Answer:
6 1/40
Step-by-step explanation:
21/8 + 17/5
105/40 + 136/40 = 241/40
241/40= 6 1/40
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
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
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∘
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]
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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Area between curves questions
Answer:
16.739
Step-by-step explanation:
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
Question
Jim's music store bought a guitar at the wholesale price of $1,200. Jim marked up the price 50%. Find the list price.
Answer: $1,800
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.
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'.
Rita has coins worth $3.00. If the coins are all dimes, how many dimes does she have?
Answer:
300 dimes I believe because 3.00 is 100 dimes?
Step-by-step explanation:
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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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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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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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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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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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
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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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
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
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%
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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2 Al gives food pellets to the animals on the farm.
• Rabbits: 0.3 kilogram
• Chickens: 1,300 grams
• Ducks: 0.7 kilogram
How many more grams of pellets does Al give
the chickens than he gives the rabbits and
ducks combined?
A 1,000 g
B 2,300 g
C 3,000 g
D 300 g
By answering the presented question, we may conclude that As a result, inequality the correct answer is D) 300 g.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions and shows the relationship between them, usually using the symbols > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).
For example, "3 > 2" is an inequality that states that 3 is greater than 2. Similarly, "x ≤ 5" is an inequality that states that the value of x is less than or equal to 5.
Inequalities are used to represent ranges of possible values and are commonly used in algebra, calculus, and other branches of mathematics. They are often used to describe constraints in optimization problems, such as finding the maximum or minimum of a function subject to certain conditions.
To begin, we must convert the weights to the same units. We can convert rabbit weight to grammes as follows:
300 grammes = 0.3 kilos
We can also convert duck weight to grammes:
700 grammes = 0.7 kilos
We can now multiply the weights of rabbits and ducks:
300 grammes plus 700 grammes equals 1000 grammes
300 grammes plus 1300 grammes plus 700 grammes equals 2300 grammes.
To calculate how many more grammes of pellets Al feeds the chickens than the rabbits and ducks combined, subtract the total weight of pellets fed to the rabbits and ducks from the weight of pellets fed to the chickens:
1300 grammes minus 1000 grammes equals 300 grammes
As a result, the correct answer is D) 300 g.
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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
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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Simplify the following
8⁶÷8
Answer: 8^5
Step-by-step explanation:
To simplify this expression, we can use the rules of exponents which state that when we divide two exponential terms with the same base, we can subtract their exponents. So we have:
8⁶ ÷ 8 = 8^(6-1) = 8^5
Therefore, the simplified expression is 8^5.
Mr. Apo Man borrowed K 2 000 from a bank to finance an extension to his home. He agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. a) What is the amount of each yearly payment? (2 marks)
If he agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. The amount of each yearly payment is K 368.51.
How to find the yearly payment?To calculate the amount of each yearly payment, we can use the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^-n) / r]
where:
PV = present value of the loan
A = annual payment
r = interest rate per year
n = number of years of the annuity
In this case, Mr. Apo Man borrowed K 2 000 from the bank at an interest rate of 14% p.a. compound interest, and agreed to pay back the loan in 8 yearly payments.
So, we have:
r = 14% = 0.14
n = 8
PV = K 2 000
We can solve for A by rearranging the formula:
A = PV * r / [(1 - (1 + r)^-n)]
Substituting the values, we get:
A = K 2 000 * 0.14 / [(1 - (1 + 0.14)^-8)]
A = K 2 000 * 0.14 / 0.7598
A = K 368.51
Therefore, the amount of each yearly payment that Mr. Apo Man needs to make to repay the loan in 8 years at 14% p.a. compound interest is K 368.51.
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The table shows the numbers of feet and the equivalent numbers of inches. Lionel painted a wall that is 12 feet long. How many inches long is the wall that Lionel painted?
A. 144
B. 122
C. 156
D. 132
The wall is 144 inches long that Lionel painted
What are unit cοnversiοns?Unit cοnversiοn is the prοcess οf cοnverting οne unit οf measurement tο anοther unit οf measurement that is equivalent tο the οriginal unit.
Given table:
Number οf feet's Number οs inches
3 36
5 60
8 96
10 120
Tο cοnvert feet tο inches, we need tο multiply the number οf feet by 12 since there are 12 inches in οne fοοt.
Fοr 12 feet, we have:
12 feet = 12 x 12 inches = 144 inches
Hence, the answer is A. 144.
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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