The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the sides of a right triangle.
The Pythagoras Theorem states that : in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of squares of lengths of other two sides.
Mathematically, the Pythagoras Theorem is written as:
⇒ c² = a² + b² ;
where c is = length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.
The Converse of Pythagoras Theorem states that : If in a triangle, the square of the length of the longest side is equal to the sum of squares of lengths of other two sides, then triangle is a right triangle.
Both the Pythagorean Theorem and its converse apply only to right triangles, which are triangles that have a right angle .
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How does the quantity of shares you own impact your dollar gains and losses?
how does the length of time you hold the shares impact your rate of return?
How does the quantity of shares you own impact your rate of return?
The quantity of shares you own can impact your dollar gains and losses, but not your rate of return. The length of time you hold the shares can have a significant impact on your rate of return, with longer holding periods generally leading to higher returns.
Investing in stocks can be a great way to earn money, but it's important to understand how your investments can impact your gains and losses. Two key factors that can impact your returns are the quantity of shares you own and the length of time you hold the shares. In this article, we'll explore how these factors can affect your rate of return.
Impact of Quantity of Shares:The quantity of shares you own can have a direct impact on your dollar gains and losses. When the stock price goes up, the value of your shares also increases. Similarly, when the stock price goes down, the value of your shares also decreases. If you own more shares, the dollar amount of your gains and losses will be greater.
But, how does the quantity of shares impact your rate of return? Rate of return is the percentage change in the value of your investment over a certain period of time. It takes into account the gains and losses as well as the length of time you held the investment.
Impact of Length of Time:The length of time you hold the shares can have a significant impact on your rate of return. Generally, the longer you hold the shares, the higher your rate of return will be. This is because the stock market tends to go up over time, and the longer you hold the shares, the more time you have to benefit from this growth.
Impact of Quantity and Time on Rate of Return:So, how does the quantity of shares you own impact your rate of return? As we mentioned earlier, the rate of return is only impacted by the percentage change in the stock price, not the quantity of shares. However, owning more shares can provide you with a higher dollar amount of gains, which can lead to a higher rate of return.
Additionally, the longer you hold the shares, the higher your rate of return will be. This means that if you own more shares and hold them for a longer period of time, you can potentially earn a higher rate of return.
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€-grade10
mathematics
Answer:
29/5
Step-by-step explanation:
hope this helps
2/5 of a gal used 1/4 for coffee. How much milk in cups
The cups of milk required for the ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee is given by 2.4 cups.
Here,
( 2 / 5 ) of a gallons is equal to 0.4 gallons.
( 1 / 4 ) of gallons used for coffee that is equal to 0.25 gallons.
Total gallons left after coffee is equal to
= ( 0.4 ) - ( 0.25 )
= ( 0.15 )gallons
Conversion of gallons to cups is given by :
1 gallon = 16 cups
⇒ ( 0.15 )gallons = 0.15 × 16 cups
⇒ ( 0.15 )gallons = 2.4 cups of milk used.
Therefore, the 2.4 cups of milk is used when ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee.
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1. You need to dig a tunnel. You begin at the surface of the ground. The tunnel slopes downward for 83 meters. The final depth below ground is 52 meters. Find the angle of depression of the tunnel's descent. Round your answer to the nearest tenth. Draw a diagram to illustrate your problem.
Answer: 38.8°
Step-by-step explanation:
See the attached diagram:
From it we can tell that the tunnel forms a right triangle, with the length of a leg and the hypotenuse given. We can use the sine function to easily answer this, (letting θ be the angle we need to find)
sinθ = 52/83
.: θ = arcsin(52/83)
(Note: arcsin is the inverse of the sine function)
.: θ ≅ 38.8°
On a certain hot summer's day, 455 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $952.25. How many
children and how many adults swam at the public pool that day?
The number of children and adults that swam at the public pool are 247 and 208 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Represent the number of children by x and the number of adult by y
this means;
x+y = 455 equation 1
1.75x + 2.5y = 952.25 equation 2
using substitution method,
x = 455-y
substitute 455-y for x in equation 2
1.75(455-y) + 2.5y = 952.25
796.25-1.75y+2.5y = 952.25
0.75y = 952.25-796.25
0.75y = 156
divide both sides by 0.75
y = 156/0.75
y = 208
substitute 208 for y in equation 1
x = 455-208
x = 247
therefore the number of children and adults in the pool are 247 and 208 respectively.
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the mean of the sample group of answer choices is always smaller than the mean of the population from which the sample was taken can never be zero none of these alternatives is correct. can never be negative
The mean of a sample is the average of all values in the sample. The mean of a sample is generally always smaller than the mean of the population from which the sample was taken, since the sample is only a small subset of the population.
The mean of a sample can never be zero or negative, since it is an average of all the values in the sample. The mean of a sample can also never be greater than the mean of the population. None of these alternatives is correct.
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Which equations are correct? select each correct answer. 8x3(3x2)=24x6 4x3(6x2)=24x6 6b3(−2b3)=−12b6 3a3(−3a4)=−9a7?
The correct equations are:8x^3 * (3x^2) = 24x^5, 6b^3 * (-2b^3) = -12b^6, 3a^3 * (-3a^4) = -9a^7. The equations are correct because they follow the rules of algebra. The equation 4x^3 * (6x^2) = 24x^5 is not correct.
The distributive property of multiplication over addition allows us to multiply a factor by each term inside a set of parentheses. In the equation 8x^3 * (3x^2), we can use the distributive property to multiply 8x^3 by each term inside the parentheses, giving us 24x^5.
Similarly, the product of two negative numbers is positive, which explains why the equation 6b^3 * (-2b^3) equals -12b^6.
Finally, multiplying two terms with the same base means we add the exponents, so in the equation 3a^3 * (-3a^4), we get -9a^7.
Therefore, these equations are correct and follow the rules of algebra.
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Question: Use the partial products 3,840 and 640 to find the product 128 x 35. How many pens arr in 35 full boxes?
Answer:
hope this helps
Step-by-step explanation:
If you drove at 50 mph in 5 hours, how far will you have traveled? NEED ASAP
a. 200 miles
b. 10 miles
c. 250 miles
d. 300 miles
Answer:
c
Step-by-step explanation:
the following dot plot summarizes the distance roger ran in each of his tennis matches last month. each dot represents one game. based on this data, what is a reasonable estimate of the probability that roger runs less than 5 55 km kmstart text, k, m, end text in his next tennis match? choose the best answer. choose 1 answer: choose 1 answer:
The estimated probability that Roger runs less than 5 km in his next tennis match is 33%.
The dot plot summarizes the distance Roger ran in his recent tennis matches. To estimate the probability that he will run less than 5 km in the next match, we can use the data from the dot plot.
So according to question, there are kilometres as :
3 km, 4 km, 5 km, 6 km, and 7 km.
Total matches he played
for 3 km- 1 match , for 4 km- 2 matches , for 5 km- 4 matches, for 6 km- 0 matches, and for 7 km- 2 matches.
Out of 9 matches, he ran less than 5 km in 3 matches.
So the probability that Roger runs less than 5 km in his next tennis match is: 3/9 = 1/3
So the percentage will be : 33.33% ≈ 33%
Therefore, the estimated probabilityrobability that Roger runs less than 5 km in his next tennis match is 1/3 or about 33%.
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Answer: 33%
Step-by-step explanation:
A study shows that at the end of a school day teenagers typically have 40% of their cell phone battery left when plugged in phone charge at a rate of 3% per minute when using the newest fast charger.
a: write an inequality to represent how many more minutes are needed to reach at least 80% battery life.
b. use the inequality to determine the how many more minutes it will take to have at least 80% battery life
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of minutes and 'y' be the total battery percentage. Then the equation is given as,
y = 3x + 40
The inequality that represents the more minutes are needed to reach 80 of battery is given as,
3x + 40 ≤ 80
Simplify the inequality, then we have
3x + 40 ≤ 80
3x ≤ 40
x ≤ 13.33 minutes
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
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the value of a building is $180,000. the value is expected to increase by 3.5% each year. write a function that represents the value y (in dollars) of the building after x years. the predict the value after 10 years
help pls! i don’t as much need the answer but to know how to do it?
Step-by-step explanation:
an inscribed angle has its vertex on the circle, and the sides of the angle are two chords of the circle.
the inscribed angle is half the size of the arc angle (the angle at the center of the circle) of the arc that the two sides cut out of the circle.
110° is the arc angle (at the center of the circle) of the arc GJ.
for the inscribed angle GFJ the vertex is F, and the angle there is half of the arc angle :
angle GFJ = 110/2 = 55°
the second problem is the opposite "direction".
we have the inscribed angle FJH = 36°.
and we want the arc angle FH.
now, since the inscribed angle is half of the arc angle, the arc angle is twice the inscribed angle :
arc angle FH = 36×2 = 72°
A standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. Two cards are chosen from the deck at random. What is the approximate probability of choosing one club and one heart?
0. 0588
0. 0637
0. 1176
0. 1275
The probability of getting one club and one heart is 0.127.
p= [tex]\frac{13*13*2*1}{52*51}[/tex]=0.1275
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.
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Please Answer ASAP!
Please Give A Clear Answer Too!!
Answer:
x + y = -9
Step-by-step explanation:
let x = -8, y = -1
the equation that passes through the point (-8,-1) is x + y = -9
2. In rectangle HOME, HM and OE are diagonals that intersect at P.
Write at least 6 unique statements about HOME and justify your statements with definitions, postulates or theorems
1. It should be noted that HD = EM and HE = OM. In this case, the opposite sides are equal in the rectangle.
2. It should be noted that EHO = HOM = OME = MEH = 90°. In this case, all angles are equal to 90°.
What are postulate?Postulates are assertions that, in the absence of evidence, are taken to be true. Postulates have two functions: they define undefined terms and act as a foundation for the proof of subsequent propositions.
A line segment is determined by two points. A line segment may be extended along a line indefinitely. The other information is attached.
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1. Find the geometric mean of the
two numbers.
4 and 42.25
Answer:
13
Step-by-step explanation:
Do anybody know this?
The proof for the congruence of triangles GHI and GFJ are given below.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
From the figure,
1) Line segment FJ ⊥ line segment FH (given)
2) ∠HGI = ∠FGJ (It is also given)
3) HI = FJ (Given). So HI ≅ FJ
4) HI ⊥ FH (given)
5) Since both the angles F and H are right angles,
∠F ≅ ∠H (since all right angles are congruent)
6) So we get that two angles and a non included side of ΔGHI are equal to the corresponding two angles and a non included side of ΔGFJ.
So by AAS congruence theorem, ΔGHI ≅ ΔGFJ.
Hence the given two triangles are congruent.
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What is the minimum value for the function shown in the graph?
Enter your answer in the box.
Answer:
The minimum value is 2.5.
Step-by-step explanation:
This is a sine wave that is parallel to the x axis. It will never go below 2.5, as shown on the graph.
a system if equations y=x-6 and y=-x-2 grap the sytsem then write the solution you can also awnser no soloution or infinite solutions.
the solution is where they intercept; (2,-4)
hey can someone help me
when a new baby is born to the johnsons the family decides to invest $5000 in an account that earns 7% interest
The amount in the college fund is $16,899.66
How to determine the amount in the college fund?In order to determine the amount in the college fund, we need to find the future value of the money.
The formula for the future value of money is:
FV = PV * (1 + r)^t
where:
FV = future value
PV = present value (initial amount)
r = interest rate (as a decimal)
t = time (in years)
PV = $5000, r = 7% = 0.07, t = 18
FV = PV * (1 + r)^t
FV = 5000 * (1 + 0.07)¹⁸
FV = 5000 * (1.07)¹⁸
FV = $16,899.66
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Complete Question
When a new baby is born to the Johnsons, the family decides to invest $5000 in an account that earns 7% interest as a way to start the baby's college fund. If they do not touch that investment for 18 years, how much will there be in the college fund?
Helppppppppppp meeeeee guyssssssss
Answer:
2. $9.99
3. 45 tickets for $27
4. 20 cents
Step-by-step explanation:
2. 79.92/8 = 9.99
3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents
4. 6/30 = 20
Answer:
Step-by-step explanation:
79.92/8= 9.12 per cd
15/20= .75
27/45=.6 better deal because it is .60 cents per ticket
6/30= .20 per can
There is a total of
wholes in 72
.
The remaining fractional part is .
2
The whole number whose sum is 72 cannot be in the ratio C. 3/4.
How to explain the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them
The whole number must be divided by sum of two ratio particularly
A.5 + 7=12
72 can be divided by 12
B.3+5=8
72 can be divided by 8
C.4+3=7
72 can not be divided by 7
D.4+5=9
72 can be divided by 9
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The whole number whose sum is 72 cannot be in the ratio
A. 5/7
B. 3/5
C. 3/4
D. 4/5
A stereo that regularly sells for $330 is on sale at 15% off. How much will a customer save on the stereo during the sale?
Answer: 49.5 dollars
Step-by-step explanation: the original price is 330, but the sale takes 15 percent off
so we turn 15% into a decimal so we can multiply 330 and 15%
we get 0.15 × 330 = 49.5
Classify each pair of angles as Complementary, Supplementary, or Neither. Drag and drop the choices into the boxes to correctly complete the table. Each category may have any number of pair of angles. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Complementary Supplementary Neither
Answer:
Complementary is 2 angles that add up to 90 degrees and supplementary is 2 angles that add up to 180 degrees
48+32=80 so that would be neither
101+77=178 so that would be neither
107+73=180 so that would be supplementary
Step-by-step explanation:
have a nice day.
Answer:
only here for points
Step-by-step explanation:
Helppp i need to find the transformations needed.
The transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
What is a transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
The given functions are f(x)=x³ and g(x)= -(x-4)³+1.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 4 Units
Vertical Shift: Up 1 Units
Reflection about the x-axis: None
Reflection about the y-axis: Reflected
Vertical Compression or Stretch: None
Therefore, the transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
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An art teacher is making packages
a. The greatest number of packages the teacher can make using all the paintbrushes and paint is 8
b. The number of paintbrushes in each package would be 3 and the number of tubes of paints would be 5
How do we determine the number of packages?In order to determine the greatest number of packages the teacher can make using all the paintbrushes and paint, we have to determine the highest common factor of the number of brushes and the number of tubes of paint
Highest common factor is the highest factor that is common to two or more numbers:
Factors of 24 = 1,2,3,4,6,8,12 and 24
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40.
Common factors of 24 and 40 = 1, 2, 4, 8
Therefore, the highest common factor is 8.
The number of paintbrushes in each package:
= Number of brushes / number of package
= 24/8
= 3 brushes
The number of tubes of paint:
= number of tubes of paints / number of package
= 40 / 8
= 5 tubes of paints
Full question "An art teacher is making packages of paint brushes and paint for his. He has 24 brushes and 40 tubes of paint. Each package will have the same number An art teacher is making packages of paintbrushes and paint for his students. of brushes and the same number of tubes of paint. Part a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work Part b. How many paintbrushes and tubes of paint are in each package?".
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what is the probability that the sample mean annual insurance cost is greater than $620? show your work.
The probability of the sample mean annual insurance cost being greater than $620 is very low, that is 0.00317% which indicating that it is unlikely to happen by chance.
Probability is a branch of mathematics that deals with the likelihood of an event happening. It is used in various fields, such as insurance, finance, and science.
To calculate the probability, we need to use the central limit theorem, which states that the distribution of sample means of a population approaches a normal distribution as the sample size increases. We also need to know the mean and standard deviation of the population.
Assuming that the population is normally distributed, we can use the following formula to calculate the probability:
z = (x - μ) / (σ / √(n))
where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we don't know the population mean and standard deviation, but we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 100 insurance costs with a mean of $600 and a standard deviation of $50.
Now, we can calculate the z-score:
z = (620 - 600) / (50 / √(100)) = 4
The z-score of 4 indicates that the sample mean of $620 is 4 standard deviations away from the mean of $600. We can use a standard normal distribution table or a calculator to find the probability of getting a z-score of 4 or higher. The probability is very small, approximately 0.0000317 or 0.00317%.
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Jayla’s parents are replacing their bathroom floor with square tiles. The tiles will be laid side by side to cover the entire bathroom with no gaps, and none of the tiles can be cut. The floor is a rectangle that is `48` inches by `60` inches. What is the side length of the largest possible tile they could use?
The largest possible side length of the tiles that can be used is `12` inches as it can cover the entire bathroom without any gaps or cutting of tiles.
The largest tile that can be used is a square tile. To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4.
`48/4 = 12`
`60/4 = 15`
The largest possible side length of the tiles that can be used is `12` inches. Jayla's parents are replacing their bathroom floor with square tiles. The floor is a rectangle that is `48` inches by `60` inches. To cover the entire bathroom with no gaps, and without having to cut any of the tiles, they need to use a tile that is the same size as the largest possible tile that can cover the entire floor without any gaps.
To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4. This is because a tile needs to cover 4 sides of the floor without any gaps, so the side length of the tile needs to be equal to the length divided by 4, or the width divided by 4.
In this case, the side length of the largest possible tile is `12` inches. This is because `48/4 = 12`, and `60/4 = 15`. As `15` is larger than `12`, the side length of the largest possible tile is `12` inches. This means that the tiles need to be `12` inches by `12` inches in size to cover the entire bathroom without any gaps.
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