After addressing the issue at hand, we can state that As a result, the square value of x to three significant figures is 5.03 cm.
what is a square?According to Euclidean geometry, a square is an equilateral quadrilateral with four equal sides and four equal angles. It is also referred to as a rectangle with two neighbouring sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Furthermore, the diagonals of the square are evenly spaced and split at a 90-degree angle. a neighbouring rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.
The Pythagorean theorem can be used to find the square's diagonal:
2x2 = diagonal2 = x2 + x2 = 2x2[tex]x * \sqrt = diagonal = sqrt(2x2) (2)[/tex]
Because the diagonal equals the circle's diameter, the radius is half of the diagonal:
x * \sqrt(2) / 2 = radius
We can now use the formula for the area of a circle to calculate x:
[tex]\pi * radius2 = area[/tex]
[tex]\Pi * (x * sqrt(2) / 2)2 = 56[/tex]
[tex]56 = pi * (x^2 / 2)[/tex]
[tex]x^2 = 112 / pi[/tex]
x = 5.027 (rounded to 3 significant figures) (rounded to 3 significant figures)
As a result, the value of x to three significant figures is 5.03 cm.
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It is an arrangement of things in a definite order
A sequence is an ordered list of elements or objects that follows a specific pattern or rule, where the order of the terms is important.
A sequence is an ordered list of numbers, symbols, or other mathematical objects. The order in which the elements appear is important and determines the identity of the sequence. For example, consider the following two sequences:
1, 3, 5, 7, 9
3, 5, 1, 7, 9
The first sequence consists of odd numbers in ascending order, while the second sequence consists of the same numbers but in a different order. These two sequences are different because the order of the terms is different.
Sequences can have different patterns or rules that determine the order of the terms. For example, the sequence of Fibonacci numbers, which is a famous sequence in mathematics, has the following pattern:
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
Each term in the sequence (starting with the third term) is the sum of the two preceding terms.
This pattern continues indefinitely, creating a sequence that has a distinct pattern and order.
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What is the arrangement of objects in a definite order called?
Evaluate. (3. 5−2/3)⋅(−2. 8+4 3/5) Enter your answer as a decimal or mixed number in simplest form in the box
Answer:
5.1, 5 1/10
Step-by-step explanation:
(3.5 − 2/3) ⋅ (−2.8 + 4 3/5) =
= (7/2 - 2/3)(-14/5 + 23/5)
= (21/6 - 4/6)(9/5)
= (17/6)(9/5)
= (17 × 9)/(6 × 5)
= 51/10
= 5.1 = 5 1/10
please help me please
251^5+8-(9x20+3)=
Answer:
996,250,626,076
Step-by-step explanation:
You want the value of the numerical expression 251^5+8-(9×20+3).
CalculatorYour calculator will evaluate this properly if you enter it as shown. See the attachment.
If you're doing this in parts, the Order of Operations tells you to start with the parentheses, then do the exponentiation.
251^5 +8 -(9·20 +3)
= 251^5 +8 -183
= 996,250,626,251 +8 -183 = 996,250,626,076
__
Additional comment
You can use a spreadsheet (or an on-line calculator) if your calculator only displays 10 digits.
The number of bacteria in a culture is given by the function
0. 3t
n(t) = 920e
where t is measured in hours.
(a) What is the relative rate of growth of this bacterium population?
Your answer is
percent
(b) What is the initial population of the culture (at t=0)?
Your answer is
(c) How many bacteria will the culture contain at time t=5?
Your answer is
a) The continuous rate of growth of this bacterium population is 45%
b) Initial population of culture at t = 0 is 950 bacteria
c) number of bacterial cultures contain at t = 5 is 9013 bacteria
The number of bacteria in a culture is given by the function n(t) =950[tex]e^{0.450t}[/tex] Where t is measured in hours
what is the continuous rate of growth of this bacterium population
The number of bacteria in a culture is given by
n(t) = 950[tex]e^{0.45t}[/tex]
a) rate of growth is
Bacteria growth model N(t) = no[tex]e^{rt[/tex]
Where r is the growth rate
hence r = 0.45
= 45%
b) Initial population of culture at t = 0
n(0) = 950[tex]e^0[/tex]
= 950
= 950 bacteria
c) number of bacterial culture contain at t = 5
n(5) = 950[tex]e^{0.45*5}[/tex]
= 9013.35
= 9013 bacteria
the complete question is-
The number of bacteria in a culture is given by the function n(t) =950e^0.45t Where t is measured in hours A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent B) what is the initial population of the culture (at t=0) your answer is __ C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria
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Sooo my friend sent me this and I’ve been puzzled, I think there are no correct options but need someone’s opinion. Any nerds like me out there?
Answer: first off i am not a nerd ur just a dummyboi second this is simple math grade 4 really the answer is 24
Step-by-step explanation:
In a cube that is 3x3, 19 cubes can be seen. 8 are hidden.
In a cube that is 4x4, 37 cubes can be seen. 27 are hidden.
In a cube that is 5x5, 61 cubes can be seen. 64 are hidden.
In a cube that is 6x6, 91 cubes can be seen. 125 are hidden.
19+8=27 if ur making a 3x3 cube answer is 24
the position (in thousands of feet) of a car driving along a straight road at time t in minutes is given by the function y
The position of a car driving along a straight road at time t in minutes is given by the function y = f(t).
The function y represents the position of the car in thousands of feet, while the variable t represents the time in minutes.
To find the position of the car at any given time, you simply need to plug in the value of t into the function and solve for y. For example, if you wanted to find the position of the car at 2 minutes, you would plug in 2 for t and solve for y:
y = f(2)
Once you have solved for y, you will have the position of the car in thousands of feet at 2 minutes. You can repeat this process for any value of t to find the position of the car at any given time.
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a certain newspaper provides the net asset value, the year-to-date percent return, and the three-year percent return for 882 mutual funds at the end of 2017. assume that a simple random sample of 12 of the 882 mutual funds will be selected for a follow-up study on the size and performance of mutual funds. use the third column of the table of random numbers, beginning with 71744, to select the simple random sample of 12 mutual funds. begin with mutual fund 744 and use the last three digits in each row of column 3 for your selection process. what are the numbers of the 12 mutual funds in the simple random sample? (enter your answers as a comma-separated list.)
The 12 mutual funds in the simple randοm samples are
714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488
What is a simple randοm sample?A simple randοm sample is a subset οf persοns picked at randοm, all with the same prοbability, frοm a larger set οf individuals. It is a methοd οf chοοsing a sample at randοm.
Here, we have
Given: a certain newspaper prοvides the net asset value, the year-tο-date percent return, and the three-year percent return fοr 882 mutual funds at the end οf 2017. assume that a simple randοm sample οf 12 οf the 882 mutual funds will be selected fοr a fοllοw-up study οn the size and perfοrmance οf mutual funds. use the third cοlumn οf the table οf randοm numbers, beginning with 71744, tο select the simple randοm sample οf 12 mutual funds.
The last three digits in each rοw οf cοlumn 6 less than 882 are
714, 041, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488
Hence, The 12 mutual funds in the simple randοm samples are
714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488.
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Help I got logged out of my account and forgot the password and the email I used to sign up is not an real to receive the code
If locked out of an account due to forgotten password and invalid email, try password recovery options or contact customer support, or create a new account.
If you've been locked out of your account. If you've forgotten your password and the email you used to sign up is not valid, it can be difficult to regain access to your account. Few steps you can try to recover your account:
Check if there's any password recovery option: Depending on the website or platform you've signed up for, there may be a password recovery option that doesn't rely on email verification. For example, some sites may allow you to answer security questions or use your phone number to reset your password.Contact customer support: If there's no password recovery option or it's not working for you, try contacting the customer support team for the website or platform. Explain the situation and provide any relevant information you can. They might be able to assist you in getting your account access back.Create a new account: If all else fails, you may need to create a new account with a valid email address. Make sure to choose a strong, unique password and consider enabling two-factor authentication to help secure your account in the future.It's important to note that in some cases, it may not be possible to regain access to your account. Always be cautious about the information you provide when signing up for online services and make sure to keep your login credentials in a safe and secure location.
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Question 2) Suppose you work for the Cheapo Coffee company and are tasked with studying their coffee shops around the country. You are interested in studying the number of cups of coffees sold per day at different cheapo coffee shops. To study this you randomly select 4 major cities from across the US. You visit each oh the cheapo coffee stores in these cities for a day and record the value is the number of customers they serve. You ultimately visit 17 shops and get the following data.
35, 43, 48, 52, 58, 67, 73, 85, 106, 125, 136, 174, 199, 213, 274, 351
a. What is the population in this question?
b. What is the sample in this question
a. The population in this question is all the Cheapo Coffee stores around the country.
b. The sample in this question is the 17 coffee shops that were visited and their daily sales data was recorded.
In statistics, a population is the entire group of individuals, items, or events that we are interested in studying. In this case, the population is all the Cheapo Coffee stores across the country, and we are interested in studying the number of cups of coffee sold per day at these stores.
However, it is often impractical or impossible to study the entire population, so we select a subset of the population, which is called a sample.
The sample is a representative subset of the population that we study to draw conclusions about the population as a whole. In this case, the sample consists of 17 Cheapo Coffee stores that were randomly selected from four major cities in the US, and the number of cups of coffee sold per day was recorded for each store.
We can use the data from the sample to estimate the average number of cups of coffee sold per day at all Cheapo Coffee stores across the country, which is the parameter of interest in this study.
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If it takes John 5/12 of an hour to work on a fence, how many minutes will it take him to finish the job?
Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
4.02 Lesson Check Arithmetic Sequences (9)
Answer:
a₉ = - 24
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₁ = 8 and d = - 4 , then
a₉ = 8 + (8 × - 4) = 8 + (- 32) = 8 - 32 = - 24
Answer:
Tn = a + (n - 1)d
T9 = 8 + (9 - 1) × -4
T9 = (8 + 8) × -4
T9 = 16 × -4
T9 = -64
Unit 8 Right Triangles & Trigonometry Homework 3: similar Right triangles & geometric mean
In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right-angled triangle ABC with drawn with angle B = 90°.
A line BD is drawn which is perpendicular to AC.
The angle BDC is also 90 degrees.
The measure for line segment AD = 12 and CD = 40.
The measure for line segment BD is x.
The side BD is common for triangle ABC and BDC.
So, by the formula of indirect measurement we have -
DC / BD = BD / AD
Substitute the values in the equation -
40 / x = x / 12
x² = 480
x = 21.908
x = 21.91
Therefore, the value of x is obtained as 21.91.
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19. What is the length of side JN? (Round your answer to the nearest tenth.) 65 39 53
We οbtain JN 44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly 44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.
What is the measurement οf a triangle's side?
The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.
The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.
Law of sines
sin(∠A)/a = sin(∠B)/b = sin(∠C)/c
Therefore,
39/sin(53°) = JN/sin(65°)
JN = (39×sin(65°))/sin(53°)
JN = 44.3
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Can you answer all of these please
The area of the composite figures are:
1: 106.28 sq. yd.
2: 79.27 sq. in.
3: 64.28 sq. m.
4: 44.82 sq. ft.
5: 406 sq. cm.
6: 629.46 sq. km.
How to find the area of a composite figure?
To find the area of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.
No. 1
Area = area of semicircle + area of rectangle + area of semicircle
Area = (1/2 * πr²) + (L*W) + (1/2 * πr²)
r = 6/2 = 3 yd, L = 13 yd and W = 6 yd
Area = (1/2 * π*3²) + (13*6) + (1/2 * π*3²)
Area = 14.14 + 78 + 14.14
Area = 106.28 sq. yd.
No. 2
Area = area of semicircle + area of triangle
Area = (1/2 * πr²) + (1/2 *base* height)
r = 10/2 = 5 in, base = 10 in and height = 8 in
Area = (1/2 * π * 5²) + (1/2 * 10 * 8)
Area = 39.27 + 40
Area = 79.27 sq. in.
No. 3
Area = area of square + area of semicircle + area of semicircle
Area = L² + (1/2 * πr²) + (1/2 * πr²)
L = 6 m, r = 6/2 = 3 m
Area = 6² + (1/2 * π * 3²) + 1/2 * π * 3²)
Area = 36 + 14.14 + 14.14
Area = 64.28 sq. m.
No. 4
Area = area of semicircle + area of rectangle
Area = (1/2 * πr²) + (L * W)
r = 5/2 = 2.5 ft, L = 7 ft and W = 5 ft
Area = (1/2 * π * 2.5²) + (7 * 5)
Area = 9.82 + 35
Area = 44.82 sq. ft.
No. 5
Area = area of triangle + area of rectangle
Area = (1/2 * base * height) + (L * W)
base = 10cm, height = 14 cm, L = 24 cm and W = 14 cm
Area = (1/2 * 10 * 14) + (24 * 14)
Area = 70 + 336
Area = 406 sq. cm.
No. 6
Area = area of semicircle + area of triangle
Area = (1/2 * πr²) + (1/2 * base * height)
r = 26/2 = 13 km, base = 28 km and height = 26 km
Area = (1/2 * π * 13²) + (1/2 * 28 * 26)
Area = 265.46 + 364
Area = 629.46 sq. km.
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For the function f(x)=3x2 +3x+8, evaluate and fully
simplify each of the following.
f(x+h)= ?
f(x+h)-f(x) / h = ?
By evaluating and simplifying f(x)=3x2 +3x+8, we get f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8 and (f(x + h) - f(x))/h = 6x + 3h + 3.
Given function is, f(x) = 3x² + 3x + 8
Evaluate f(x + h)
Expanding f(x + h) => f(x) + hf′(x) + h²/2f″(x)
Applying formulae in the given function f(x + h) = 3(x + h)² + 3(x + h) + 8=> 3x² + 6xh + 3h² + 3x + 3h + 8Now, f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8
Evaluate (f(x + h) - f(x))/h
Expanding both the terms f(x + h) and f(x) and simplifying, (f(x + h) - f(x))/h = [3x² + 6xh + 3h² + 3x + 3h + 8 - (3x² + 3x + 8)]/h=> [3x² + 6xh + 3h² + 3x + 3h + 8 - 3x² - 3x - 8]/h=> [6xh + 3h² + 3h]/h=> 6x + 3h + 3
Therefore, the required value is f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8and (f(x + h) - f(x))/h = 6x + 3h + 3.
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-5 x blank equals 35
Answer:
-7
Step-by-step explanation:
A negative number times a negative number is positive. Because -5 is negative and 35 is positive the other factor must be negative as well.
5 x 7 = 35
So, -5 x -7 also equals 35
Consider the t distribution with 5 degrees of freedom.
(a) What proportion of the area under the curve lies to the right of t = 2. 015?
(b) What proportion of the area lies to the left of t = −3. 365?
(c) What proportion of the area lies between t = –4. 032 and t = 4. 032?
(d) What value of t cuts off the upper 2. 5% of the distribution?
The cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.
(a) 0.974
(b) 0.998
(c) 0.996
(d) 2.571
(a) To find the proportion of the area under the curve to the right of t = 2.015, we first calculate the cumulative probability of t = 2.015 from the t-distribution table. The cumulative probability of t = 2.015 is 0.974, which means that 0.974 or 97.4% of the area under the curve lies to the right of t = 2.015.
(b) To find the proportion of the area under the curve to the left of t = −3.365, we calculate the cumulative probability of t = −3.365 from the t-distribution table. The cumulative probability of t = −3.365 is 0.998, which means that 0.998 or 99.8% of the area under the curve lies to the left of t = −3.365.
(c) To find the proportion of the area under the curve between t = –4.032 and t = 4.032, we calculate the cumulative probability of t = 4.032 and subtract the cumulative probability of t = −4.032. The cumulative probability of t = 4.032 is 0.995 and the cumulative probability of t = −4.032 is 0.003. Subtracting the two gives us 0.996, which means that 0.996 or 99.6% of the area under the curve lies between t = –4.032 and t = 4.032.
(d) To find the value of t that cuts off the upper 2.5% of the distribution, we calculate the cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.
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I seriously cannot figure this out please help me :( IT'S SO LATE PLEASE
Tia's statement that the graph is a x^5 function is correct
How to determine who is correctThe statements from the question are:
Tia = x^5 functionMarcus = x^4 functionThe zeros and the multiplicities in the format (zero, multiplicity) from the question are (-3, 1), (-1, 2), (2, 1) and (3, 1)
The equation of the polynomial can be expressed as
P(x) = (x - zero)^multiplicity
When the zeros and the multiplicities are substituted, we have
P(x) = (x + 3)(x - 3)(x - 2)(x + 1)^2
Expand
P(x) = (x^2 - 9)(x - 2)(x + 1)^2
When evaluated, we have
P(x) = x^5 - 12x^3 - 2x^2 + 27x + 18
The above is a x^5 function
Hence, Tia is correct
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please help if you can
Using variation, the model for F = 42(m/p)
What do you mean by variation?There is a direct variation between the two variables whenever one quantity directly influences the other, such as when one quantity increases relative to the other and vice versa. There is a connection between two variables when one of them is a constant multiple of the other. Because of their immediate connection, the two variables are referred to as directly proportional.
Inverse variation establishes a proportionality between two quantities that are inversely related. There are two separate proportionalities. They are the direct variation and inverse variation. The two quantities are said to be directly proportional if an increase or decrease in one generates an equal increase or decrease in the other. In an inverse variation, on the other hand, one quantity increases while the other falls.
Now as F is directly proportional to m and inversely to p, so we can form a model as:
F = 42(m/p)
So that F=36 when m =6 and p =7.
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Matthew has an investment that is now worth $21 537.82. Find the original amount
he invested if he has had the money invested at 2.5% per month for 3 years.
town A is 60 km from town B and 61km from town C a road connects town B and C directly find the length of the road for class 7 ncert
Answer:Using the triangle inequality, we can conclude that the distance between towns B and C must be less than 121 km (the sum of the distances between towns A and B, and between towns A and C).
To find the exact length of the road connecting towns B and C, let's use the Pythagorean theorem.
Let x be the length of the road connecting towns B and C. Then we have:
x^2 = 61^2 + 60^2
x^2 = 3721 + 3600
x^2 = 7321
x ≈ 85.6 km
Therefore, the length of the road connecting town B and C is approximately 85.6 km.
Step-by-step explanation:
The two charges q are fixed at the vertices of an equilateral triangle with sides of length
a. If k = 1/4π ε0, the work required to move q from the other vertex to the center of the line joining the fixed charges is:
The work required to move q from the other vertex to the center of the line joining the fixed charges is (1/4π ε0) x 2 x q 2/a.
To solve this problem, we can use the principle of superposition to calculate the potential at the center of the equilateral triangle due to each of the two fixed charges, and then add them up to get the total potential.
Let's first find the potential due to one of the fixed charges at the center of the triangle. We can use the formula for the electric potential due to a point charge q at a distance r from it, which is given by:
V = k x q/r
In this case, the distance from one of the fixed charges to the center of the triangle is: r = a/2
So the potential due to one fixed charge at the center of the triangle is:
V1 = kq/r = kq/(a/2)
Next, let's find the potential due to the other fixed charge at the center of the triangle. Since the triangle is equilateral, the distance from the other fixed charge to the center of the triangle is also a/2. So the potential due to the other fixed charge at the center of the triangle is:
V2 = k x q/(a/2)
Now, the total potential at the center of the triangle due to the two fixed charges is simply the sum of the individual potentials:
V_total = V1 + V2 = kq/(a/2) + kq/(a/2) = 2kq/a
The work required to move a charge q from infinity to the center of the triangle is equal to the change in potential energy of the charge, which is given by:
W = q x (V_final - V_initial)
In this case, the initial potential is zero (since the charge is at infinity), and the final potential is 2kq/a (which we just calculated). So the work required is:
W = q x (2kq/a - 0) = 2kq 2/a
Substituting the given value of k, we get:
W = (1/4π ε0) x 2 x q2/a
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you deposit 4,000 in an account earning 5% interest compounded
continuously. Write an equation that model this situation.
A(t)=
The interest compounded equation to model the given situation is A(t) = 4000[tex]e^{0.05t}[/tex].
To model the given situation, the interest compounded can be written as the given equation of:
A(t) = A0e^(rt)
Where:
A(t) is the amount of money after t years
A0 is the initial amount of money, in this case,
r is the interest rate expressed as a decimal
t is the time in years that the money is invested.
From the case, we know that:
Initial deposit = $4,000
Interest rate = 5%
Time period = t (undetermined)
So, substituting the values given in the problem, the equation to model the given situation is:
A(t) = A0e^(rt)
A(t) = 4000e^(0.05t)
Therefore, A(t) = 4000e^(0.05t) is the required equation that models the given situation.
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(10 POiNTS!!!)Find the value of x that makes this a true statement.
−3(x − 100) = −5(x − 100) + 6
Answer: x = 100
Step-by-step explanation:
What’s the first step in evaluating the expression 6-(4/2X5)2?
The first step in evaluating the expression 6 - (4/2 x 5)² is to simplify the expression inside the parentheses first.
What is an expression?An expression is a mathematical phrase that consists of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that are combined according to certain rules to represent a mathematical calculation.
Following the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), as shown below:
4/2 = 2, so we can replace 4/2 with 2:
6 - (2 x 5)²
2 x 5 = 10, so we can replace 2 x 5 with 10:
6 - 10²
10² means 10 multiplied by itself, which equals 100:
6 - 100
Therefore, the expression simplifies to -94.
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There is a 50% chance that a newborn baby will be a boy. For families with four children, what is the probability that all the children are boys?
Select one:
A. 0.2512 B. 0.0625 C. 0.3754 D. 0.1587
The option B, 0.0625, is the correct answer.
The probability that all children are boys is 1/2 × 1/2 × 1/2 × 1/2 = 1/16. The probability of the event is 0.0625. The probability that all the children are boys is 0.0625.Therefore, option B, 0.0625, is the correct answer.
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The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?
6
20
27
30
[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{"y" varies}\\ \textit{directly with "x"}\\ \textit{inversely with "z"} \end{array}\qquad y=\cfrac{kx}{z}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ z=4\\ y=15 \end{cases} \\\\\\ 15=\cfrac{k(10)}{4}\implies \cfrac{4}{10}\cdot 15=k\implies 6=k\hspace{8em}\boxed{y=\cfrac{6x}{z}} \\\\\\ \textit{when x = 20 and z = 6, what's "y"?}\qquad y=\cfrac{6(20)}{6}\implies y=20[/tex]
Answer:
I think is 500 hope it helps
In 2019 and in 2020, consumers in Dexter purchased only books and pens.
The prices and quantities for 2019 and 2020 are listed in the table.
The reference base period for Dexter's CPI is 2019, and 2019 is also the year of the Consumer Expenditure Survey.
What is the inflation rate in 2020?
The inflation rate in 2020, given the CPI in 2020 and the price in both years, would be 95. 5 %.
How to find the inflation rate ?To find the inflation rate from the CPI (Consumer Price Index), subtract the beginning CPI from the end CPI. This gives you the increase in the price level over the time period.
Divide the increase in the price level by the beginning CPI. Multiply the result by 100 to get the inflation rate as a percentage. Basically, the formula is:
= (CPI in 2020 - CPI in 2019 ) / CPI in 2019
= ( 195.5 - 100 ) / 100
= 95. 5 %
Note : The CPI for 2020 is 195.5 and the assumed CPI for 2019 would be 100 as a base year.
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A gardener will use up to 250 square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least four times the area used for
flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all
values of x and y that satisfy these requirements.
The inequality equation that can be used to solve this problem is x + y ≤ 250 and y ≥ 4x
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
Let x denote the area (in square feet) used for flowers and y denote the area (in square feet) used for vegetables.
A gardener will use up to 250 square feet for planting flowers and vegetables, hence:
x + y ≤ 250 (1)
She wants the area used for vegetables to be at least four times the area used for flowers. Hence:
y ≥ 4x (2)
Plotting both equations using geogebra, the solution is the darker region.
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Find the length of AC in this right-angled triangular
prism.
Give your answer in centimetres (cm) to 1 d.p.
44 cm
A
E
42 cm
B
F
57 cm
с
The length of AC in this right-angled triangular prism is approximately 60.66 cm.
What is Pythagoras theorem?
For right angle triangle,
Hypotenuse² = Height²+Base²
However, we can use the Pythagorean theorem to find the length of AC if we know the lengths of AE and EC and ED.
If we assume that face AEC is the base of the prism and the right angle is at vertex E, then we can use the Pythagorean theorem to find the length of AC:
AC² = AE²+ EC²
We are given that AE = 43 cm, but we don't know the length of EC. However, we can use the fact that the base of the prism is a rectangle to find EC. Since opposite sides of a rectangle are equal, we have:
EC = 51 cm and ED = 45 cm
Substituting this into the equation above, we get:
AC² = 43² + 51²
AC² = 3680
AC ≈ 60.66 cm (to 1 decimal place)
Therefore, the length of AC in this right-angled triangular prism is approximately 60.66 cm.
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Correct question is "Find the length of AC in this right-angled triangular prism. Give your answer in centimetres (cm) to 1 d.p.
Base is ED 51 cm and height is AE 43 cm of the prism."