Answer: 0.0294117647
Please help asap, i need it fast
After 13 years, the account will have a balance of $[tex]12,197.97[/tex].
Account balance or bank balance?The final cash amount for just a bank account that appears on the financial statements is known as the bank balance. When a query is made about the bank's records of the cash amount in an account, the bank balance may also be obtained at any time.
Can I utilize the balance on my account?Indeed, as your bank balance balance informs you of the amount of money in your account. That money serves a purpose when you remove or leave in situ, potentially in order to receive interest costs on it.
[tex]A = P (1 + r/n)^{nt}[/tex]
A = final amount
P = initial principal (or investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
Substituting the given values, we have:
[tex]P = 6,759[/tex]
[tex]r = 0.05[/tex]
[tex]n = 2[/tex]
[tex]t = 13[/tex] years
[tex]A = 6,759 (1 + 0.05/2)^{2*13}[/tex]
[tex]A = 6,759 (1.025)^{26}[/tex]
[tex]A = 6,759 (1.80611)[/tex]
[tex]A = 12,197.97[/tex]
Therefore, the account balance after [tex]13[/tex] years will be $[tex]12,197.97[/tex].
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5.9 rounded to the nearest tenth
Step-by-step explanation & Answer
5.9 roundest to the nearest ten is:
5.9 .9 is a tenth which can be rounded
But since you said nearest tenth answer is
= 5.9
Look at picture :)
Thus the answer to your problem is, 5.9
I need help with this please
The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.
What is a line plot?In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:
Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)
Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)
Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8
Total sugar consumed = 22/8 + 1/4
Total sugar consumed = (22 + 2)/8
Total sugar consumed = 24/8
Total sugar consumed = 3 units of sugar.
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10. Patrick is walking around an amusement park looking at the following map. Use the following diagram
and the following information to calculate the desired distances. Sides of grid squares represent 500 feet.
(HINT: The statement in bold will be important when calculating your answers.) Round your answers to the
nearest hundredth.
Bumper Cars
-654-3 -2 -1
Water Slide
JA
1
-1-
23
3
Ferris Wheel
Rollercoaster
1 2 3 4 5 6
Restrooms.
a) How far must she travel from the Bumper Cars to the Ferris Wheel?
b) What is the distance from the Water Slide to the Rollercoaster?
c) How far is it from the Bumper Cars to the Restrooms?
feet
d) If Sasha gets a direct distance from the Water Slide to the Ferris Wheel, how far is it?
a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet or 1.5 miles. b) 1000 feet or 1 mile. c) 2000 feet or 2 miles. d) 2500 feet or 2.5 miles.
What is distance?Distance is the measurement of how far apart two points are on a surface.
a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet. To calculate this, we can count the number of squares (3) from the Bumper Cars to the Ferris Wheel. Each square represents 500 feet, so the total distance is 1500 feet or 1.5 miles.
b) The distance from the Water Slide to the Rollercoaster is 2 squares or 1000 feet.
To calculate this, we can count the number of squares (2) from the Water Slide to the Rollercoaster. Each square represents 500 feet, so the total distance is 1000 feet or 1 mile.
c) The distance from the Bumper Cars to the Restrooms is 4 squares or 2000 feet.
To calculate this, we can count the number of squares (4) from the Bumper Cars to the Restrooms. Each square represents 500 feet, so the total distance is 2000 feet or 2 miles.
d) The direct distance from the Water Slide to the Ferris Wheel is 5 squares or 2500 feet.
To calculate this, we can count the number of squares (5) in a straight line from the Water Slide to the Ferris Wheel. Each square represents 500 feet, so the total distance is 2500 feet or 2.5 miles.
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Multiply and simplify the following complex numbers: ( − 4 + 4 � ) ⋅ ( 3 + 2 � ) (−4+4i)⋅(3+2i)
Answer:
Step-by-step explanation:(−4+4i)⋅(3+2i);
= -4(3+2i)+4i(3+2i);
=-12-8i+12i-8;
= -20+4i
The grocery store is Two Thirds of a mile from John’s office. His house is One and Two Thirds miles from the office in the opposite direction. How many miles is his house from the grocery store
John's home is thus two kilometers away from the supermarket.
What does the distance calculation mean?the algebraic equation known as the distance formula, which provides the distances between two locations as an expression of their coordinates. (see coordinate system). The distance formulas for locations in rectangular coordinates in two- and multidimensional Euclidean spaces are founded on the theorem known as Pythagorean.
To find how many miles John's house is from the grocery store, we need to add the distance from John's house to the office and the distance from the office to the grocery store.
Distance from John's house to the office = 1 and 2/3 miles
Distance from the office to the grocery store = 2/3 miles
Total distance from John's house to the grocery store = (1 and 2/3) + (2/3) = 2 miles
Therefore, John's house is 2 miles from the grocery store.
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22. Morality In a recent poll, the Gallup Organization found
that 45% of adult Americans believe that the overall state of
moral values in the United States is poor. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that
(a) exactly 250 of those surveyed feel the state of morals is poor.
(b) no more than 220 of those surveyed feel the state of morals is poor.
(c) more than 250 of those surveyed feel the state of morals is poor.
(d) between 220 and 250, inclusive, believe the state of morals is poor.
(e) at least 260 adult Americans believe the overall state of
moral values is poor. Would you find this result unusual? Why?
The probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.
(To find the probability that exactly 250 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.
Then, we can standardize the value of 250 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.
z = (250 - 225) / 10.42 ≈ 2.4
Using a standard normal table or calculator, we find that the probability of z being less than or equal to 2.4 is approximately 0.9918.
Therefore, the probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.
(b) To find the probability that no more than 220 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.
Then, we can standardize the value of 220 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.
z = (220 - 225) / 10.42 ≈ -0.48
Using a standard normal table or calculator, we find that the probability of z being less than or equal to -0.48 is approximately 0.3146.
Therefore, the probability that no more than 220 of those surveyed feel the state of morals is poor is approximately 0.3146.
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find the length of ab
Answer:
[tex]AB \approx 5.6 \text{ cm}[/tex]
Step-by-step explanation:
We can find the length of side AB using the trigonometric ratio cosine.
[tex]\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}[/tex]
↓ plugging in the given values
[tex]\cos(62\°) = \dfrac{AB}{12}[/tex]
↓ multiplying both sides by 12
[tex]12 \cdot \cos(62\°) = AB[/tex]
↓ plugging into a calculator
[tex]\boxed{AB \approx 5.6 \text{ cm}}[/tex]
. QUESTION 8: You are 765 feet above in the air. You are descending at a rate of 12 feet per minute. Write an equation in slope intercept form to represent this situation. b: Equation:
Step-by-step explanation:
You need the line in y = mx + b form:
y = -12x + 765 where x = minutes y = height in feet
A 500g packet of beans costs £1.55
A 125g packet of the same beans costs £0.36
Which packet is better value for money?
The packet is better value for money is a 125 g packet of beans which costs £0.36.
The better value for money of packet of beans can be calculated as follows?The first step we can check on the first packet value for money by calculating the costs of 1 g of beans as follows :
[tex](1/500) \times \£1.55 = \£0,003[/tex]
The second step we can check on the second packet value for money by calculating the costs of 1 g of beans as follows :
[tex](1/125) \times \£0.36 = \£0,0028.[/tex]
Hence, the better value for money between those two packet of beans is the second packet of beans which given by 125 g and costs £0.36.
Answer:
125g
Step-by-step explanation:
Find 1g of beans for both packets
500g /500 = 1
£1.55 / 500 = £0.0031 per gram
125 / 125 = 1
£0.36 / 125 = £0.00288 per gram
0.00288 < 0.0031
125g packet is better value for money
Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 4, centered at the origin where the endpoints are A(−2,−3) and B (−4,−5).(1 point)
Answer: A'(-8,-12); B'(-16,-20)
Step-by-step explanation:
Since the line is scaled about the origin, simply multiplying the points (x,y) by 4 will give you A' and B'.
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary. (Please show step by step on how to figure this out! I want to understand!)
The length segment of the circle indicated is 6 units.
How to find the radius of a circle?A circle is a round-shaped figure that has no corners or edges. Therefore, let's find the length segment of the circle.
Therefore, the diameter of a circle is the line that passes through the centre and meets the circumference at opposite ends.
Therefore, the radius of a circle is the distance from the centre of the circle to any point on it's circumference.
The radius is half of a diameter.
Therefore, the length x is the radius of the circle and it is 6 units.
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Area between curves questions
Answer:
16.739
Step-by-step explanation:
Write the prime factorization of 25 use exponents when appreciate, and order the factors from least to greatest
Answer:5^2
Step-by-step explanation:
25
/ \
5 5
Since both 5 and 5 are prime, it can't be simplified more so the answer is 5^2.
FIND THE SIZE OF XYZ
The angle of XYZ is approximately 87.6 degrees.
To find the angle of XYZ, you need to use the Law of Cosines, which states that c² = a² + b² - 2ab cos(C), where c is the side opposite the angle C. Given the side lengths of the triangle XYZ, you can find the measure of angle XYZ as follows:
First, use the Pythagorean Theorem to find the length of side XY: XY² = 5² + 12² = 169, so XY = √169 = 13.
Next, use the Law of Cosines to find the measure of angle YXZ: 13² = 7² + 8² - 2(7)(8)cos(YXZ), which simplifies to 169 = 113 - 112cos(YXZ). Solving for cos(YXZ), you get cos(YXZ) = (113 - 169) / (278) = -0.125.
Finally, take the inverse cosine (cos⁻¹) of -0.125 to find the measure of angle YXZ in degrees: YXZ ≈ 102.4°.
Therefore, the measure of angle XYZ is 180° - 90° - 102.4° = 87.6°.
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There were 15 kids at the park. When it began to rain, k of them went home. Write an expression that shows the number of kids left at the park.
The calcualted expression for the number of kids left at the park would be 15 - k
Calculating the expression of the kids that leftGiven that
Number of kids = 15
Kids that wet home = k
If there were originally 15 kids at the park and k of them went home due to rain, then the expression for the number of kids left at the park would be:
15 - k
This is because the total number of kids at the park (15) is reduced by the number of kids who left due to the rain (k).
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4.) Ayana wants to be a marine biologist when she grows up. Her entire room is
ocean-themed, so she is painting her bed frame blue to match. She estimates
that she will need 800 milliliters of paint, but the hardware store only sells
paint in liters. If Ayana buys 1 liter of paint, how many milliliters will she have
left?
Answer:
200ml
Step-by-step explanation:
1000ml =1l
1000-800=200
The circle below is centred at O.
AB is a tangent to this circle.
Work out the size of angle X.
Justify your answer.
52°
Step-by-step explanation:
It's 180-(90+38)= 52°
Answer:
52∘
Step-by-step explanation:
Since AB is tangent to the circle and OA is a radius, that means, ∠OAB = 90∘
A triangle has 180∘, so:
180∘ - 90∘ - 38∘ = 52∘
a trapezoid is shown with bases AD and BC. if slopCe of AD is 1/2, what is the slope of BC
The slope of BC is 1/2, since the slope of AD is 1/2. This is because the rise and run of the two bases are the same.
What is slope?The slope of a line is defined as the ratio of the vertical change (the rise) to the horizontal change (the run).
In the case of an isosceles trapezoid, the two bases (AD and BC) are parallel and of equal length. Therefore, the slope of the two bases is the same.
Given that the slope of AD is 1/2, the slope of BC is also 1/2.
This is because the rise and run of the two bases are the same. Therefore, the ratio of rise to run is the same and the slope of both bases is 1/2.
To understand this better, let us consider the rise and run of the two bases:
AD: Rise = y² − y1, Run = x² − x1
BC: Rise = y² − y1, Run = x² − x1
Therefore,
Slope of AD = (y² − y1)/(x² − x1)
Slope of BC = (y² − y1)/(x² − x1)
Since the rise and run of the two bases are the same, the slope of the two bases is also the same.
Therefore, the slope of BC is 1/2, since the slope of AD is 1/2.
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P=$4655, R= 13.83% per year, T=42 months
Answer:
6,908.25$
Step-by-step explanation:
First, convert R to a decimal.
So R=0.1383
Next, 42 months = 3.5 years
A=4655(1+(0.1383 * 3.5)) = 6,908.25275
Integers a and b are such that
[tex](a + 3 \sqrt{5} ) {}^{2} + a - b \sqrt{5} = 51 [/tex]
Find the possible values of a and the corresponding values of b.
(Answers are a= -3 , 2 and b= -18 , 12. But I don't know how to show the working so please help, thx)
The possible values of a and the corresponding values of b are; a= -3, 2 and b= -18, 12.
How to calculate possible and the corresponding values?Expanding the left-hand side of the equation:
(a + 3√5)² + a - b√5 = a² + 6a√5 + 45 + a - b√5
Combining like terms:
2a² + (2a - b)√5 + 45 = 51
Simplifying further:
2a² + (2a - b)√5 = 6
Now, since √5 is irrational, the only way the left-hand side can equal 6 is if both the rational and irrational parts are equal to 0. Therefore two equations:
2a² + 2a - b = 0 (Equation 1)
2a - b = 0 (Equation 2)
Solving Equation 2 for b:
b = 2a
Substituting this into Equation 1:
2a² + 2a - 2a = 0
Simplifying:
2a² = 0
Thus, a = 0 is a solution. However, a = 0 does not satisfy the original equation, since the left-hand side would be 45, which is not equal to 51. Therefore, we can divide both sides of Equation 1 by 2a to get:
a + 1 - b/2a = 0
Multiplying both sides by 2a:
2a² + 2a - b = 0
Substituting b = 2a:
2a² + 2a - 2a = 0
Simplifying:
2a² = 0
Thus, a = 0 is a solution. However, as noted above, a = 0 does not satisfy the original equation. Therefore, we must consider the case where a ≠ 0. Dividing both sides of Equation 2 by 2:
a - b/2 = 0
Solving for b:
b = 2a
Substituting into the original equation:
(a + 3√5)² + a - 2a√5 = 51
Expanding:
a² + 6a√5 + 45 + a - 2a√5 = 51
Combining like terms:
a² + 7a√5 - 6 = 0
Using the quadratic formula:
a = (-7√5 ± √(7²√5² - 4(1)(-6))) / 2(1)
Simplifying:
a = (-7√5 ± 13) / 2
Therefore, the possible values of a are -3 and 2. For each value of a, we can use b = 2a to find the corresponding value of b. Thus, the possible values of b are -18 and 12.
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Four part spinner is spun twice total number of possible outcomes. What is the probability of spinning pink on both spins? What is the probability of not spinning orange either spin?
Probability of spinning pink on both spins = 1/4 and Probability of not spinning orange on either spin = 9/16.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
If a four-part spinner is spun twice, there are 16 possible outcomes (4 options on the first spin, multiplied by 4 options on the second spin).
To find the probability of spinning pink on both spins, we need to first determine how many outcomes result in pink on both spins. If we label the four parts of the spinner A, B, C, and D, and assume that pink is on part A, then there are four possible outcomes where pink appears on both spins: AA, AB, AC, and AD. Each of these outcomes has a probability of 1/16, since there are 16 total possible outcomes. So the probability of spinning pink on both spins is:
Probability of spinning pink on both spins = (number of outcomes where pink appears on both spins) / (total number of possible outcomes)
Probability of spinning pink on both spins = 4/16
Probability of spinning pink on both spins = 1/4
To find the probability of not spinning orange either spin, we need to determine how many outcomes do not have orange. If we assume that orange is on part B, then there are three outcomes on the first spin that do not result in orange: AB, AC, and AD. On the second spin, there are again three outcomes that do not result in orange: BA, CA, and DA. So there are a total of 3 x 3 = 9 outcomes where orange does not appear on either spin.
Again, each of these outcomes has a probability of 1/16, so the probability of not spinning orange on either spin is:
Probability of not spinning orange on either spin = (number of outcomes where orange does not appear on either spin) / (total number of possible outcomes)
Probability of not spinning orange on either spin = 9/16
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Find the area of the parallelogram.
Answer: 33.34
Step-by-step explanation: first we have to cut this shape up like you would a pizza
2 triangles and 1 rectangle, we know that the rectangle is 10 by 3 cm, but we don't have all the measurements for the triangle.
Find the last side using this equation:
3.2 squared = 10.24
3 squared = 9
subtract
1.24
square root of 1.24 = 1.11
Area of rectangle:
10 x 3 = 30
Area of triangle:
1.11 x 3 ≈ 1.67
Final Area:
30 + 1.67x2 = 33.34
Calculate the arithmetic mean of these numbers. -12 and 7
Answer:
The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
Step-by-step explanation:
Therefore, the arithmetic mean of -12 and 7 is -2.5
What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
a cylinder with a radius labeled 2.6 meters and height labeled 6.1 meters
82 square meters
91 square meters
96 square meters
142 square meters
Answer:
142 square meters
Step-by-step explanation:
To find the Surface Area of a Cylinder you have to use the formula [tex]A= 2\pi rh+2\pi r^2[/tex]
Plug in the radius, height, and pi to get
[tex]A=(2*3.14*2.6*6.1)+(2*3.14*2.6^2)\\A= (99.6008)+(42.4528)\\A= 142.0536\\[/tex]
You can round the answer to 142
click (with your mouse) on the image that best represents a 0.02 correlation
Answer:
Step-by-step explanation:
it would be the third one
Camila saved 4/5% of her allowance. What is this percent expressed as a fraction and as a decimal
4/5% would easily be represented as 80%. In decimal form, this could be represented as 0.80 or 0.8 if you needed to simplify.
Answer:
Decimal: 0.8
Fraction:4/5
Percent: 80%
Hi i need help on this question please real answers!
Answer:
0.75
Step-by-step explanation:
0.75
or 3/4
Answer: 3/4
3/8x2= 3/4
8-21. Inspect each data set below and the statement made about it. Each statement is false. Without making any calculations, determine how you can explain or justify that the statement is false. a. "The set of 24, 25, 26, and 28 has a mean of 30." b. "15 is the median of this data set: 12, 14, 15, 13, and 16."
The first statement about mean is false.
The second statement about median is false.
What is mean and median?
The "mean" is the "average" of any data set. Sum of all the data and dividing that by the number of data will give the mean.
The "median" is the "middle" value in the given list of data.
At the first statement the values are 24,25,26,28.
Now the smallest value is 24 and the greatest value is 28. so the average or mean must be in between 24 and 28. It cant exceeds the value 28.
Here given that mean is 30 which is obviously greater than 28. So it cant be the mean of the given data set.
At the second statement the data are 12,14,15,13,16.
The listed values are not in ascending order Without making the values in ascending order we cant find the median. Now if we arrange the values in ascending order the list will be 12,13,14,15,16.
As there are 5 terms so there are odd number of terms. For that the median must be the middle value which is 14.
But here median is 15.
So it cant be the median of the data.
Hence both the statements are false.
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Helppp please
A population of bacteria is growing according to the equation p(t)=1000e^0.21t
Use a graphing calculator to estimate when the population will exceed 2627.
t =------------
The population will exceed 2627 when t is greater than approximately 6.05.
What is inequality?Inequality is a mathematical cοncept that expresses a relatiοnship between twο values οr expressiοns, indicating that οne is greater than, less than, οr nοt equal tο the οther. An inequality is usually represented using symbοls such as < (less than), > (greater than), ≤ (less than οr equal tο), ≥ (greater than οr equal tο), and ≠ (nοt equal tο).
To solve for the value of t when the population exceeds 2627, we can set up the inequality:
p(t) > 2627
Substituting the given equation for p(t), we get:
1000[tex]e^{0.21t}[/tex] > > 2627
Dividing both sides by 1000, we get:
[tex]e^{0.21t}[/tex] > 2.627
Taking the natural logarithm of both sides, we get:
0.21t > ln(2.627)
Solving for t, we get:
t > ln(2.627)/0.21 ≈ 6.05
Therefore, the population will exceed 2627 when t is greater than approximately 6.05.
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