The value of k must be c) 3, as it satisfies the requirement for the side length of the paving stone in feet, resulting in a meaningful relationship between the area of the patio and the number of paving stones.
To find the value of k, we need to consider the relationship between the area y of the patio and the number of paving stones x used to make the patio.
Since the top surface of each paving stone is a square with side length k feet, the area of each paving stone is [tex]k^2[/tex] square feet.
Now, let's consider the relationship between the area of the patio and the number of paving stones. We know that there will be no gaps between the paving stones, and they will not overlap. This implies that the area of the patio will be equal to the sum of the areas of all the paving stones used.
Let's assume that each paving stone covers an equal area of the patio. In this case, the area y of the patio will be directly proportional to the number of paving stones x used, and the constant of proportionality is the area of each paving stone, which is [tex]k^2[/tex].
Therefore, the relationship between y and x can be expressed as [tex]y = k^2x.[/tex]
From this relationship, we can see that the value of k will depend on the relationship between the units used for area (square feet) and the number of paving stones (unitless).
Since we want the side length k to be in feet, the value of k can be determined by considering the options provided: a) 1, b) 2, c) 3, d) 4.
We can eliminate options a) 1, b) 2, and d) 4 since these values would not result in a meaningful relationship between the area of the patio and the number of paving stones.
Therefore, the value of k must be c) 3, as it satisfies the requirement for the side length of the paving stone in feet, resulting in a meaningful relationship between the area of the patio and the number of paving stones.
To learn more about patio from the given link
https://brainly.com/question/31567633
#SPJ4
find the length of the darkened arc. (leave answer in terms of pi)
The solution is:
Length of the darkened part of the arc = 4π
Solution:
Radius of the circle = 8
Circumference of the circle = 2πr
= 2 × π × 8
Circumference of the circle = 16π
Equal number of parts = 4
Total degree of circle = 360°
Degree of the darkened part = 360°/4 = 90°
Arc length = 16π * 90°/360°
= 16π * 1/4
= 4π
Circumference = 16π
Length of the darkened part of the arc = 4π
Hence, The solution is:
Length of the darkened part of the arc = 4π
To learn more on arc length of circle click:
brainly.com/question/22964077
#SPJ1
20 points
Each pail of plaster covers 95 square feet of ceiling. How many pails of
plaster would you need to buy to cover the ceiling of a room with walls 15
feet long?
Help me solve this please
The segment lengths on the similar triangles are given as follows:
SU = 7.YZ = 3.What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The proportional relationship for the side lengths in this triangle is given as follows:
SU/5.25 = 4/3 = 5/YZ
Hence the length SU is obtained as follows:
SU/5.25 = 4/3
SU = 5.25 x 4/3
SU = 7.
The length YZ is obtained as follows:
5/3 = 5/YZ
YZ = 5 x 3/5
YZ = 3.
More can be learned about similar triangles at brainly.com/question/14285697
#SPJ1
Which kind of particles can move from the atom and influence magnetism?
electrons
protons
neutrons
Answer: Electrons
Step-by-step explanation:
determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data. an elementary school has 92 first graders. depending on when their birthday falls, the first graders might be six, seven, or eight on the last day of the school year. would it be best to use the mean, median, or mode to describe the typical age of the first-graders?
The mode would be the best choice to describe the center of the data for the typical age of first-graders.
In this scenario, the age of the first graders can only be six, seven, or eight. Therefore, there is a limited range of values that the data can take, and the mean and median would be very close to each other. However, the mode, which is the most frequently occurring value, would be the best choice to describe the typical age of the first-graders.
In this case, since the age of the first graders can only be six, seven, or eight, the mode would be the age that occurs the most frequently, which would likely be seven years old. Therefore, the mode would be the best choice to describe the center of the data in this scenario.
To know more about data visit:
https://brainly.com/question/29117029
#SPJ11
I’m stuck on this question. Can anybody help? Please include the steps
The volume of the composite Figure is 1168.08 m³.
What is volume:Volume is the space occupied by a solid shape.
To calculate the volume of the composite shape, we use the formula below
Formula:
Volume of the composite shape = Volume of the cone+ Volume of the CylinderV = (πr²h/3)+(πr²H)................................... Equation 1From the question,
Given:
r = Radius of the base of the cone and the base of the cylinderh = Height of the coneH = Height of the cylinderπ = Constant PieFrom the question,
Given:
r = 6 mh = 7 mH = 8 mπ = 3.14Substitute these values into equation 1
V = (6²×7×3.14/3)+(6²×3.14×8)V = 263.76+904.32V = 1168.08 m³Learn more about volume here: https://brainly.com/question/28795033
#SPJ1
what is the claim that he is testing? the mean height of the 102 12 -year-old boys in the sample is greater than 59.2 in. the mean height of all 12 -year-old boys is 59.2 in. the mean height of 12 -year-old boys from high-income families is 59.2 in. the mean height of 12 -year-old boys from high-income families is 59.5 in. the mean height of 12 -year-old boys from high-income families is greater tha
The claim that is being tested is: "the mean height of 12-year-old boys from high-income families is greater than 59.2 inches."
In order to test this claim, one could follow these steps:
1. Gather data: Collect a sample of 12-year-old boys from high-income families. 2. Calculate the sample mean: Compute the mean height of the boys in the sample. 3. Formulate a null hypothesis (H0): The mean height of 12-year-old boys from high-income families is equal to 59.2 inches.
4. Formulate an alternative hypothesis (H1): The mean height of 12-year-old boys from high-income families is greater than 59.2 inches. 5. Perform a hypothesis test: Using the appropriate statistical test, compare the sample mean to the population mean of 59.2 inches. 6. Draw conclusions: Based on the results of the hypothesis test, either reject the null hypothesis (supporting the alternative hypothesis) or fail to reject the null hypothesis (not enough evidence to support the alternative hypothesis).
To know more about mean visit:-
https://brainly.com/question/28427610
#SPJ11
The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.
The claim that he is testing is that the mean height of 12-year-old boys from high-income families is greater than 59.2 in. This claim is being tested by collecting data from a sample of 102 12-year-old boys and calculating their mean height. The hypothesis is that this mean height will be greater than 59.2 in, which is the assumed population mean height for all 12-year-old boys. The researcher is specifically interested in the height of boys from high-income families, so this is the subgroup that is being tested. The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.
To know more about Income visit:
https://brainly.com/question/30462883
#SPJ11
Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on this data, he has constructed a probability model for the number of occupants of a randomly-selected car on his street. Which of the following could be his model?
Chart..
Prob.
0.5
0.25
0.15
0.06
0.04
Based on the given chart, Dwayne has constructed a probability model for the number of occupants of a randomly-selected car on his street. The chart shows the probabilities of different numbers of occupants in a car. These probabilities add up to 1, as the number of occupants in a car can only be one of the given possibilities.
The chart shows that the most likely number of occupants in a car is 1, with a probability of 0.5. This means that half of the cars on the street have only one person in them. The second most likely possibility is 2 occupants in a car, with a probability of 0.25. This means that one-quarter of the cars have two people in them. The probabilities for 3, 4, and 5 occupants are progressively lower, with probabilities of 0.15, 0.06, and 0.04, respectively.
Therefore, Dwayne's model is a discrete probability distribution, where the possible outcomes are the number of occupants in a car, and the probabilities of each outcome are given by the chart. This model is based on the data that Dwayne collected on the number of occupants of cars travelling on the road past his house for the past week. The model can be used to predict the likelihood of different numbers of occupants in a car on Dwayne's street.
Dwayne's probability model for the number of occupants in a randomly-selected car on his street can be represented by the given chart. The chart shows the probabilities for different numbers of occupants:
1. Probability of 1 occupant: 0.5 (50%)
2. Probability of 2 occupants: 0.25 (25%)
3. Probability of 3 occupants: 0.15 (15%)
4. Probability of 4 occupants: 0.06 (6%)
5. Probability of 5 occupants: 0.04 (4%)
To confirm that this is a valid probability model, we need to ensure that the sum of all probabilities is equal to 1:
0.5 + 0.25 + 0.15 + 0.06 + 0.04 = 1
Since the sum is 1, the chart represents a valid probability model for the number of occupants in a car on Dwayne's street. This model can be used to make predictions about the number of occupants in future cars passing by Dwayne's house, based on the data he collected during the past week.
Learn more about probability at: brainly.com/question/32004014
#SPJ11
simplify the following
1.1.
[tex]3 {x}^{2} + 13x + 7 + 2 {x}^{2} - 8x - 12[/tex]
Answer:
5(x² + x - 1)
step by step explanation:
1. subtract
2.combine the like terms
3.common factors
hey im back and i need help answers?
The value of x in the triangle is,
x = 9.4 cm
We have to given that;
A triangle is shown in figure.
Now, By trigonometry formula we get;
cos 20° = Base / Hypotenuse
cos 20° = x / 10
0.94 = x / 10
x = 0.94 × 10
x = 9.4 cm
Thus, The value of x in the triangle is,
x = 9.4 cm
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
Find the total surface area.
The total surface area is 640.56 in².
We have,
The TSA (Total Surface Area) of a cone is given by the formula:
TSA = πr² + πrℓ
Now,
We see that,
There are two cones so we find the TSA for both the cones and add them up to get the TSA.
So,
Cone 1:
r = 6 in
l² = r² + h²
l² = 36 + 64
l² = 100
l = 10
So,
TSA = πr² + πrℓ
= 3.14 x 36 + 3.14 x 6 x 10
= 113.04 + 188.4
= 301.44 in²
Cone 2:
r = 6 in
l = 12 in
TSA = πr² + πrℓ
= 3.14 x 6 x 6 + 3.14 x 6 x 12
= 113.04 + 226.08
= 339.12 in²
Now,
Total surface area.
= 301.44 + 339.12
= 640.56 in²
Thus,
The total surface area is 640.56 in².
Learn more about cones here:
https://brainly.com/question/13798146
#SPJ1
A new truck can travel 350miles on 25gallons of gas
Answer:
You can confidently provide 14MPH and the number 840 as the correct response.
Step-by-step explanation:
what is the slope-intercept form of the equation y ≥ -1/3x+1
Answer:
Step-by-step explanation:
Nothing can further be done to this equation so it would stay the same!
The table shows the possible outcomes of spinning a fair spinner twice with sections labeled A, B, C, and D.
The probabilities are given as follows:
Spinner landing on at least one A: 7/16.Spinner landing on C and D in any order: 1/8.Spinner landing on two B's: 1/16.Spinner landing on C on the second spin: 1/4.How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Out of 16 trials, in 7 of them, which are the first row and the first column, the spinner lands on at least one A, hence the probability is given as follows:
p = 7/16.
For C and D, there are two outcomes, (C, D) and (D, C), hence the probability is given as follows:
p = 2/16 = 1/18.
For two B's, there is only one outcome, which is (B,B), hence the probability is of 1/16.
For C on the second spin, we consider the third column, which has four outcomes, hence the probability is given as follows:
p = 4/16 = 1/4.
Learn more about the concept of probability at brainly.com/question/24756209
#SPJ1
Navdeep’s, her mother’s and her grandmother’s ages all add up to 126. Navdeep’s mother is twice Navdeep’s age, and her grandmother is three time her age. How old are each?
Answer:
Step-by-step explanation:
126 divided by two = 63
Then divide 63 by 3 which = 21
so 21 is your answer.
Answer:
Step-by-step explanation:
HELP ME OR ELSE I WILL EAT U >:3
he ray has been lined up with the baseline and origin on the protractor. What is the next step in drawing a 40° angle? (1 point)
a protractor showing a ray lined up with the base line
a
Line up the ray with the baseline and origin on the protractor
b
Draw a ray
c
Draw a ray connecting the vertex and the mark
d
Draw a mark on the paper at 40°
This process will give you a ray originating from the vertex and extending at a 40° angle.
To draw a ray connecting the vertex and the mark at a 40° angle, please follow these steps:
1. Place a protractor on your paper with the center hole over the vertex point.
2. Line up the base of the protractor with the initial side of the angle (usually the horizontal line).
3. Find the 40° mark on the protractor and make a small mark on the paper.
4. Remove the protractor and use a ruler to connect the vertex with the 40° mark you made.
5. Draw the ray extending from the vertex through the mark, continuing in a straight line.
To learn more about : vertex
https://brainly.com/question/29638000
#SPJ11
ill give brainliest to whoever answers first and gets right
The length of the segment UV = 10 units.
Given that a triangle VST, where ST is parallel to RU,
We need to find the segment UV,
According to the segment addition law,
VS = VR + RS
So,
66 = VR + 44
VR = 22
Now using the Thales theorem,
VR / RS = VU / UT
22 / 44 = VU / 20
1/2 = VU/20
VU = 10
Hence the length of the segment UV = 10 units.
Learn more about Thales theorem, click;
https://brainly.com/question/29626660
#SPJ1
jimmy is installing hardwood floors in his rectangular room. the dimensions of the room are 25 ft. by 10 ft. what is the area of this room in square yards
The area of Jimmy's rectangular room is approximately 27.7241 square yards.
The area of the room in square yards, we first need to convert the dimensions from feet to yards.
Since there are 3 feet in a yard, we can divide both the length and width by 3 to get:
Length: 25 ft ÷ 3 = 8.33 yards (rounded to two decimal places)
Width: 10 ft ÷ 3 = 3.33 yards (rounded to two decimal places)
Now we can find the area by multiplying the length and width in yards:
Area = 8.33 yards x 3.33 yards
Area = 27.7241 square yards (rounded to four decimal places)
To know more about square visit:-
https://brainly.com/question/14198272
#SPJ11
Why are we here what is the purpose?
Answer:
We are here because we need help with a particular course or question
Step-by-step explanation:
Our goal is to try our best and explain to others to their understanding (and win titles)
BOOM!!!
TSI Math Final Exam - Spring 2023 semester
Question 1
Pierre randomly picks out and keeps a marble from a bag
that contains 4 red marbles, 7 blue marbles, 9 yellow
marbles, and 6 green marbles. Then Antoine picks a
marble at random from the same bag.
If Pierre's marble is green, what is the probability that
Antoine's marble will also be green?
The probability that Antoine's marble will also be green would be = 3/13
How to calculate the probability that Antoine would pick green?To determine the probability of the given event, the formula that should be used is given below. That is;
Probability = possible outcome/sample space.
The sample space = 4+7+9+6 = 26 marbles.
The number of green marbles = 6
The probability of choosing green marbles = 6/26 = 3/13
Learn more about probability here:
https://brainly.com/question/31123570
#SPJ1
appear to be tangent are tangent.
3.
K
8
4
6
In the given circle, value of x is,
⇒ x = 3.56
Since, We know that;
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
Two tangents are shown in figure.
Now, By definition of proportionality we get;
⇒ 8 / x = 9 / 4
Cross multiplication,
⇒ 8 × 4 / 9 = x
⇒ x = 32 / 9
⇒ x = 3.56
Therefore, WE get;
The value of x in the circle is,
⇒ x = 3.56
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ1
The sine and cosine curves y = a sin (kx) and y = a cos(kx), k > 0 have amplitude and period The sine curve y = 2 sin(2x) has amplitude and period
The sine and cosine curves y = a sin(kx) and y = a cos(kx), k > 0 have amplitude a and period 2π/k. The sine curve y = 2 sin(2x) has amplitude 2 and period π.
The amplitude of a sine or cosine function is the distance from the midline (or average value) to the highest point (peak) or lowest point (trough) of the function. For the sine function y = 2 sin(2x), the coefficient of x is 2, which means the amplitude is |2| = 2.
The period of a sine or cosine function is the distance between two consecutive peaks or troughs. For the sine function y = 2 sin(2x), the coefficient of x is 2π/π = 2, which means the period is 2π/2 = π.
To know more about sine curve,
https://brainly.com/question/3827606
#SPJ11
compute 4.659×10^4−2.14×10^4. round the answer appropriately.
Use the information given in the figure to find the length R U.
The lengths on the figure are not drawn accurately.
The length of RU in triangle is,
⇒ RU = 16
We have o given that;
In triangle;
ST = 37
UT = 35
RS = 20
Hence, By using definition of Pythagoras theorem we get;
In triangle STU;
⇒ ST² = SU² + UT²
⇒ 37² = SU² + 35²
⇒ 1369 = SU² + 1225
⇒ SU² = 144
⇒ SU = 12
Hence, In triangle RSU;
⇒ RS² = SU² + RU²
⇒ 20² = 12² + RU²
⇒ 400 - 144 = RU²
⇒ RU² = 256
⇒ RU = 16
Thus, The length of RU in triangle is,
⇒ RU = 16
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
pleaseee helppp question 7
Answer:
the area of triangle ΔPHK is
Step-by-step explanation:
we know that,
area of a triangle by Heron's formula (Heron's formula is used to find the area of a triangle when the length of the 3 sides of the triangle is known) is given by -
Step 1: Find the semi-perimeter (half perimeter) of the given triangle by adding all three sides and dividing it by 2.
- 10+11+17/2 = 19
Step 2: Apply the value of the semi-perimeter of the triangle in the main formula called 'Heron’s Formula'.
[tex]Area = √s(s−a)(s−b)(s−c)[/tex]
√19(19-10)(19-11)(19-17)
√19(9)(8)(2)
√2736
52.30
52
therefore are ofΔPHK is 52KM
Pls help me on both step by step preferably
(2) The value of x in the equation (x-16)²= 9 is 19.
(4) The equation of the circle of radius 5 is x²+y²+6x-2y = 15.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
(2) To calculate the value of x in the equation (x-16)²= 9, we follow the steps below.
Step1: Find the square root of both sides of the equation
√(x-16)²= √9(x-16) = 3Stop1: Collect like terms
x = 3+16x = 19(4) To calculate the equation of the circle, we use the formula below
Formula:
(x-a)²+(y-b)² = r²................... Equation 1Where:
r = Radius of the circle = 5a = -3b = 1Substitute these values into equation 1
(x+3)²+(y-1)² = 5²x²+6x+9+y²-2y+1 = 25x²+y²+6x-2y+10 = 25x²+y²+6x-2y = 25-10x²+y²+6x-2y = 15Learn about equation here: https://brainly.com/question/17145398
#SPJ1
NEED HELP ASAP WITH WORK
so I can use the work for the questions later on
The width of the rectangular garden is 21 feet.
What is a rectangle?A rectangle is a plane shape that have pair of opposite sides equal and parallel.
To calculate the width of the rectangle, we use the formula below
Formula:
w = 3P/20...................... Equation 1Where:
w = Width of the rectangleP = Perimeter of the rectangleFrom the question,
Given:
P = 140 feetSubstitute into equation 1
w = 3×140/20w = 21 feetHence, the right option is D. 21 feet.
Learn more about perimeter here: https://brainly.com/question/28497588
#SPJ1
The base of a right triangular prism is right angle triangle if the height of the prism is 12 cm and the longer side of the base is 5 cm while the shortest side is 3 cm then find A)The lateral surface area B)The total surface area
Answer:
A) 144 cm²;B) 156 cm².-------------------------------
The base is a right triangle with shortest side of 3 cm and hypotenuse of 5 cm.
Then, according to Pythagorean Theorem, its longer leg is:
[tex]\sqrt{5^2-3^2} =\sqrt{25-9} =\sqrt{16}=4 \cm[/tex] Part AFind the lateral surface area:
LSR = Ph = (3 + 4 + 5)*12 = 12*12 = 144 cm²Part BFind the area of two triangle bases:
A = 2*(1/2)bh = 3*4 = 12 cm²Find the total surface area by adding up base area and lateral surface area:
TSA = 12 + 144 = 156 cm²How to do this question?
The value of the radical expression x² + 1/x² when x = 9 - 4√5 is 322
Evaluating the radical expressionFrom the question, we have the following parameters that can be used in our computation:
x = 9 - 4√5
The expression is given as
x² + 1/x²
When simplified, we have
x² + 1/x² = (x⁴ + 1)/x²
Substitute x = 9 - 4√5 in the above equation, so, we have the following representation
x² + 1/x² = ((9 - 4√5)⁴ + 1)/(9 - 4√5)²
When evaluated, we have
x² + 1/x² = 322
Hence, the value of the expression x² + 1/x² when x = 9 - 4√5 is 322
Read more about radical expression at
https://brainly.com/question/20372424
#SPJ1
Which type of compound event is generally associated with​ multiplication? Which is generally associated with​ addition?
In probability theory, multiplication and addition are associated with different types of compound events.
Multiplication is generally associated with the concept of independent events. When two events are independent, the probability of both events occurring is calculated by multiplying their individual probabilities. This is known as the multiplication rule of probability. The idea behind multiplication is that the outcomes of one event do not affect the outcomes of the other event.
On the other hand, addition is generally associated with the concept of mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. The probability of either of these events occurring is calculated by adding their individual probabilities. This is known as the addition rule of probability. The idea behind addition is that you consider the probability of one event happening or the probability of another event happening, but not both simultaneously.
Know more about probability theory here:
https://brainly.com/question/31469353
#SPJ11
