB *CB
9 * ( 9 + 2r) = 16 * 16 {Distributive property}
9*9 + 9*2r = 256
81 + 18r = 256
Subtract 81 from both sides,
18r = 256 - 81
18r = 175
Divide both sides by 18,
r = 175÷ 18
[tex]\boxed{\bf r = 9.7 \ m }[/tex]
What is the probability that a resident is male and in the age group 60-79
Answer:
c. 0.29
Step-by-step explanation:
edge
Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3. What is P(27.42 ≤ x ≤ 34.08)?
The answer to this question is 0.6826, or 68.26%. To calculate this probability, we need to use the z-score formula.
What is z-score formula?The z-score formula is a statistical measurement that is used to identify how far a raw score is from the mean score of a population. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.
This formula allows us to convert a given value into a standardized score relative to the mean and standard deviation of the normal distribution. In this case, the z-score for 27.42 is -1 and the z-score for 34.08 is 1.
We can then use the cumulative normal distribution function to calculate the probability of x being between 27.42 and 34.08. This function allows us to calculate the area under the normal distribution curve between two given points. Since the normal distribution is symmetrical, the area under the curve between -1 and 1 is 0.6826 or 68.26%. This is the probability of x being between 27.42 and 34.08.
To summarize, in order to calculate the probability of x being between 27.42 and 34.08, we need to calculate the z-scores of these two values and then use the cumulative normal distribution function to calculate the area under the curve between the two z-scores. The area under the curve between -1 and 1 is 0.6826 or 68.26%, which is the probability of x being between 27.42 and 34.08.
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What value of n makes the equation true? Show your work.
Answer:6
Step-by-step explanation:
[tex]\frac{a^{b} }{a^{c}} =a^{b-c} \\a^{b} *a^{c} =a^{b+c}\\ \frac{(-4)^{10}}{(-4)^{n}}=(-4)^{2}*(-4)^{2} \\(-4)^{10-n}=(-4)^{4}\\ 10-n=4\\ -n=-6\\n=6[/tex]
Answer:
n = 6
Step-by-step explanation:
[tex]\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2}*(-4)^{2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2+2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{4}[/tex]
If they have the same base which is -4 we can either add or subtracting the exponent.
Add the exponenet when multiplying.
Subtract the exponent when dividing.
[tex](-4)^{10-n}=(-4)^4\\\\10-n=4\\10=4+n\\n= 6[/tex]
[tex]\frac{(-4)^{10}}{(-4)^{6}}=(-4)^{10-6}=(-4)^4[/tex]
Pls help simplify liner expressions
The answers to the questions are in the picture
I need help what is, 8y - 7 - 4y =
show work
Answer:
Step-by-step explanation:
8y-7-4y=
8y-4y= -7
4y=-7
DBS by 4
y=1.75
f(x) =
4 if x≤3
-4 if x>3
What is the functions range ?
Answer:
(−∞,∞)
Step-by-step explanation:
Please help meee this is due Friday!!! A fully loaded and fueled spacecraft can weigh close to 5.1 million pounds. What is this weight converted to tons?
Answer:
A fully loaded and fueled spacecraft weighing 5.1 million pounds is equivalent to 2550 US tons
Step-by-step explanation:
Find the equation of a line that passes through the point (-2,-3) and has a gradient of -3.
Leave your answer in the form
Answer:
you need to put the answers down
Step-by-step explanation:
.
Giselle wants to buy a condo that has a purchase price of $163,000. Giselle earns $2,986 a month and wants to spend
no more than 25% of her income on her mortgage payment. She has saved up $33,000 for a down payment. Giselle is
considering the following loan option: 20% down, 30 year at a fixed rate of 6.25%. What modification can be made to this
loan to make it a viable option, given Giselle's situation?
a. Change to a 15 year fixed loan
b.
Change the interest to 5.5%
c. Change the down payment to 18% down
d.
None. This is a viable option for Giselle.
Correct option is B, modification that can be made to this loan to make it a viable option, given Giselle's situation Change the interest to 5.5%.
What modification can be made to this loan to make it a viable option, given Giselle's situation?Giselle may either lower the interest rate to 5.5% or increase the down payment to 18% down in order to make the 20% down, 30-year fixed loan option financially feasible. Giselle's maximum monthly payment of $746.50 is exceeded by the monthly payment for the current loan option. The monthly payment would rise if the loan was shortened to 15 years, rendering it unprofitable. As a result, Giselle should choose a mortgage with a lower interest rate or put more money down in order to bring the monthly payment within her means.
Given Giselle's circumstances, the modification that may be made to this loan to make it an attractive alternative is to raise the interest rate to 5.5%.
Changes to the loan that will be made:
Price of acquisition: $163,000
Monthly income equals $2,986
25% of people are unwilling to spend money.
$33,000 is the down payment.
20% decline rate
Analysis
163,000 less $33,000 is the balance of the loan.
Amount remaining on loan is $130,000.
Condo loan balance = $163,000.20
Condo loan balance = $32,600
Down rate increase equals $163,000 x 20.25%
A higher down payment equals $33,007.50
The optimal solution, based on the research above, is to change the interest rate to 5.5% because it will result in a lower overall payment cost and make the loan amount a viable option.
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Q. 1 Solve the following In equality 7(x – 2) + x > – 4(5 – x) – 12
Answ
Step-by-step explanation:
x is equal to -9/2
Determining Whether a Point Lies on a Circle
10
8
-10 8-6-4-2
6
4
2
-2
-6
8
-10
Y
2
6 8 10
A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8. √17).
O Yes, the distance from the origin to the point
(8,√17) is 9 units.
Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.
The correct statement regarding whether (8, √17) lies on the circle is given as follows:
Yes, the distance from the origin to the point (8,√17) is 9 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The parameters for this circle are given as follows:
Center (0,0).Radius 9.Hence the equation is given as follows:
x² + y² = 81.
For point (8, √17), we have that:
8² + (√17)² = 81
64 + 17 = 81
81 = 81.
Hence the point lies on the circle.
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Which student found the total surface area of a cylinder with a height that was two times greater than its radius?
The total surface area of a cylinder with a height that was two times greater than its radius is 6πr²
What is the total surface area of a cylinder?The total surface area of a cylinder is the region occupied by the cylinder. It is given by A = 2πr(r + h) where
r = radius of cylinder and h = height of cylinderSince we want to find which student found the total surface area of a cylinder with a height that was two times greater than its radius.
We proceed as follows.
Since we have that the height that was two times greater than its radius. So, for that cylinder, h = 2r
So, to find the surface area, we substitute the values of the variables into the equation for the total surface area.
So, A = 2πr(r + h)
Given that h = 2r, we have that
A = 2πr(r + h)
A = 2πr(r + 2r)
A = 2πr(3r)
A = 6πr²
So, the area is 6πr²
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Let f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6. Identify the solution(s) of
f(x) = g(x).
The solutions of the function as required to be determined is; x = 8 or x = -4.
What is the solution of the equation?As evident in the task content; the given equation are;
f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6.
The solution of the equation can be determined as follows;
9x² - 5x - 58 = 7x² + 3x + 6.
2x² -8x - 64 = 0
x² - 4x - 32 = 0
(x - 8) (x + 4) = 0
x = 8 Or x = -4.
Ultimately, the solutions of the equation are; x = 8 or x = -4.
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what has a sum of 147
Answer:
146 and 1
Step-by-step explanation:
146+1=147
A is five times as old as B. after 10 years a will be 3 times as old as B will be then. find their present age
According to given information, A is 50 years old and B is 10 years old.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be evaluated to produce a numerical result or a value.
According to given information :Let's use algebra to solve the problem.
Let A's current age be x, and B's current age be y.
From the problem, we know that:
x = 5y (A is five times as old as B)
x + 10 = 3(y + 10) (After 10 years, A will be 3 times as old as B)
We can use the first equation to substitute x in the second equation:
5y + 10 = 3(y + 10)
Simplifying this equation gives:
5y + 10 = 3y + 30
2y = 20
y = 10
So B is currently 10 years old. We can use the first equation to find A's current age:
x =5y = 5(10) = 50
So A is currently 50 years old.
Therefore, according to given information, A is 50 years old and B is 10 years old.
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a block exerts a force of 7nm on the ground. what is the pressure on the ground in nm2 when its flat on the grounds the area of its base is 0.04m2
The pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is [tex]175 nm^{-2[/tex].
First, we need tο cοnvert the area οf the blοck's base frοm square meters tο square nanοmeters, since the fοrce is given in newtοn-meters (N m) and we want tο find the pressure in newtοn-meters-squared ([tex]N/m^2[/tex] οr[tex]Nm^{-2[/tex]):
[tex]0.04 m^2 = 0.04 \times 10^18 nm^2 (since 1 m = 10^9 nm)[/tex]
Next, we can use the fοrmula fοr pressure, which is:
pressure = fοrce/area
Substituting the given values, we get:
[tex]pressure = 7 N m / 0.04\times 10^{18} nm^2[/tex]
Simplifying this expressiοn, we get:
[tex]pressure = (7 / 0.04) \times 10^{(-9)} N/nm^2[/tex]
[tex]pressure = 175 \times 10^{(-9)} N/nm{^2[/tex]
[tex]pressure = 175 nm^{-2[/tex]
Therefοre, the pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is[tex]175 nm^{-2[/tex].
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