Step-by-step explanation:
To determine the constant of proportionality (k) in a proportional relationship, we need to compare corresponding values of x and y and calculate the ratio between them.
Let's examine the given values:
2. UX: x 6 15 9 y 42 200
To find the constant of proportionality (k), we can take any pair of corresponding values and calculate their ratio. Let's choose the first pair: (6, 42).
k = y / x
k = 42 / 6
k = 7
So, the constant of proportionality (k) is 7.
Now, let's find the missing values for the second set of values:
d. X: 14 y: 21 6 15 3 7 8
Since we know the constant of proportionality is 7, we can calculate the missing values of y by multiplying each corresponding x value by 7.
Missing values for y:
- For x = 21, y = 21 * 7 = 147
- For x = 6, y = 6 * 7 = 42
- For x = 15, y = 15 * 7 = 105
- For x = 3, y = 3 * 7 = 21
- For x = 7, y = 7 * 7 = 49
- For x = 8, y = 8 * 7 = 56
Therefore, the missing values of y are: 147, 42, 105, 21, 49, and 56.
I REALLY NEED HELP I DONT UNDERSTAND IT!
The area of the pentagon using the composite area formula is 37 in².
What is a pentagon?
A pentagon is one of the many types of polygon having five sides and five angles.
To calculate the area of the pentagon, we use the formula below
Formula:
A = BH/2+LW+bL................... Equation 1From the diagram,
Given:
B = 6 inH = 4 inL = 5 inW = 4 inb = 1 inSubstitute these values into equation 1
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Use the table that shows the recent population, in millions, of the ten largest U.S. cities.
Find the mean absolute deviation. Round to the nearest hundredth.
The mean absolute deviation =________million.
The mean absolute deviation for the data-set in the table is given as follows:
1.52 million.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.The mean for the data-set in this problem is given as follows:
(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.
The deviations are given as follows:
|1.5 - 2.54| = 1.04.|3.8 - 2.54| = 1.26.|1.3 - 2.54| = 1.24.|1.6 - 2.54| = 1.06.|2.9 - 2.54| = 0.46.|1.4 - 2.54| = 1.14.|0.9 - 2.54| = 1.64.|2.3 - 2.54| = 0.24.|8.4 - 2.54| = 5.86.|1.3 - 2.54| = 1.24.Hence the mean absolute deviation is given as follows:
(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.
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3. Which of the following is equivalent to 5/x= 3/x-12
Answer: 5(x - 12) = 3x
Step-by-step explanation:
We can cross-multiply to answer this question.
[tex]\frac{5}{x} =\frac{3}{x-12}[/tex]
5 * (x - 12) = 3 * x
5(x - 12) = 3x
Answer:
b) 5(x - 12) = 3x
Step-by-step explanation:
Given expression,
→ 5/x = 3/(x - 12)
Now we have to,
→ Find the equivalent expression.
Let's find the required answer,
→ 5/x = 3/(x - 12)
Cross multiplying both sides:
→ 5(x - 12) = 3(x)
→ 5(x - 12) = 3x
Applying Distributive property:
→ 5(x) - 5(12) = 3x
→ 5x - 60 = 3x
Solving for the value of x:
→ 5x - 3x = 60
→ 2x = 60
→ x = 60/2
→ [ x = 30 ]
Hence, the value of x is 30.
Calculate the interest of an investment of $3500 at 2.75% for 3 years.
Use the functions:
A = P (1+r/n)nt and A = Pe rt
Fill out the table below for given values.
A =
P =
r = (as decimal)
t =
Answer: We can use both formulas to calculate the interest on an investment of $3500 at 2.75% for 3 years.
Using the formula A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years, we have:
A = 3500(1+0.0275/1)^(1*3) ≈ $3843.84
Therefore, the interest earned is:
Interest = A - P = $3843.84 - $3500 = $343.84
Using the formula A = Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.71828, we have:
A = 3500e^(0.0275*3) ≈ $3843.84
Therefore, the interest earned is:
Interest = A - P = $3843.84 - $3500 = $343.84
The interest earned is $343.84 in both cases.
Factor out the greatest common factor.
polynomial.
3
2x³ - 10
The greatest common factor of the given polynomial is 2, so we can factor it out to get: 2(x³ - 5)
We have to factories 2x³ - 10
So, 2x³ = 2 . x . x . x
10 = 2 . 5
Then, 2x³ - 10
= 2. x . x . x - 2. 5
= 2( x . x .x - 5)
= 2 (x³ - 5)
The greatest common factor of the given polynomial is 2, so we can factor it out to get: 2(x³ - 5)
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Volume of an open rectangular is 24.3m³.height is 2.7m. what is surface area.
If the volume of an open rectangular object or space is 24.3m³ with a height of 2.7m, the surface area is 9m.
How is the surface area determined?The surface area can be determined by dividing the volume by the height.
This is because the product of the surface area and the height gives the volume.
The surface area is a product of the length and width, while the volume is the product of the length, width, and height.
Volume = 24.3m³
Height = 2.7m
Surface area = 9m (24.3m³ ÷ 2.7)
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Find all possible values of x.
Using the secant-secant theorem, the possible values of x are x = 6 and x = -10. -10 cannot be a value of x because length cannot be negative.
Secant-secant theorem: Calculating the value of of xFrom the question, we are to determine the value of x in the given diagram.
The Secant-secant theorem states that
"Given two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other segment and its external segment"
Thus,
We can write that
5 × (5 + 7) = x × (x + 4)
Simplifying
5 × 12 = x² + 4x
60 = x² + 4x
x² + 4x - 60 = 0
Solve the quadratic equation
x² + 4x - 60 = 0
x² + 10x - 6x - 60 = 0
x(x + 10) - 6(x + 10) = 0
(x - 6)(x + 10) = 0
x - 6 = 0 or x + 10 = 0
x = 6 or x = -10
Since x cannot be negative,
x = 6
Hence, the value of x is 6
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URGENT
Georgia will use the pattern shown to make a square pyramid out of cardboard. The square pyramid will not have a bottom.
A net of a square pyramid. The square base has side lengths of 9 inches. The triangular sides have heights of 14 inches.
How much cardboard will she need if a = 14 in. and b = 9 in.?
Group of answer choices
378 square inches
630 square inches
504 square inches
252 square inches
Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.
To calculate the amount of cardboard needed to construct the square pyramid, we need to find the surface area of each individual face and then add them together.
Given that the base of the pyramid is a square with side length [tex]\(b = 9\) inches[/tex] and the height of the triangular sides is [tex]\(a = 14\) inches[/tex], we can proceed as follows:
The surface area of the square base is [tex]\(b^2 = 9^2 = 81\)[/tex] square inches.
Each triangular face has a base equal to the side length of the square base, [tex]\(b = 9\) inches[/tex], and a height of [tex]\(a = 14\) inches[/tex]. Therefore, the surface area of each triangular face is [tex]\(\frac{1}{2} \times b \times a = \frac{1}{2} \times 9 \times 14 = 63\)[/tex] square inches.
Since there are four triangular faces in a square pyramid, the total surface area of the triangular faces is [tex]\(4 \times 63 = 252\)[/tex] square inches.
Adding the surface area of the square base and the total surface area of the triangular faces, we get [tex]\(81 + 252 = 333\)[/tex] square inches.
Therefore, Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.
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In 2017 32.2% of college students were minorities. If you took a random group of 500 college students in 2017, then how many of these 500 college students would you expect to be minorities?
In 60
60
seconds, Darrell walks 90
90
meters.
Select the two answers that describe the unit rate at which he walks.
CLEAR CHECK
1.5
1
.
5
seconds per meter
1.5
1
.
5
meters per second
90
90
meters per second
112
1
1
2
meters every second
30
30
meters every second
30
30
seconds per meter
The two answers that describe the unit rate at which Darrell walks are 1.5 seconds per meter and 1.5 meters per second
To find the unit rate at which Darrell walks, we need to determine how many meters he walks per second. We are given that he walks 90 meters in 60 seconds.
Step 1: Divide the total distance by the total time to find the unit rate.
Unit rate = (total distance) / (total time)
Step 2: Plug in the given values and calculate.
Unit rate = 90 meters / 60 seconds
Step 3: Simplify the fraction.
Unit rate = 1.5 meters per second
The two answers that describe the unit rate at which Darrell walks are:
1. 1.5 meters per second
2. 30 seconds per meter (the reciprocal of the unit rate)
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If m<6= 97°, what is m<5
The measure of value of ∠5 is 83°.
Now, It is given that;
Two Lines m and n are parallel with each other and l is the transversal crossing the two given parallel lines.
And, m∠6 = 97°,
Since, Two rays combined into an angle have a single terminal. The point is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
Hence, Then by using the property of liner pair angles, we have
⇒ m∠5 + m∠6=180°
(Because they form a linear pair angles.)
⇒ m∠5 + 97 = 180
Subtract 97 both side, we get;
⇒ m∠5 + 97 - 97 = 180 - 97
⇒m∠5 = 180 - 97
⇒m∠5 = 83°.
Therefore, the value of the measure of ∠5 is,
⇒ ∠5 = 83°.
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whats the longest word ever?
Answer:
Step-by-step explanation:
Pneumonoultramicroscopicsilicovolcanoconiosis
Answer: Supercalafragilisticexpialadocious
Step-by-step explanation:
Find the value of x. Round your answer to two decimal places. Enter deg after any degree value
[tex]\cos(40^o )=\cfrac{\stackrel{adjacent}{32}}{\underset{hypotenuse}{x}} \implies x=\cfrac{32}{\cos(40^o)}\implies x\approx 41.77[/tex]
Make sure your calculator is in Degree mode.
help me- Name the triangle with the following characteristics. sides: 5 cm, 6 cm, 7 cm; Angles: 75° and 60°.
A) acute scalene triangle
B) acute isosceles triangle
C) obtuse scalene triangle
D) right isosceles triangle
Answer
I think it's acute scalene triangle
Step-by-step explanation:
All the angles are less than 90 degrees, which is acute.
Identify any bias in the following survey question.
Do you think the school newspaper should more frequently cover the hockey team and the academic decathlon team?
Choose the correct answer below.
A. There is a bias because the question uses words that cause strong reactions.
B. There is a bias because the question suggests a particular answer.
C. There is a bias because the question combines two or more issues.
D. There is no bias in the survey question.
There is a bias because the question suggests a particular answer. Option B
What is bias?A systematic inaccuracy or departure from the true value that causes inaccurate conclusions to be drawn about a population or topic under study is referred to as bias in research. Any step of the research process, including study design, data collecting, analysis, and interpretation, is susceptible to bias.
It may be caused by a number of variables, including the sample strategy, participant selection, measuring methods, the researcher's own ideas and preconceptions, or the influence of outside variables like funding sources or political motivations.
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What is the volume of the object?
Two rectangular prisms are side by side. The dimensions of the larger rectangular prism are 8 c-m, 6 c-m, and 13 c-m and the dimensions of the smaller rectangular prism are 3 c-m, 4 c-m, and 7 c-m.
A
41cm3
B
526cm3
C
708cm3
D
52,416cm3
The total volume is the one in option C, 708 cubic centimeters.
What is the volume of the object?We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.
Then the volume of the first prism is:
V = 8cm*6cm*13cm = 624 cm³
And the volume of the second prism is:
v' = 3cm*4cm*7cm = 84 cm³
Adding that we will get:
total volume = 624 cm³+ 84 cm³ = 708 cm³
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Explain why every positive number has two square roots.
Answer:
Squaring positive and negative numbers always yields a positive number; the product of two negative numbers is always a positve number. Using √4 as an example, we know the positive answer is 2 since 2 * 2 = 4. However, the negative answer is -2 since -2 * -2 = 4 also.
hat is the domain of the function on the graph?
Answer:
The domain of a function is the set of all possible input values for the function. In this case, the function is a graph, so the domain is the set of all possible x-values that correspond to points on the graph.
To find the domain, we need to consider all of the points on the graph. We can see that the graph extends infinitely to the left and right, so all real numbers are possible input values. Therefore, the domain of the function is all real numbers, or R.
Here is a more formal definition of the domain of a function:
The domain of a function is the set of all real numbers x for which the function f(x) is defined.
In other words, the domain is the set of all input values for which the function produces a valid output value.
Step-by-step explanation:
During the first week of the "Cash for Clunkers" program, the average increase in gas mileage for the new car purchased versus the car traded in was 61%. If the average gas mileage of the new cars was 25.4 miles per gallon, what was the average gas mileage of the cars traded in? Round the answer to the nearest tenth.
The average gas mileage of the cars traded is 15.8 miles per gallon round to the nearest.
Let's assume that the average gas mileage of the cars traded in is x miles per gallon. According to the problem, the average increase in gas mileage for the new car purchased versus the car traded in was 61%. This means that the new car gets 61% more miles per gallon than the car traded in. We can express this relationship mathematically as:
25.4 = x + 0.61x
Simplifying the right-hand side of the equation, we get:
25.4 = 1.61x15.78
Dividing both sides by 1.61, we get:
x = 15.78
Therefore, the average gas mileage of the cars traded in was approximately 15.8 miles per gallon, rounded to the nearest tenth.
To understand this result, we can interpret it as follows: for the first week of the "Cash for Clunkers" program, the average gas mileage of the new cars purchased was 25.4 miles per gallon, which is 61% higher than the average gas mileage of the cars traded in. This suggests that the program was successful in incentivizing people to trade in their old, less fuel-efficient cars for new, more fuel-efficient cars.
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Plants are sold in three different sizes of tray.
A small tray of 10 plants costs £2.50
A medium tray of 40 plants costs £8.40
A large tray of 90 plants costs £12.60
Which size tray of plants is the best value for money?
The size tray of plants which is the best value for money is large tray.
Which size tray of plants is the best value for money?A small tray of 10 plants costs £2.50
Cost per unit = Total cost / number of plants
= £2.50 / 10 plants
= £0.25 per plant
A medium tray of 40 plants costs £8.40
Cost per unit = Total cost / number of plants
= £8.40 / 40 plants
= £0.21 per plant
A large tray of 90 plants costs £12.60
Cost per unit = Total cost / number of plants
= £12.60 / 90 plants
= £0.14 per plant
Hence, the large tray of 90 plants costs £12.60 is the best buy for your money.
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PLEASE ANSWER URGENTLY
Drag the tiles to the correct boxes to complete the pairs. Match the y-coordinates with their corresponding pairs of x-coordinates on the unit circle.
the x coordinates are matched as follows
For y = √110/11 x = ± 1/√(11)
For y = 7/11 x = ± 6√(2) /11
For y = 5/11 x = ±4√(6) /11
For y = 9/11: x = ±2√(10) /11
How to find the x valuesUsing the equation of the unit circle
x² + y² = 1
For y = √110 / 11
x² + (√110/11)² = 1
x² + 110/121 = 1
x² = 1 - 110/121
x² = 11/121
x = ±√(11)/11
x = ± 1/√(11)
For y = 7/11
x² + (7/11)² = 1
x² + 49/121 = 1
x² = 1 - 49/121
x² = 72/121
x = ±√72/11
x = ± 6√(2) /11
For y = 5/11
x² + (5/11)² = 1
x² = 1 - 25/121
x² = 96/121
x = ±4√(6) /11
For y = 9/11
x² + (9/11)² = 1
x² = 1 - 81/121
x² = 40/121
x = ±√40/11
x = ±2√(10) /11
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Quatre ouvriers mettent 12 jours pour réaliser un travail. Dans les mêmes conditions combien de temps mettraient six ouvriers pour réaliser ce travail ?
Find the derivative of f(x)=(3x^2-4x+1)^4
Step-by-step explanation:
[tex]f'(x)=[(3x^2-4x+1)^4]'=4(3x^2-4x+1)^3*(3x^2-4x+1)'=4(3x^2-4x+1)^3*(6x-4)=8(3x^2-4x+1)^3(3x-2);[/tex]
The required derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)
We can use the chain rule and power rule of differentiation to find the derivative of f(x).
Let u = 3x² - 4x + 1, then we have:
f(x) = u⁴
Using the chain rule, we get:
f'(x) = 4u³ * u'
To find u', we can differentiate u with respect to x using the power rule:
u' = d/dx (3x² - 4x + 1) = 6x - 4
Substituting u' and u into f'(x), we get:
f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)
Therefore, the derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)
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What’s 137% x 680? give your answer to 1 decimal place
if we will divide 137 with 100 and then multiply it with 680 you will gett your answer
the answer is 931.6
Answer:
931.6
Step-by-step explanation:
We need to change the percent to decimal form.
137% = 1.37
Multiply this by 680.
1.37 * 680
931.6
HELP PLEASE its worth 30 points
Answer:
i'm pretty sure it is "the graph forms a parabola"
Step-by-step explanation:
What is the area of the patio rounded to the nearest tenth? Use 3.14 for pi
Answer:b
Step-by-step explanation:b
Please help with problems 1-7 please
The probability of drawing a red or green M&M is 29/74.
The probability of drawing an M&M that is not blue or green is 36/74.
the probability of drawing an M&M that is not brown is 69/74.
The probability of drawing a red or green M&M is the sum of their probabilities, since they are mutually exclusive events (meaning that an M&M can't be both red and green at the same time):
P(red or green) = P(red) + P(green) = 8/74 + 21/74 = 29/74
The probability of drawing an M&M that is not blue or green is the complement of the probability of drawing a blue or green M&M:
P(not blue or green) = 1 - P(blue or green) = 1 - (P(blue) + P(green)) = 1 - (17/74 + 21/74) = 36/74
The probability of drawing an M&M that is not brown is the complement of the probability of drawing a brown M&M:
P(not brown) = 1 - P(brown) = 1 - 5/74 = 69/74
To determine which is more likely, drawing a red M&M or drawing an orange M&M, we need to compare their probabilities:
P(red) = 8/74
P(orange) = 12/74
Since 12/74 is greater than 8/74, it is more likely to draw an orange M&M than a red M&M.
The color with the highest chance of being drawn is the one with the highest probability, which is green with a probability of 21/74.
The probability of drawing any M&M is 1, since there is a 100% chance of drawing an M&M when you draw from the bag.
Probability is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
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Find the area under the curve y = 2x4x from 0 to 1. guys pls help me thank you
Given: OA = AC = 2
AB is a tangent line to k(O)
Find: AB
Answer:
AB = 2√3 units-----------------------
Tangent is perpendicular to radius, hence ΔAOB is right triangle.
Given that OA = AB, and we know OA = OC as two radius. Therefore OAC is equilateral triangle, hence all its angles are same:
m∠AOC = 180°/3 = 60°It means ΔOAB is a specific 30x60x90 right triangle.
The ratio of its sides is:
OA : AB : OB = 1 : √3 : 2It gives us that:
AB = OA√3AB = 2√3what's 1=7 x 67.8=75+90
The solutions of the given equations are x = 0 and x = -36.
We have,
To solve these equations:
9x - 7 = -7
We can add 7 to both sides to isolate the variable:
9x - 7 + 7 = -7 + 7
Simplifying the left-hand side and the right-hand side, we get:
9x = 0
Finally, dividing both sides by 9, we get:
x = 0
Next, to solve:
-1 = 5 + x/6
We can begin by subtracting 5 from both sides:
-1 - 5 = 5 + x/6 - 5
Simplifying the left-hand side and the right-hand side, we get:
-6 = x/6
Finally, multiplying both sides by 6, we get:
-36 = x
Thus,
The solutions of the given equations are x = 0 and x = -36.
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The complete question.
9x - 7 = -7
-1 = 5 + x/6
