Answers
Answer:
x = 7.9 (nearest tenth)
y = 24.6° (nearest tenth)
Step-by-step explanation:
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:
[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 7.9.
[tex]\hrulefill[/tex]
The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 24.6°.
Related Questions
The Ferris Wheel can carry 4 passengers in each of its 15 cars in one ride. How many passengers can it carry on a total of 35 rides?
Answers
The Ferris Wheel can carry 2100 passengers on a total of 35 rides.
According to the question,
Number of cars in the Ferry Wheel = 15
Number of passengers in each car = 4
∴ Number of passengers in 15 cars = 15×4 = 60
So, the number of passengers on the Ferry Wheel = 60
Now,
The number of passengers the Ferry Wheel carries in one ride = 60
∴ The number of passengers in 35 rides = 60×35 = 2100.
Hence the Ferris Wheel can carry 2100 passengers on a total of 35 rides.
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Jordan's monthly bank statement showed the following deposits and withdrawals:
$7.72,
−
−$84.26, $70.42,
−
−$50.15, $107.46
If Jordan's balance in the account was $92.66 at the beginning of the month, what was the account balance at the end of the month?
Answers
Jordan's account balance at the end of the month would be $143.85.
What is the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To determine Jordan's account balance at the end of the month, we need to add up the deposits and withdrawals to the initial balance.
Initial balance: $92.66
Deposits: $7.72 + $70.42 + $107.46 = $185.60 (sum of positive amounts)
Withdrawals: -$84.26 + (-$50.15) = -$134.41 (sum of negative amounts)
To calculate the account balance at the end of the month, we can add the deposits and withdrawals to the initial balance:
Account balance at the end of the month = Initial balance + Deposits - Withdrawals
= $92.66 + $185.60 - $134.41
= $143.85
Hence, Jordan's account balance at the end of the month would be $143.85.
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Please help!!!!!!!!!!!
Solve for X
Find the measure of each angle using the solution to part C
Answers
Suppose that the functions f and g are defined as follows.
Find f.g and f+ g. Then, give their domains using interval notation.
Answers
Using interval notation, the domain of f.g and f+g is [1/4, ∞).
Given, f(x)= 1/ (5x² + 3) and [tex]g(x) = \sqrt{4x-1}[/tex]
To find f.g, we substitute g(x) into f(x) and simplify:
f.g(x) = f(g(x))
[tex]=f(\sqrt{4x-1})[/tex]
[tex]=\frac{1}{5(\sqrt{4x-1})^2 +3}[/tex]
= 1/(5(4x-1)+3)
= 1 / (20x - 2)
To find f+g, we add the functions f(x) and g(x):
f+g(x) = f(x) + g(x)
= [tex]\frac{1}{5x^2+3}+\sqrt{4x-1}[/tex]
The domain of f.g and f+g is the intersection of the domains of f(x) and g(x).
The domain of f(x) is all real numbers except for the values of x that make the denominator zero, i.e., 5x² + 3 = 0. This equation has no real solutions, so the domain of f(x) is all real numbers.
The domain of g(x) is the set of all real numbers that make the argument of the square root non-negative, i.e., 4x - 1 ≥ 0. Solving this inequality, we get x ≥ 1/4.
Therefore, the domain of f.g and f+g is x ≥ 1/4.
Using interval notation, the domain of f.g and f+g is [1/4, ∞).
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Help please
The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 1000 years? -----------
Answers
after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
what is approximately ?
Approximately means "about" or "roughly" and is used to indicate an estimated or approximate value or quantity, rather than an exact or precise one. For example, if someone says "the population of the city is approximately 1 million people," it means that the population is around 1 million,
In the given question,
The half-life of Radium-226 is 1590 years, which means that in 1590 years, half of the original sample will have decayed. After another 1590 years (or a total of 2 half-lives), half of the remaining sample will have decayed, leaving 25% of the original sample.
To find how much of the original sample remains after 1000 years, we need to first determine how many half-lives have passed.
Number of half-lives = elapsed time ÷ half-life = 1000 years ÷ 1590 years/half-life = 0.63
So, approximately 0.63 half-lives have passed. Therefore, the fraction of the original sample remaining is:
fraction remaining = (1/2)⁰°⁶³ ≈ 0.518
To find the remaining mass, we can multiply the fraction remaining by the initial mass:
remaining mass = fraction remaining x initial mass
remaining mass = 0.518 x 500 mg ≈ 259 mg
Therefore, after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.
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Plsss help meeee quick
Answers
Answer:
B
Step-by-step explanation:
Lateral surface contains B,C and D (because A and E are bases)
A (lateral surface area) = 70 + 70 + 56 = 196 cm^2
HELP ME PLEASE!
Whoever answers right gets brainliest!
Answers
Therefore, the range of the relation shown is (1, 3, 4, 6, 7). Option C is the correct answer.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are used to model relationships between variables in many areas of mathematics and other fields such as physics, engineering, economics, and computer science. They are used to describe various phenomena, such as the growth of populations, the trajectory of a projectile, or the behavior of financial markets. Functions are also important tools in calculus, where they are used to study rates of change and continuity, among other things.
Here,
The range of a relation refers to the set of all possible output values or y-values of the relation. Looking at the image reference, we can see that the y-values or the outputs are 1, 3, 4, 6, and 7.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
Answers
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
How to solveHeight (in centimeters) Frequency
0 - 3 | 5
4 - 6 | 10
7 - 9 | 15
10 - 12 | 7
13 - 15 | 3
To find the average height, we can follow these steps:
Determine the midpoint of each height range.
Multiply the midpoint of each range by the frequency.
Add up the products from step 2.
Add up the frequencies.
Divide the sum from step 3 by the sum from step 4.
Step 1: Determine the midpoint of each height range.
Height Range Midpoint
0 - 3 | 1.5
4 - 6 | 5
7 - 9 | 8
10 - 12 | 11
13 - 15 | 14
Step 2: Multiply the midpoint of each range by the frequency.
Height Range Frequency Midpoint Midpoint x Frequency
0 - 3 | 5 | 1.5 | 7.5
4 - 6 | 10 | 5 | 50
7 - 9 | 15 | 8 | 120
10 - 12 | 7 | 11 | 77
13 - 15 | 3 | 14 | 42
Step 3: Add up the products from step 2.
7.5 + 50 + 120 + 77 + 42 = 296.5
Step 4: Add up the frequencies.
5 + 10 + 15 + 7 + 3 = 40
Step 5: Divide the sum from step 3 by the sum from step 4.
296.5 / 40 = 7.4125
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
What is the average height of the bean plants in Mr. Anderson's class after 7 days?
Leslie invests in a bank account that earns interest compounded quarterly. The expression 500(1.026)4t can be used to find the account balance in t years.
Part A
What was Leslie’s initial investment?
$
Part B
What is the quarterly interest rate the account earns?
Answers
Leslie's initial investment was $500 and the quarterly interest rate the account earns is 10.4%.
To find the initial investment and quarterly interest rate we can use the following compound formula of
A = P [tex](1 + \frac{r}{n} )^{nt}[/tex]
Given expression =[tex]500(1.026)^{4t}[/tex]
principal P = $500
rate of interest r = 1.026
A) Leslie's initial investement A = [tex]500 (1.026) ^{0}[/tex] = 500 [ initially time t = 0]
B) for finding quarterly interest,
given expression =[tex]500(1.026)^{4t}[/tex]
=[tex]500(1 + 0.026)^{4t}[/tex]
= [tex]500(1 + 0.026 * 4/4)^{4t}[/tex]
= [tex]500(1 + \frac{0.104}{4} )^{4t}[/tex]
From the above expression, we can conclude that the quarterly interest is 0.104 which is 10.4%
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Hi can someone please help me out and explain the question in the picture? Thanks I appreciate it. I’ll give brainly :)
Answers
Answer:
$52.50
Step-by-step explanation:
1500 * 3.5% = 52.50
Answer:
$52.5 for the first year
Step-by-step explanation:
You can derive a decimal from a percentage by dividing by 100.
For example, 1% is 0.01
3.5% is 0.035
You can also move the decimal point back 2 places, but that's cringy.
So the problem says how much interest she will have to pay after one year, when the interest rate is 3.5%.
Therfore, we must multiply:
1500 by 3.5%
We stated that 3.5% is 0.035, so we can replace that
1500 * 0.035
Plug that into a caluclator and we get.....
$52.5 for the first year
ANSWER CHOICE 1
Phew! That was a long problem! May I please have Brainliest?
Triangle GFH has vertices G(2, –3), F(4, –1), and H(1, 1). The triangle is rotated 270° clockwise using the origin as the center of rotation. Which graph shows the rotated image?
On a coordinate plane, triangle G prime H prime F prime has points (negative 3, negative 2), (1, negative 1), (negative 1, negative 4).
On a coordinate plane, triangle G prime H prime F prime has points (3, 2), (negative 1, 1), (1, 4).
On a coordinate plane, triangle G prime H prime F prime has points (2, negative 3), (1, 1), (4, negative 1).
On a coordinate plane, triangle G prime H prime F prime has points (2, 3), (4, 1), (1, negative 1).
Answers
Check the picture below.
Answer:
b
Step-by-step explanation:
edge 2023
An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–5, 8), (3, 8), (–5, –4), and (3, –4). What is the area, in square inches, of the label needed to cover the face of the box?
96 in2
48 in2
40 in2
20 in2
Answers
The area, in square inches, of the label needed to cover the face of the box is 96 in².
Option A is correct.
How do we calculate?We must first determine the length and breadth of the rectangle before multiplying them together to determine the area of the rectangular face.
The distance between the x-coordinates of two opposite points determines the length of the rectangle:
length equals 3 - (-5) = 8.
The distance between the y-coordinates of the same two opposite points determines the rectangle's width:
width = 8 + (-4) = 12
In conclusion, the rectangle's size is: 8 × 12 = 96 square inches is the area formula.
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A radioactive isotope has a half-life of 1,920 years. Let f(t)
be the amount of isotope, in milligrams, that is present after t years. If the sample originally contained 21 milligrams, write an equation modeling this situation.
F(t)=
Answers
The equation that models the given situation is: f(t) = 21e^(-0.000361)t
How to solve an exponential decay function?We can model this situation with an exponential decay function.
f(t) = Pe^(rt)
Where:
f(t) = amount of isotope
P = starting amount
r = growth rate
t = time
Let's assume that there is 1 mg of our isotope. Thus,in 1920 years, we will have 1/2 mg. Thus:
(1/2) = (1)e^(1920r)
Take the natural log of both sides to bring the exponent down and to cancel out the e
ln(1/2) = ln(e^(r(1920))
ln(1/2) = r(1920)
ln(1/2)/1920 = r
r = -0000361
Thus, we have:
f(t) = Pe^(-0.000361)t
Plug in 21 for P to get:
f(t) = 21e^(-0.000361)t
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Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
Answers
we should expect 4 white horses among the next 20 horses that come to board. we can solve by equation .
what is equation ?
An equation is a mathematical statement that uses symbols and variables to show that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables, constants, and mathematical operations such as addition
In the given question,
Out of the 15 horses currently boarded, 3 are white. This means that the proportion of white horses among the currently boarded horses is:
3 / 15 = 0.2 or 20%
Therefore, if we assume that the next 20 horses that come to board will have a similar distribution of coat colors, we can expect approximately 20% of them to be white.
So, the expected number of white horses among the next 20 horses that come to board is:
20 x 0.2 = 4
Therefore, we should expect 4 white horses among the next 20 horses that come to board.
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Jamar is going to invest $2200 and leave it in an account for 14 years. Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200
Answers
Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.
How is the interest rate for continuous compounding determined?Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:
Total P+I (A) = $4,200.00
Principal (P) = $2,200.00
Compound (n) = Compounding Continuously
Time (t in years) = 14 years
R = 4.619% per year
The calculation steps are as follows:
Solving for rate r as a decimal
r = ln(A/P) / t
r = ln(4,200.00/2,200.00) / 14
r = 0.0461877
Then convert r to R as a percentage:
R = r * 100
R = 0.0461877 * 100
R = 4.62%/year
Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.
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A certain drug is used to treat asthma. In a clinical trial of the drug, 30 of 298 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 9% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below.
1-PropZTest
prop<0.09
z=0.643690407
p=0.7401118941
p=0.1006711409
n=298
Question content area bottom
Part 1
a. Is the test two-tailed, left-tailed, or right-tailed?
Right tailed test
Two-tailed test
Left-tailed test
Part 2
b. What is the test statistic?
z=enter your response here
(Round to two decimal places as needed.)
Part 3
c. What is the P-value?
P-value=enter your response here
(Round to four decimal places as needed.)
Part 4
d. What is the null hypothesis, and what do you conclude about it?
Identify the null hypothesis.
A.Upper H 0 : p greater than 0.09
H0: p>0.09
B.Upper H 0 : p less than 0.09
H0: p<0.09
C.Upper H 0 : p not equals 0.09
H0: p≠0.09
D.Upper H 0 : p equals 0.09
H0: p=0.09
Part 5
Decide whether to reject the null hypothesis. Choose the correct answer below.
A.
Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
B.
Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α.
C.
Reject the null hypothesis because the P-value is less than or equal to the significance level, α.
D.
Reject the null hypothesis because the P-value is greater than the significance level, α.
Part 6
e. What is the final conclusion?
A.
There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
B.
There is sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.
C.
There is sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
D.
There is not sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.
Answers
For the drug used to treat asthma in a clinical trial:
a) A, right-tailedb) 0.64c) 0.7401d) A, p > 0.09A, Fail to reject the null hypothesise) DHow to determine hypothesis?Part 1:
The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.
Part 2:
The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).
Part 3:
The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).
Part 4:
The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
Part 5:
We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.
Part 6:
The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
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Find the volume of the cylinder. Use π = 3.14.
(If answered correctly with an explanation giving brainlyest)
A. 321.54 ft3
B. 10,048 ft3
C. 8,038.4 ft3
D. 100.48 ft3
Answers
The volume of a cylinder whose diameter measures 32 feet and has a height of 10 feet is equal to: C. 8,038.4 ft³.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Note: Radius = diameter/2 = 32/2 = 16 ft.
By substituting the parameters, we have:
Volume of cylinder, V = 3.14 × 16² × 10
Volume of cylinder, V = 8,038.4 cubic feet.
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crack the code
09, 15. 18. 20, 22, 25, 03
Answers
The next number in the sequence would be 25 + 4 = 29.
How to break the sequence?
First off, we rearrange these numbers in ascending order and this gives us:
3 9 15 18 20 22 25
Next, we try and find the pattern:
The pattern seems to be adding consecutive odd numbers starting from 3.
3 + 6 = 9
9 + 6 = 15
15 + 3 = 18
18 + 2 = 20
20 + 2 = 22
22 + 3 = 25
Therefore, the next number in the sequence would be 25 + 4 = 29.
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crack the code
09, 15. 18. 20, 22, 25, 03
Find the next number
Help me please How would you informally prove that you are taking courses online?
A) You could show a registrar’s receipt with the current date.
B) You could show your course notes with the current date.
C) You could repeat all the material you learned.
D) You could ask for an enrollment verification notice from the school.
Answers
Answer: b is correct
Step-by-step explanation:
diegos family spend 130$ total on a night ouy. they purchases 5 tickets to the fair and a family dinner for 55$ how much did each ticket to the fair cost
Answers
If Diego's family spent a total of $130, on a night out, then the each ticket for the fair cost's $15.
In order to find the "total-cost" of the tickets, we subtract the cost of the family dinner from the total amount spent;
⇒ Total cost of tickets = Total amount spent - Cost of family dinner,
⇒ Total cost of tickets = $130 - $55,
⇒ Total cost of tickets = $75.
Next, we divide the total cost of the tickets by the number of tickets purchased to find the cost of each ticket:
So, Cost per ticket = (Total cost of tickets)/(Number of tickets),
⇒ Cost per ticket = $75/5,
⇒ Cost per ticket = $15,
Therefore, each ticket to the fair cost $15.
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Answer questions 3 – 5 about the circle.
Answers
Answer:
3. radius = 9.4
4. radius = 22.6
5. diameter = 13.3
Step-by-step explanation:
The diameter of a circle = 2 * radius
For problem 3 and 4, you need to multiply the given radius by 2 to get the diameter.
For problem 5, you need to divide the diameter by 2 to get the radius.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The solution of the inequality, log₂ 2m > log₂ (m + 5) is {m | m > 5 / 2}.
How to solve logarithm inequality?An inequality is an expression that have <, >, ≤ and ≥ . Therefore, let's solve the logarithmic inequality for the variable m.
Hence,
log₂ 2m > log₂ (m + 5)
Therefore, let's divide both sides by log₂.
Hence,
2m > m + 5
subtract m from both sides of the inequality
2m > m + 5
2m - m > m - m + 5
2m > 5
divide both sides by 2
2m / 2 > 5 / 2
Therefore,
m > 5 / 2
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In 2011 Staci invested $14,500 in a savings account for her newborn son. The account pays 3.5% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.
Answers
The accrued value of Staci's investment in the account in the year 2029 is $26933.59
Calculating the accrued value of the accountThe statements in the question can be sumarrized as
Invested amount = $14,500Rate of interest = 3.5% compounded annually.The formula to calculate amount on investment is
Amount = P * (1 + r)ⁿ
Where
P = Principal = 14,500r = Rate = 3.5%n = time = 2029 - 2011 = 18When the values are substituted in the amount equation, we have
Amount = 14500 * (1 + 3.5%)¹⁸
Evaluate
Amount = 26933.59
Hence, the amount after the investment is $26933.59
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1.) The average student takes 5 classes a semester. The table represents the probability distribution of the number of classes an average student passes in a given semester.
x P(X=x)
0 0.001
1 0.098
2
3 0.175
4 0.419
5 0.195
a. Find the missing probability
b. Find the expected number of classes passed.
c. Is it unusual for an average student to pass at most 2 class in a given semester?
Answers
a. The missing probability is 0.112
b. The expected number of classes passed is 3.38.
c. Is it unusual for an average student to pass at most 2 classes in a given semester is 0.211
a. Since the whole of all probabilities must rise to 1, we are able to discover the lost likelihood by subtracting the whole of the given probabilities from 1:
1 - 0.001 - 0.098 - 0.175 - 0.419 - 0.195 = 0.112
Subsequently, P(X=2) = 0.112.
b. The anticipated number of classes passed can be found by increasing each possible value of X by its particular likelihood, and after that summing the items:
E(X) = 0(0.001) + 1(0.098) + 2(0.112) + 3(0.175) + 4(0.419) + 5(0.195)
= 3.38
Hence, the anticipated number of classes passed is 3.38.
c. To decide in case it is bizarre for an average student to pass at most 2 classes in a given semester, we have to calculate the likelihood of passing at most 2 classes:
P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)
= 0.001 + 0.098 + 0.112
= 0.211
Since this likelihood is more noteworthy than 0.05 (i.e., the commonly utilized threshold for determining whether an occasion is unordinary), it isn't abnormal for a normal understudy to pass at most 2 classes in a given semester.
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Find cordinates of point of inter section
7x+4y=23
8x-10y=19
Answers
Answer:
To find the coordinates of the point of intersection between the two lines, we can solve the system of equations by elimination or substitution. Here, we will use the elimination method.
First, we will multiply the first equation by 10 and the second equation by 4, in order to eliminate the y term:
- 70x + 40y = 230
- 32x - 40y = 76
Adding these two equations, we get:
- 102x = 306
Dividing both sides by 102, we get:
- x = 3
Now we can substitute this value of x into either equation to find the value of y. Using the first equation:
- 7(3) + 4y = 23
- 21 + 4y = 23
- 4y = 2
- y = 1/2
Therefore, the point of intersection is (3, 1/2).
Answer:
Step-by-step explanation:
How much would you need to deposit in an account now in order to have $2000 in the account in 15years? Assume the account earns 7% interest compounded monthly.
Answers
Answer:
To calculate the amount you would need to deposit in the account now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount you will have after 15 years, P is the principal amount (the amount you need to deposit now), r is the annual interest rate (7%), n is the number of times the interest is compounded per year (12 for monthly compounding), and t is the time in years (15).
Plugging in the values, we get:
2000 = P(1 + 0.07/12)^(12*15)
Simplifying the right side, we get:
2000 = P(1.00583)^180
Dividing both sides by (1.00583)^180, we get:
P = 2000 / (1.00583)^180
P = $775.80 (rounded to the nearest cent)
Therefore, to have $2000 in the account in 15 years with an annual interest rate of 7% compounded monthly, you would need to deposit $775.80 now.
Which explanation correctly analyzes the difference between an irrational number and a rational number?
Answers
The statement that analyzes difference between an irrational number and a rational number is: the expression √25 - √21 can be rewritten as 5 - √21. since the exact value of √21 cannot be found, the difference is irrational, The Option D is correct.
What is difference between irrational number & rational number?A rational number refers to number that can be expressed as the ratio of two integers where the denominator is not zero. For example 1/2, 3/4, and -5/7 all rational numbers.
Irrational number refers to one that cannot be expressed as a ratio of two integers. Examples include pi (π) and the square root of 2 (√2).
The difference is that one is expressed as a ratio of two integers or a decimal that either terminates or repeats other cannot be expressed as a ratio of two integers and have a decimal representation that does not terminate or repeat.
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a rectangle has a length of 5.25cm and area of 44.625cm2. what does the length of the rectangle have to be?
Answers
Answer:5.25cm
Step-by-step explanation:
1)look back at your question
2)look after the 6th word
Find the value of linear correlation coefficient r (statistics)
Answers
Answer:
r=1
Step-by-step explanation:
The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and weight are correlated (they will be - the taller people are, the heavier they're likely to be).
James takes a 150000 mortgage for 20 years and makes a monthly payment of 915.00. What percent of the total loan does he pay back in interest?
Answers
James pays back approximately 82.33% of the total loan in interest over the 20-year period.
To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.
Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately 0.35% (4.25% annual rate divided by 12 months). The monthly payment of $915.00 is comprised of both principal and interest.
In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.
To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months (20 years x 12 months/year = 240 months) and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.
To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:
$123,500 ÷ $150,000 x 100 ≈ 82.33%
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