Answer:
If the origin is the only point with 0 for both coordinates, then it must be the point of intersection of the x-axis and the y-axis. In other words, the origin is the point (0,0), where the x-coordinate and y-coordinate are both zero. It is the unique point in the Cartesian plane that satisfies this condition.
Step-by-step explanation:
Can someone answer this question?
Answer:
Step-by-step explanation:
It's a negative slope so A and B are out
-.89 slope is a little flatter than -1 I think the correlation is a little flatter so I'd go with C. Could be D, since the slopes are so similar and you are just estimating. But I think C looks better.
Oliver saves 10% of his weekly earnings for living expenses. He usually makes $520 each v week Calculate the amount of spending money Oliver has left for this week. What error did C
The amount of spending money Oliver has left for this week will be $52.
Given that:
Oliver sets aside 10% of his weekly income for savings. He typically earns $520 every week.
If Oliver saves 10% of his weekly earnings, then he spends 100% - 10% = 90% of his weekly earnings on living expenses.
The amount of money Oliver spends on living expenses each week is:
=> 0.9 x $520
=> $468
Therefore, the amount of spending money Oliver has left for this week is:
=> $520 - $468
=> $52
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$9,000 is invested in an account earning 8% interest (APR), compounded daily.
Write a function showing the value of the account after t years, where the annual
growth rate can be found from a constant in the function. Round all coefficients in
the function to four decimal places. Also, determine the percentage of growth per
year (APY), to the nearest hundredth of a percent.
Answer:
The formula for calculating the value of an account with compound interest is:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal (starting amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period in years
For this problem, we have:
P = $9,000
r = 8% = 0.08 (APR)
n = 365 (compounded daily)
t = number of years
So the function for the value of the account after t years is:
f(t) = 9000(1 + 0.08/365)^(365t)
Simplifying and rounding to four decimal places:
f(t) = 9000(1.000219178)^t
f(t) = 9000(1.0002)^t
To determine the annual percentage yield (APY), we can use the formula:
APY = (1 + r/n)^n - 1
where r = 0.08 (APR) and n = 365 (compounded daily)
APY = (1 + 0.08/365)^365 - 1
APY = 0.0833 or 8.33%
So the account is growing at an annual rate of 8.33%.
Use rise/run for this
Answer:
The table displays a higher rate because the slope in the table is bigger than the slope in the graph.
What does a graph's slope mean?
The graph's slope serves as a gauge for a line's steepness. It is the ratio of any two places on the line's vertical change (rise) to horizontal change (run). Slope is defined mathematically as: Slope (m) = (change in y)/(change in x).
The slope from the table is:
y2 - y1/x2 - x1
m = 42 - 30/7 - 5
= 6
The slope from the graph is:
8 - 0/1.5 - 0
m = 5.33
Daniel bought a new car for 15000 he also pays
Daniel's down payment was $1,367.91.
To determine the amount of the down payment, we need to first calculate the total cost of the car, including the fees and sales tax. The total cost can be found by adding up the purchase price and the fees:
Total cost = Purchase price + Fees
Total cost = $15,000 + $450 + $275
Total cost = $15,725
Next, we need to calculate the amount of sales tax that Daniel paid on the car:
Sales tax = 8.75% x Total cost
Sales tax = 0.0875 x $15,725
Sales tax = $1,373.94
Now we can calculate the total amount that Daniel paid for the car, including the sales tax:
Total amount = Total cost + Sales tax
Total amount = $15,725 + $1,373.94
Total amount = $17,098.94
Finally, we can calculate the amount of the down payment by taking 8% of the total amount, including sales tax:
Down payment = 8% x Total amount
Down payment = 0.08 x $17,098.94
Down payment = $1,367.91
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Complete Question:
Daniel bought a new car for $15,000. He also paid two fees for the car dealership:
• $450 for an extended warranty
• $275 for a stereo upgrade In addition, he paid sales tax, which was 8.75% of the total cost, including the purchase price and fees.
Daniel initially gave the dealership 8% of the total amount, including sales tax, as a down payment. What was the amount of the down payment?
Karma borrowed Nu 50,000 at a rate of 15% compounded monthly. He agreed to the following repayment plan: ● Nu 20,000 at the end of first month ●Nu 25,000 at the end of second month ●A final repayment of the remaining at the end of third month a) Calculate the amount of the final repayment.
The total repayment will therefore be Nu. 6,083.12.We must determine the sum left after the subsequent payment before we can determine the total amount of the final payback.
Why is there interest?Amount of funds that is earned or paid out on a sum or money over time is referred to as interest in mathematics. It is the fee for borrowing money or the return on an investment.
Interest may be complex or simple. Simple interest is determined over a specific time period as a proportion of the original principal sum. Contrarily, compound interest is calculated over a period of time using the principal amount along with any prior interest that has accrued.
The sum after the initial payment is:
50k as the principal
15% divided by 12 equals 1.25% each month in interest.
the first month
50k as the principal
15% divided by 12 equals 1.25% each month in interest.
First month's interest equals 50,000 times 1.25 percent, or 625. First month's payment equals 20,000.
After the initial payment, the balance is equal to 30,625 (50,000 + 625 - 20,000).
The balance left after the second instalment is:
15% divided by 12 equals 1.25% each month in interest.
Second-month interest equals 30,625 times 1.25 percent, or 383.02.
The second month's payment was for $25,000
After the second payment, the balance is equal to 6,008.02 (30,625 + 383.02 - 25,000).
The sum left over in the third month of payment, including interest, must be calculated to determine the total payback amount.
15% divided by 12 equals 1.25% each month in interest.
Interest for the third month: 6,008.02 x 1.25% = 75.1
After the third month, the balance is equal to 6,008.02 plus 75.1, or 6,083.12.
The total repayment will therefore be Nu. 6,083.12.
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At the end of the third month, Karma still owes Nu 20,519.06.the amount of the final repayment is the outstanding balance at the end of the third
What is compound interest?
Compound interest is the interest earned not only on the initial principal amount, but also on any interest that has accumulated in previous periods.
To calculate the final repayment, we need to determine the amount that Karma would have to repay at the end of the third month, which would include the principal amount borrowed plus the accumulated interest.
First, we need to determine the monthly interest rate, which is given by:
i = (r / 100) / 12
where r is the annual interest rate.
In this case, the annual interest rate is 15%, so the monthly interest rate is:
i = (15 / 100) / 12 = 0.0125
Next, we can use the formula for the future value of an annuity to calculate the amount that Karma would have to repay at the end of the third month:
FV = R * [tex]((1 + i)^{(n - 1)}[/tex] / i
where R is the monthly repayment amount, i is the monthly interest rate, and n is the number of periods.
For the first two months, Karma makes repayments of Nu 20,000 and Nu 25,000, respectively. So, at the end of the second month, the outstanding balance on the loan is:
P2 = P1 * (1 + i) - R1
where P1 is the principal amount borrowed, R1 is the first monthly repayment, and P2 is the outstanding balance at the end of the second month.
Using the values given, we get:
P2 = 50000 * (1 + 0.0125) - 20000 = 32125
So, Karma still owes Nu 32,125 at the end of the second month.
Using the same formula, we can calculate the outstanding balance at the end of the third month:
P3 = P2 * (1 + i) - R2
where R2 is the second monthly repayment, and P3 is the outstanding balance at the end of the third month.
Using the values given, we get:
P3 = 32125 * (1 + 0.0125) - 25000 = 20519.06
So, at the end of the third month, Karma still owes Nu 20,519.06.
Finally, the amount of the final repayment is the outstanding balance at the end of the third
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A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
Answer:
The area of the tile can be found by dividing it into two triangles and one trapezoid. The area of the trapezoid is (5+3)/2 x 6 = 24 cm^2. The area of the two triangles can be found using the height of 5 cm and the base of 6 cm and 2 cm, respectively. The total area is then 24 + (5 x 6)/2 + (5 x 2)/2 = 24 + 15 + 5 = 44 cm^2. Therefore, the closest answer choice is 42.5 cm^2. The answer is (C) 42.5 cm^2.
Step-by-step explanation:
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HELP!!
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is 40 or older is chosen at random what is the probability that hey have only completed highschool? ROUND YOUR ANSWER TO THE NEAREST TENTH!!
Answer: .1 or 12.2%
Step-by-step explanation:
probability is the part out of the whole
the part = those taken high school only and over 40 =388+1448=1836
the whole are all the people which is 15048
1836/15048=.1 or 12.2%
How long will it take $15,000 to double if you invest the money in an account earning
4.75% interest compounded continuously? Round to the nearest tenth of a year.
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$15000\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ t=years \end{cases}[/tex]
[tex]30000 = 15000e^{0.0475\cdot t} \implies \cfrac{30000}{15000}=e^{0.0475t}\implies 2=e^{0.0475t} \\\\\\ \log_e(2)=\log_e(e^{0.0475t})\implies \log_e(2)=0.0475t \\\\\\ \ln(2)=0.0475t\implies \cfrac{\ln(2)}{0.0475}=t\implies 14.6\approx t[/tex]
Find the sale price of the item. Round to two decimal places if necessary.
Original price: $76.00
Markdown: 32%
Answer:
32% off the original price = 68% of the original price. So the sale price is:
$76.00 × .68 = $51.68
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The Surface Area of the cube that has a side length of 4 yards is calculated as: 96 square yards.
What is the Surface Area of a Cube?A cube has equal side length, and all its faces have the same area. Therefore, we have:
Surface Area of a cube = 6a² [note that a is the length of the side or edge of the cube].
Given the following:
Side length (a) = 4 yards
Plug in the value of a into the formula:
Surface Area of the cube = 6(4²)
Surface Area of the cube = 6(16)
Surface Area of the cube = 96 square yards.
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A loan in the amount of $14,800 was opened on January 22, at an interest rate of 9%. The maturity value of the loan is $15,799. What is the due date of the loan?
a. October 22nd
b. October 31st
c. September 22nd
d. September 30th
The due date of the loan in the amount of $14,800, opened on January 22, at an interest rate of 9% and with the maturity value of the loan as $15,799, is a. October 22nd.
How is the due date determined?The due date can be determined using an online finance calculator, which shows that it will take almost 9 months for the loan's due date.
I/Y (Interest per year) = 9%
PV (Present Value) = $14,800
PMT (Periodic Payment) = $0
FV (Future Value) = $15,799
Results:
Loan Period (N) = 8.742 months
≈ 9 months
Total Interest = $999.00
Thus, 9 months to January 22 falls on October 22nd.
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a fast food restaurant executive wishes to know how many fast food meals adults eat each week. they want to construct a 90% confidence interval with an error of no more than 0.06 . a consultant has informed them that a previous study found the mean to be 3 fast food meals per week and found the variance to be 1.69 . what is the minimum sample size required to create the specified confidence interval? round your answer up to the next integer.
The minimum sample size required to construct a 90% confidence interval with an error of no more than 0.06, given a population mean of 3 fast food meals per week and a population variance of 1.69, is 166.
To find the minimum sample size required to construct the specified confidence interval, we need to use the following formula
n = [Z² × σ²] / E²
where n is the sample size, Z is the Z-score for the desired level of confidence (90% in this case), σ² is the population variance, and E is the maximum error or margin of error.
First, we need to find the Z-score for the 90% confidence level using a standard normal distribution table or calculator. For a two-tailed test, the Z-score is 1.645.
Next, we plug in the given values
n = [1.645² × 1.69] / 0.06²
n = 165.82
We round up to the nearest whole number since we cannot have a fraction of a person in our sample
n = 166
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Please answer the question shown in the image below:
The distance between given point A and point B on the graph is 3√2 units.
Hence the correct option is (A).
We know that the distance between two points having coordinates (a, b) and (c, d) is = √((c - a)² + (d - b)²).
From the given graph we can see that,
the coordinates of the point A = (-2, -1)
the coordinates of the point B = (1, 2)
So the distance between the point A and point B is given by,
= √((1 - (-2))² + (2 - (-1))²)
= √((1 + 2)² + (2 + 1)²)
= √(3² + 3²)
= √(9 + 9)
= √18
= 3√2 units
Hence the correct option will be (A).
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Enola is going to invest in an account paying an interest rate of 5.1% compounded continuously. How much would Enola need to invest, to the nearest cent, for the value of the account to reach $12,800 in 10 years?
Answer:
$7,686.34
Step-by-step explanation:
You want to know the amount that needs to be invested at 5.1% compounded continuously for 10 years to achieved an account value of $12,800.
Compound interestThe value of an account accumulating interest at rate r compounded continuously is ...
A = P·e^(rt)
where P is the principal invested and t is the number of years.
We want to find P for A=12800, r=0.051, t=10.
12800 = P·e^(0.051·10)
12800·e^-0.51 = P ≈ 7686.34
Enola needs to invest $7,686.34 for the account value to reach $12,800 in 10 years.
__
Additional comment
Dividing by e^0.51 is the same as multiplying by e^-0.51.
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Enola needs to invest $7,686.34 for the account value to reach $12,800 in 10 years.
What's the amount?You want to know the amount that needs to be invested at 5.1% compounded continuously for 10 years to achieved an account value of $12,800.
The value of an account accumulating interest at rate r compounded continuously is ...
A = P·[tex]e^{rt}[/tex]
where P is the principal invested and t is the number of years.
We want to find P for A=12800, r=0.051, t=10.
12800·[tex]e^{-0.51 }[/tex] = P ≈ 7686.34
Enola needs to invest $7,686.34 for the account value to reach $12,800 in 10 years.
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Please help!!!!! (Klick the pic)
3 of 6
Find the value of the length a rounded to 1 DP
80
P=
27°
31m
The diagram is not drawn accurately.
m
x
Answer: x=5.9
Step-by-step explanation:
Use SOH CAH TOA to find full length then subtract to find x
full angle is 27+8=35
they gave adjacent and opposite to the angle so use TOA
tan 35 =[tex]\frac{y}{31}[/tex]
y=31 tan 35
y=21.71 this is the full length
now we do same for the shorter part lets call z
tan 27 = [tex]\frac{z}{31}[/tex]
z= 31 tan 27
z= 15.80 this is th bottom part of line
subtract to find x
x = y - z
x = 21.71 - 15.80
x=5.9
Please help 7th grade math
NUMBER 3
Answer:
your writing to read difficult
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.
lim (√1 + 7x-√1-4x)/x
x → 0
To get the limit of the function (lim(√(1 + 7x) - √(1 - 4x))/x as x → 0), let's first try an elementary method. However, in this case, the elementary method does not seem to lead to a simple solution. Therefore, we will use l'Hospital's Rule, which can be applied when the limit is in the form of 0/0 or ∞/∞.
Step:1. First, differentiate the numerator and denominator with respect to x:
Numerator derivative: d(√(1 + 7x))/dx - d(√(1 - 4x))/dx = (7/2)(1 + 7x)^(-1/2) - (-4/2)(1 - 4x)^(-1/2)
Denominator derivative: dx/dx = 1
Step:2. Now, apply l'Hospital's Rule by taking the limit of the derivatives:
lim((7/2)(1 + 7x)^(-1/2) - (-4/2)(1 - 4x)^(-1/2))/1 as x → 0
Step:3. Plug in x = 0:
(7/2)(1)^(-1/2) - (-4/2)(1)^(-1/2) = (7/2) - (-4/2) = 11/2
Therefore, the limit of the function as x → 0 is 11/2.
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the owner of prices limited claims that 75% of all the items in the store are less than $5. suppose that you check a random sample of 146 items in the store and find that 105 have prices less than $5. does this indicate that the percentage of items in the store costing less than $5 is different from 75%? use a 1% level of significance.
From hypothesis testing, the p-value is greater than the level of significance ( 0.01), so there's no sufficient evidence to reject the null hypothesis or support the owner's claim that 75% of all the items in the store are less than $5.
Hypothesis Testing for a Proportion : Hypothesis testing is a statistical way carried out to determine whether the null hypothesis should be rejected or whether it is not to be rejected. We have to owner'claim regarding the limited of prices all the items in the store. For this Set null and alternative hypotheses: [tex]H_o : P = 0.75 [/tex]
[tex]H_a : P ≠ 0.75 [/tex]
Calculate the test statistic value by z test,
[tex]z = \frac{ \hat p - p)}{\sqrt{ \frac{ p( 1 -p)}{n}}}[/tex]
Calculate the sample proportion, [tex]\hat p = \frac{105}{146}[/tex] = 0.72
then, [tex]z = \frac{ 0.72 - 0.75)}{\sqrt{ \frac{ 0.75( 1 -0.75)}{146}}}[/tex]
= - 0.84
Now, using the distribution table, the p-value for z = -0.84 is equals to the 0.401. As we see the p-value is greater than the level of significance, there's no sufficient evidence to reject the null hypothesis. aSo, the 75% of all the items in the store are less than $5.
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help please!!!!!!!!!!!
The measure of the angle m∠T for triangle formed by the tangent line ST is equal to 66°
Tangent to a circle theoremThe tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
The triangle SQU is an isosceles triangle which implies that;
m∠SQU + 2(78°) = 180° {sum of interior angles of an isosceles triangle}
m∠SQU + 156° = 180°
m∠Q = 180° - 156° {collect like terms}
m∠Q = 24°
m∠T + m∠Q + m∠S = 180°
m∠T + 24° + 90° = 180°
m∠T + 114° = 180°
m∠T = 180° - 114°
m∠T = 66°.
Therefore, the measure of the angle m∠T for triangle formed by the tangent line ST is equal to 66°
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Express 9/81 and -9/81 as powers of a rational number.
Step-by-step explanation:
9/81 = 3^2 / 3^4 = 3^ (2-4) = 3 ^-2
- 9/81 = - (3^-2 )
a study is designed to test the effect of light level on exam performance of students. the researcher believes that light levels might have different effects on men and women, so wants to make sure both are equally represented in each treatment. the treatments are fluorescent overhead lighting, yellow overhead lighting, no overhead lighting (only desk lamps). what is the response variable?
The response variable in this study is the exam performance of the students.
The response variable is the main outcome measure of interest in a study. In this case, the researcher is interested in testing the effect of light level on the exam performance of students, which is the response variable. The researcher is also concerned about the potential differences in the effect of light levels between men and women, so wants to ensure that both groups are equally represented in each treatment.
By measuring the exam performance of the students under different lighting conditions, the researcher can determine whether light levels have a significant impact on exam performance and whether this effect differs between men and women.
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For a concert Vishaka spent ₹4,74,560 on musical instruments, ₹8,12,320 on
food, ₹3,28,254 on decoration and ₹ 56,480 on advertisement. Find the total
amount spent by her
The total amount spent by Vishaka on the concert was ₹16,71,614.
To find the total amount spent by Vishaka, we need to add up all of the expenses she incurred. This is known as the "total" of the expenses. We can do this using addition, which is a fundamental mathematical operation.
In this scenario, we have four expenses: ₹4,74,560 for musical instruments, ₹8,12,320 for food, ₹3,28,254 for decoration, and ₹56,480 for advertisement. To find the total amount spent by Vishaka, we can add these expenses together as follows:
Total amount spent = ₹4,74,560 + ₹8,12,320 + ₹3,28,254 + ₹56,480
To make the addition easier, we can align the numbers according to their place values, as follows:
4,74,560
+ 8,12,320
+ 3,28,254
56,480
_____________
16,71,614
-------------------------
By adding these expenses together, we get the total amount spent of ₹16,71,614.
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The table shows the running time for different movies.
Create a line plot to display the data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Answer:
see attached
Step-by-step explanation:
You want a line plot of the given data.
Line plotA line plot of the data can be formed by making a mark above the number line for each point that has that value. For example, there are two instances of the value 1.50, so the plot will have two marks above 1.50 on the number line.
The line plot is shown in the attachment.
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I need help with this assignment
A rectangle has an area of 96 in2.One side is 8in.What is the other side length?
Answer:
11.5
Step-by-step explanation:
96 divided by 8 is 11.5
Answer:
12in
Step-by-step explanation:
If a rectangle has an area of 96 in²
and 1 side is 8in, then this means we have to find the other side length.
The formula for a rectangle area is:
[tex]A=lw[/tex]
We know the area and length so let's substitute:
96=8w
divide both sides by 8
12=w
The other side is 12in, hope this helps!
ALGEBRA 1
15. Consider the equation y=x²-x+3.
Select all ordered pairs that are solutions to the equation.
Pick up to 6 answers.
A (-8.-5)
8. (-4,-3)
C. (-2,4)
D. (2.2)
E. (4,-5)
*plss explain how u got the answer bc I’m so clueless*
A car dealership increased the price of a certain car by13% . The original price was 32600.
Answer:
If the original price of the car was $32600 and the dealership increased the price by 13%, we can start by calculating the amount of the increase:
Increase = 13% of 32600
Increase = 0.13 x 32600
Increase = 4238
So the increase in price is $4238. To find the new price of the car, we need to add this increase to the original price:
New price = Original price + Increase
New price = 32600 + 4238
New price = 36838
Therefore, the new price of the car is $36,838.
1. Find the following products using patterns
a. Starting from (-2)*(-4),find2*(-4)
The product of 2*(-4) by using a pattern is determined as - 8.
What is the product of the numbers?The product of 2*(-4) is calculated by using a pattern where we multiply the initial value by the desired factor and then divide by the original factor.
Starting from (-2)(-4), we can find 2(-4) as follows:
(-2)*(-4) = 8
To get to 2*(-4), we multiply the initial value (8) by 2 and then divide by the original factor (-2);
(8 x 2) / (-2) = -8
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