For the given circle the value of x = [tex]18^{0}[/tex] and the value of y = [tex]10^{0}[/tex] .
What about circle?
A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius of the circle. The diameter of a circle is the distance across the circle passing through the center, which is equal to twice the radius.
The circumference of a circle is the distance around the outside edge of the circle and is given by the formula C = 2πr, where "r" is the radius of the circle, and "π" (pi) is a mathematical constant equal to approximately 3.14159. The area of a circle is given by the formula A = πr^2, where "r" is the radius.
The circle is a fundamental shape in geometry and is used in many areas of mathematics, science, and engineering. It has many properties that make it useful, such as being able to inscribe it in a square with equal sides, as well as being the shape that minimizes the perimeter for a given area.
According to the given information:
As, we know that when diameter passes through center of circle is form a right angle .
So,
[tex]5x^{0} = 90^{0} \\\\x^{0} = 18^{0}[/tex]
In the same way as we know that sum of all angle of triangle is = [tex]180^{0}[/tex]
i.e.
[tex]5x^{0} + 50^{0} + 4y^{0} = 180^{0}\\\\90^{0} + 50^{0} + 4y^{0} = 180^{0} \\\\4y^{0} = 180^{0} - 90^{0} - 50^{0} \\\\y^{0} = 10^{0}[/tex]
To know more about circle visit:
https://brainly.com/question/29193733
#SPJ1
in metroville 600 total number of residents injured from roller-skating 1,800 total number of deaths from roller-skating 90 total number of deaths from all causes 900 the crude death rate for all causes was:
The crude death rate for all causes in Metroville is 1 per 1,000 residents if the total number of deaths from all causes is 900.
total number of residents injured from roller-skating = 1,800
total number of deaths = 90
deaths from all causes = 900
Therefore, we can set up a proportion:
90 deaths / x residents = 1,000 deaths per 1,000 residents
x = 90,000 / 1,000
x = 90
The total population of Metroville is 90,000 residents.
The crude death rate for all causes is then:
Crude death rate = (total number of deaths / total population) * 1,000
Crude death rate = [tex](90 / 90,000) * 1,000[/tex]
Crude death rate = 1 per 1,000 residents
Therefore, we can conclude that the crude death rate for all causes in Metroville is 1 per 1,000 residents.
To learn more about the Death rate
https://brainly.com/question/14148819
#SPJ4
Harry is organizing a picnic. He can spend at most $24. 00 on beverages. Iced tea costs $2. 00 per gallon and lemonade costs $2. 50 per gallon. If x represents the number of gallons of iced tea and y represents the number of gallons of lemonade, which inequality shows the number of gallons of each drink that he can buy? Identify the number of gallons of iced tea that Harry can buy if he buys 5 gallons of lemonade.
Answer:
Harry can buy 5 gallons of lemonade and 5 gallons of iced tea and still have $1.50 left over from his original $24 dollar budget
Step-by-step explanation:
4. A fish tank is in the shape of a cuboid. It
has a base of width 80cm and length of 1.2 m.
Water is put into the tank to a depth of 70cm.
There are 700 000 small fish in the tank. Each
one of them needs a litre of water.
Is there enough water for the fish in the tank?
The volume of water in the tank won't be enough for the fish.
What is volume of a cuboid?A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;
V = l×w× h
where l is the length, w is the width and h is the height.
The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.
The volume of water the tank can occupy is
V = l× b× h
V = 80× 1200× 70
V = 6,720,000cm³
in litres ;
V = 6,720,000/1000
V = 6720litres
therefore the volume water in the tank is not enough for the fish
learn more about volume of cuboid from
https://brainly.com/question/46030
#SPJ1
at what rate is the base of the triangle changing when the altitude is 20 cm and the area is 120 cm2?
The rate at which the base of the triangle is changing when the altitude is 20 cm and the area is 120 cm^2 is 0 cm/s.
To solve this problem, we need to use the formula for the area of a triangle, which is:
A = (1/2)bh
Where A is the area, b is the base, and h is the altitude.
We know that the area is 120 cm^2 and the altitude is 20 cm. So we can plug in these values and solve for the base:
120 = (1/2)b(20)
240 = 20b
b = 12 cm
Now we need to differentiate both sides of the equation with respect to time (t):
dA/dt = (1/2)(db/dt)h
We are given the value of dh/dt (which represents the rate at which the altitude is changing) is 3 cm/s. We need to find db/dt (which represents the rate at which the base is changing).
Plugging in the values we know, we get:
dA/dt = (1/2)(db/dt)(20)
Solving for db/dt, we get:
db/dt = (2dA/dt)/h
Plugging in the values we know, we get:
db/dt = (2)(0)/20
db/dt = 0 cm/s
Since the area is constant (120 cm²) and the altitude is constant (20 cm), the base of the triangle is not changing. Therefore, the rate at which the base is changing is: 0 cm/s
Learn about application of derivatives here: brainly.com/question/25120629
#SPJ11
if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?
The equation with the new substitutions and conversion factor is a'B'T' = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)*a^6/6 where k is (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2) The intercept value of the log-log graph would have been -1.108.
Starting with Equation 4: T = ka^6/6, we can substitute a = (d/k)^(1/6) and b = (2/3)^(1/2) * (d/k)^(1/3) to get
T = k[(d/k)^(1/6)]^6/6
T = k(d/k)^(1/2)/6
T = (k^(1/2)/6) * d^(1/2)
Now we can rearrange the equation so that a, b, and t are on the left side
a'B'T' = ka^6/6
(a/d)^(1/6) * b^(2/3) * T' = k[(a/d)^(1/6)]^6/6 * T'
(a/d)^(1/6) * (2/3)^(1/2) * (d/k)^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'
(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'
(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) = k^(1/2)/6
k = [(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3)]^2/6
k = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)
With this new conversion factor, the intercept of the log-log graph would have changed. The intercept represents the value of T when a = 1 (since log(1) = 0). Using the new conversion factor, we have
T = (1/6) * (2/3)^(1/3) * d^(1/2) * a^(1/3)
T = (1/6) * (2/3)^(1/3) * d^(1/2)
log(T) = log[(1/6) * (2/3)^(1/3) * d^(1/2)]
log(T) = log(1/6) + log[(2/3)^(1/3)] + log(d^(1/2))
log(T) = log(1/6) + (1/3) * log(2/3) + (1/2) * log(d)
So the intercept of the log-log graph would be log(1/6) + (1/3) * log(2/3) = -1.108, assuming that d is held constant. This intercept represents the value of log(T) when log(a) = 0, or when a = 1. In other words, when a = 1, the predicted value of T would be 0.162 (or 16.2% of its maximum value).
To know more about log graph:
https://brainly.com/question/17009226
#SPJ4
--The given question is incomplete, the complete question is given
" Plug the two substitutions into Equation 4 (T = ka^6/6)). Rearrange the equation so that a, b,t are on the left side of the equation and d remains on the right side, e.g. a'B'T' = ka^6/6 you will figure out what the "k" if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?"--
Springtown Hardware kept an inventory of 697,500 lawnmowers in the past. With a change in management, the hardware store now keeps an inventory of 24% more lawnmowers. How many lawnmowers is that?
Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.
Explain about the percentage:In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. The Latin word "per centum," which meaning "per 100," is where the word "percent" comes from. % is the symbol used to represent percentages.
When a number is expressed in decimal form, you can calculate its percentage by multiplying it by 100. For instance, multiplying 0.5 by 100 gives you the percentage 50%.
Given data:
Springtown Hardware's inventory - 697,500 lawnmowers.
Current inventory of 24% more lawnmowers.
Current inventory = old inventory + 24% of old inventory
Current inventory = 697,500 + 24 % of 697,500
Current inventory = 697,500 + 24 * 697,500/ 100
Current inventory = 697,500 + 24* 6,975
Current inventory = 864,900
Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.
Know more about the percentage:
https://brainly.com/question/24877689
#SPJ1
q= 2-4t/t+3
make t the subject of the formula
(please include steps!!!!) ty
Therefore (t) can be written as **(2 - 3Q) / (Q + 4)**.
Define Q?Within the given equation, Q is a variable. It stands for an unknowable amount or value that can be ascertained by equation-solving.
What exactly is variable?A quantity that can take on any one of a number of values is referred to as a variable. A variable in mathematics is a symbol or letter that denotes an unknowable amount or value. The variable Q in the given equation stands for an unknowable quantity or value that can be ascertained by resolving the equation.
The equation is as follows:
Q = (2 - 4t) / (t + 3)
When we divide both sides by (t + 3), we obtain:
Q(t + 3) = 2 - 4t
When we increase the left side of the equation, we obtain:
Qt + 3Q = 2 - 4t
The result of adding 4t to both sides of the equation is:
Qt + 3Q + 4t = 2
Combining related concepts gives us:
t(Q + 4) = 2 - 3Q
The result of dividing both sides by (Q + 4) is:
t = (2 - 3Q) / (Q + 4)
t can therefore be written as **(2 - 3Q) / (Q + 4)**.
To know more about variable visit:
brainly.com/question/29583350
#SPJ1
Mark earns $8 per hour at a store.
Part A: Write an equation for this situation.
Part B: Create a table. Use h for hours worked and p for pay in dollars.
Part C: What part of your rule shows the number of hours Mark worked?
Part D: One week Mark earned $168. How many hours did he work that week?
Part E: Explain whether or not the equation is a direct variation.
p=8h is the equation.This part is represented in tabular form.The coefficient of h. Mark worked 21 hours that week.Yes, the equation is a direct variation.
What is an equation?An equation is a statement that shows the equality of two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, and division. Equations are commonly used in mathematics, science, and engineering to model real-world situations and solve problems.
Define direct variation?Direct variation is a mathematical relationship between two variables, where a change in one variable results in a proportional change in the other variable. In other words, if two variables are in direct variation, when one variable increases, the other variable increases as well, and when one variable decreases, the other variable decreases as well, in a constant ratio.
Part A: The equation for this situation is p = 8h, where p represents the pay in dollars and h represents the number of hours worked.
Part B:
| Worked (hrs) | Pay (p) |
|------------------|---------|
| 1 | 8 |
| 2 | 16 |
| 3 | 24 |
| 4 | 32 |
| 5 | 40 |
| 6 | 48 |
and so on.
Part C: The coefficient of h, which is 8, shows the number of hours Mark worked.
Part D: We can use the equation p = 8h and substitute p = 168 to find the number of hours Mark worked.
168 = 8h
h = 21
Therefore, Mark worked 21 hours that week.
Part E: Yes, the equation is a direct variation because the pay (p) is directly proportional to the number of hours worked (h) and the constant of variation is 8.
Learn more about direct variation here:
https://brainly.com/question/13977805
#SPJ1
state the name for this figure...50 points
Answer: Trapezoid
Step-by-step explanation:
Answer:
it's also called a quadrilateral with 1 right angle
Ms. Yamato's gross pay is $2644. Her deductions total $548.30.
What percent of her gross pay is take-home pay?
A. 84%
B. 79%
C. 21%
D. 18%
Thus, the correct Percent response is B) 79%.
what is a percent?Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".
If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.
We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:
$2644 - $548.30 = $2095.702.
By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:
($2095.70 / $2644) * 100% = 79%
Thus, the correct response is B) 79%.
To know more about percent visit:
brainly.com/question/28670903
#SPJ1
6²
Which theorem is shown by the diagram above?
a + b = c
C
D
a - b = c
a² + b² = c²
a²-b² = c²
The theorem is shown in a pythagoras theorem is c² = a² + b²
Which theorem is shown in a pythagoras theoremThe theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.
The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Mathematically, we can express this as:
c² = a² + b²
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.
Read more about pythagoras theorem at
https://brainly.com/question/231802
#SPJ1
a quality-control inspector examined 290 iphones and found 9 of them to be defective. at this rate, how many defective iphones will there be in a batch of 16,530 iphones?
The total number of defective iphones from a batch of 16,530 iphones is equal to 513 .
Total number of iphones examined by quality-control inspector =290
Total number of iphones in a batch = 16,530
Number of iphones defective out of 290 = 9
Let us consider x be the number of defective iPhones in the batch of 16,530 iPhones.
Use proportions to find out how many defective iPhones there will be in a batch of 16,530 iPhones.
The proportion of defective iPhones in the sample of 290 iPhones is,
= 9/290
Proportion of defective iPhones in a batch of 16,530 iPhones,
Set up a proportion,
9/290 = x/16530
To solve for x, we can cross-multiply,
⇒ 9 x 16530 = 290 x
⇒ 148,770 = 290 x
⇒ x = 513
Therefore, there will be approximately 513 defective iPhones in a batch of 16,530 iPhones.
Learn more about defective here
brainly.com/question/12937169
#SPJ4
Please help me with this homework
Answer: Circumference = 18 π cm
Step-by-step explanation:
We can use this formula to find the circumference of a circle:
➜ r is equal to the radius, also known as half the width of a circle.
C = 2πr
We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 18.
C = 2πr
C = 2π(9)
C = 18 π cm
Answer: 18π
Step-by-step explanation:
The circumference of a circle is equal to 2πr, with r being equal to the radius. The radius of a circle is defined as the length from any point on the circle to its middlemost point. In this case, we are given the value of the radius as defined by the line. The radius equals 9, which we can plug into the equation.
C= 2πr
C = 2π(9)
C = 18π = 56.55
Hope this helps!
the table shows several packages of assorted spools of thread available at a store. what is the price per spool of each kind of thread?
I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.
However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.
To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).
You can use this method to find the price per spool for each type of thread in the table you are looking at.
For more questions like Spool visit the link below:
https://brainly.com/question
#SPJ11
In the diagram, ABC undergoes a dilation with D as the center of the dilation to create A’ B’ C’. What are possible scale factors of the dilation that will create a A’ B’ C’? Select all that apply.
The scale factor of the dilation must be greater than 1. if the image A'B'C' is bigger than the preimage ABC
What are possible scale factors of the dilationIf the image A'B'C' is bigger than the preimage ABC, then the scale factor of the dilation must be greater than 1.
In other words, the length of any segment in the image is larger than the corresponding segment in the preimage by the same factor.
Since D is the center of the dilation, we can use the ratio of the corresponding side lengths of the image and preimage triangles to find the scale factor.
For example, if we want to find the scale factor for A', we can use:
scale factor = B'C'/BC
Read more about scale factor at
https://brainly.com/question/29229124
#SPJ1
‼️WILL MARK BRAINLIEST‼️
The average distance of electric cars is 275.
The range of the data set is 300.
How to solveGiven:
Average of the data set = 275Range of the data set = 300To find: Average distance of electric cars
Solution:
The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:
250, 250, 250, 400, 300, 300, 350, 100
To find the average distance of electric cars, we can use the formula:
Average = (Sum of all the data points) / (Number of data points)
Substituting the given values, we get:
Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8
Average = 2200 / 8
Average = 275
Therefore, the average distance of electric cars is 275.
Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.
Range = Maximum value - Minimum value
Range = 400 - 100
Range = 300
Therefore, the range of the data set is 300.
Read more about range here:
https://brainly.com/question/24326172
#SPJ1
by considering the curve traced by the parametrisation z(t) = t 2 it3 with −1 ≤ t ≤ 1, show why the condition that z ′ (t) never vanishes is necessary to ensure that smooth curves have no cusps.
To ensure that smooth curves have no cusps, we need to require that z'(t) never vanishes. This condition ensures that the tangent line to the curve changes smoothly and continuously as we move along the curve, without any abrupt changes in direction that would create cusps.
To understand why the condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps, we first need to understand what a cusp is. A cusp is a point on a curve where the tangent line changes direction abruptly, creating a sharp point or corner in the curve.
Now, let's consider the curve traced by the parametrization z(t) = t^2it^3 with -1 ≤ t ≤ 1. To determine whether this curve has any cusps, we need to calculate the derivative of z(t) with respect to t:
z'(t) = 2it^3 + 3t^2i
If we set z'(t) equal to zero and solve for t, we get:
2it^3 + 3t^2i = 0
t^2(2i t + 3i) = 0
This equation has two solutions: t = 0 and t = -3/2i. These are the points on the curve where z'(t) vanishes.
At t = 0, the curve passes through the origin, which is a smooth point. However, at t = -3/2i, the curve has a cusp. To see why, we can look at the behavior of z(t) near this point.
As t approaches -3/2i from either side, the magnitude of t^2 increases without bound, while the magnitude of t^3 remains constant. This means that z(t) approaches infinity along a straight line with slope -3/2i. In other words, the curve has a sharp corner or cusp at this point.
To learn more about tangent visit;
brainly.com/question/30260323
#SPJ11
PLS HURRY!!
The length of ribbons found at a seamstress are listed. 3, 6, 9, 11, 12, 13 What is the appropriate measure of variability for the data shown, and what is its value?
Thus, the appropriate measure of variability found for the given data is 10.
Explain about the range of the data:The difference here between maximum and smallest values in a data set is known as the range. Utilizing the exact same units as the data, it measures variability. More variability is shown by larger values.
The range in statistics refers to the distribution of your data between the lowest and greatest value in the distribution. It is a widely used indicator of variation. Measures of variability provide you with descriptive statistics for summarising your data set in addition to measurements of central tendency.Given length of ribbons:
3, 6, 9, 11, 12, 13
Minimum value = 3
Maximum value = 13
Actually, the range, which is determined by deducting the lowest value from the greatest value in the dataset, would be the proper measure of variability for this data.
Range = Maximum value - Minimum value
Range = 13 - 3
Range = 10
Thus, the appropriate measure of variability found for the given data is 10.
Know more about the range of the data:
https://brainly.com/question/24326172
#SPJ1
ASAP Please help me do a two column proof for this. I am struggling
∠A = ∠C in trapezoid ABCD with arcAB = arcCD, can be proven with the property of isosceles triangles.
How to prove the relation?Since arcAB = arcCD, the lengths of the two arcs are equal. This implies that the lengths of the segments subtended by these arcs, AB and CD, are also equal.
Let E and F be the midpoints of the non-parallel sides AD and BC, respectively. Connect E and F with a line segment EF.
Since E and F are midpoints, DE = EA and BF = FC. In addition, since AB = CD = L, we can say that:
DE + EA = BF + FC
EA = FC
So, by the Hypotenuse-Leg (HL) theorem of congruence, triangles AEF and CFE are congruent:
ΔAEF ≅ ΔCFE
Now, since the triangles are congruent, their corresponding angles are equal:
∠A = ∠C
Find out more on trapezoids at https://brainly.com/question/26303997
#SPJ1
Can please someone help me ASAP? It’s due tomorrow. I will give brainliest if it’s all correct!!
Please do part a, b, and c
The sample space are:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
The favorable outcomes care:
{RS, RT, SR, ST, TR, TS}
The probability is 0.3 or 30%
How to find the sample spacePart A:
The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.
The sample space can be represented as follows:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
Part B:
The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.
The favorable outcomes can be represented as follows:
{RS, RT, SR, ST, TR, TS}
Part C:
To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.
The number of favorable outcomes is 6, and the size of the sample space is 20.
Therefore, the probability of selecting 2 cards that are consonants is:
P(consonants) = favorable outcomes / sample space
P(consonants) = 6 / 20
P(consonants) = 0.3 or 30%
Learn more about sample space at
https://brainly.com/question/10558496
#SPJ1
HELP ME PLEASE!!!!!!!
Answer:
Step-by-step explanation:
Graph # Matching equation
1 |-3x|
2 |-x|
3 -|2x|
You can tell which one matches by finding the slope and whether the V points up or down
Grandpa is shoveling snow on a very cloudy cold windy day. The shovel is
made of aluminum and has a wooden handle. He is all bundled up with a
wool scarf and hat. His gloves and boots are made of leather. What part of
this scene is a part of the biosphere?
Your answer
The first statement which says that the day is cloudy, cold, and windy represents the part of the biosphere respectively.
What is a biosphere?The term "biosphere" (from the Greek "o" for "life" and "sharia" for "sphere"), also referred to as "ecosphere" (from "o" for "environment" and "sphaira"), refers to the whole of all ecosystems on Earth.
It is also known as the Earth's life zone. In terms of matter, the biosphere—which is technically a spherical shell—is a closed system with few inputs and outputs.
It is an open system in terms of energy, with photosynthesis absorbing solar energy at a rate of about 130 terawatts annually.
According to the broadest definition of physiology, the biosphere is the entire ecological system that includes all living things and their interactions, including those with the lithosphere, cryosphere, hydrosphere, and atmosphere.
Therefore, the first statement which says that the day is cloudy, cold, and windy represents the part of the biosphere respectively.
Know more about a biosphere here:
https://brainly.com/question/12467010
#SPJ1
miles around a track each day. If you jogged that distance 4
times last week, how many miles did you jog
According the question given you jogged around the distance of 26[tex]\frac{2}{3}[/tex] miles.
What is an improper fraction?
When the numerator value exceeds the denominator value, the fraction is incorrect. Incorrect fractions can also be expressed in the form of a whole number and a proper number, where the numerator is the remainder and the denominator is left unchanged.
Here, we have
Given: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week.
We have to find out how many miles did you jog.
The total jogging distance will be
= 4(6 2/3) miles
= 4 × 20/3 miles
= 80/3 miles
= 26[tex]\frac{2}{3}[/tex] miles.
Hence, you jog 26[tex]\frac{2}{3}[/tex] miles.
Question: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?
To learn more about the improper fraction from the given link
https://brainly.com/question/20302951
#SPJ1
Prism A and prism B are similar. The volume of prism A is 27 cubic units while the volume of prism B is approximately 512 cubic units. If the surface area of prism B is 128 square units, what is the surface area of prism A?
Answer:
Surface area of prism A is approximately 12.4 square units.
Step-by-step explanation:
Since prism A and prism B are similar, their corresponding side lengths are proportional. Let's use the scale factor k to represent the ratio of the side lengths of prism B to those of prism A. Then, the volume of prism B is (k³)(27) = 27k³ cubic units. Similarly, the surface area of prism B is (k²)(surface area of prism A).
We are given that the volume of prism B is approximately 512 cubic units. Therefore, we can solve for k:
27k³ = 512
k³ = 512/27
k ≈ 3.62
Now, we can use k to find the surface area of prism A:
surface area of prism B = (k²)(surface area of prism A)
128 = (3.62²)(surface area of prism A)
surface area of prism A ≈ 12.4 square units
Therefore, the surface area of prism A is approximately 12.4 square units.
Which sequence of transformations produces R’S’T’ from RST?
On a coordinate plane, triangle R S T has points (0, 0), (negative 2, 3), (negative 3, 1). Triangle R prime S prime T prime has points (2, 0), (0, negative 3), (negative 1, negative 1).
the sequence of transformations that produces R'S'T' from RST is translation 2 units to the right and 3 units down, followed by a rotation of 90 degrees clockwise, and finally a reflection across the x-axis.
What is triangle?A triangle is a polygon since it has a total of three faces along with three vertices. It belongs to the fundamental geometric shapes. Triangles having vertex positions alternating between A and B are referred to as triangles ABC. A unique plane and a triangle in Euclidean geometry appear when the three vertices are not collinear. Due to its three sides and three corners, triangles are considered polygons. The corners of a triangle are defined as the locations where its three sides meet. Three triangle angles are multiplied to get 180 degrees.
To transform triangle RST to R'S'T', we can use the following sequence of transformations:
Translation: Move the triangle 2 units to the right and 3 units down. This will result in triangle R''S''T'' with vertices (2, -3), (-2, 0), (-3, -2).
Rotation: Rotate triangle R''S''T'' 90 degrees clockwise about the origin. This will result in triangle R'''S'''T''' with vertices (3, 2), (0, 2), (2, 3).
Reflection: Reflect triangle R'''S'''T''' across the x-axis. This will result in triangle R'S'T' with vertices (3, -2), (0, -2), (2, -3).
Therefore, the sequence of transformations that produces R'S'T' from RST is translation 2 units to the right and 3 units down, followed by a rotation of 90 degrees clockwise, and finally a reflection across the x-axis.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 3.5 to create triangle A′B′C′. Determine the vertex of point C′.
C′(−10.5, 1)
C′(−10.5, 3.5)
C′(−3, 3.5)
C′(−10.5, −3.5)
The correct option is C′(−10.5, 3.5) i.e. the vertex of point C′ is (-10.5, 3.5).
What is dilation?
In mathematics, dilation is a type of transformation that changes the size of a geometric object, but not its shape or orientation. Dilation is similar to scaling, but it involves a fixed point called the center of dilation, and a scale factor that determines the degree of expansion or contraction.
To determine the vertex of point C′, we need to apply the dilation transformation to the coordinates of the original vertex C(-3,1) using a scale factor of 3.5.
The coordinates of C′ can be found by multiplying the coordinates of C by the scale factor:
C′ = (3.5)C = (3.5)(-3,1) = (-10.5,3.5)
Therefore, the vertex of point C′ is (-10.5, 3.5).
Thus, the correct option is C′(−10.5, 3.5).
To learn more about dilation visit the link:
https://brainly.com/question/3457976
#SPJ1
The dimensions of a triangular prism are given in the diagram find the volume of the prism in cubic feet
The volume of the prism is gotten as 312 cm³.
What is volume?Volume is described as a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units.
The basic formula for volume is length × width × height.
The formula for the volume of triangular prism = area of triangle x length
area of triangle = 1/2 x base x height
⇒ area of triangle = 1/2 x 8 x 6 = 24 cm²
Therefore, volume of the prism = 24 x 13 = 312 cm³
Learn more about volume at: https://brainly.com/question/27710307
#complete question is shown in the diagram
#SPJ1
Find the 11th term of the geometric sequence shown below.
-9x²,-18x7, -36x¹2
12
"...
the 11th term in the given geometric sequence is equal to [tex]-9216x^{52}[/tex]
What is a geometric sequence.A sequence is a list of numbers indexed by the natural numbers 1,2,3,4,5.. A common notation for a sequence is [tex]a_1,a_2,a_3,\cdots[/tex]. Most often for interesting sequences there is some pattern in the list of numbers, and there is some formula to generate the nth number in the sequence. A sequence is called a geometric sequence if the next number number is got from the previous number by multiplying it by a fixed number r. This number is called the common ratio r of the sequence. So if the first number is a, then the second number is ar, the third is [tex]ar^2[/tex]... So that the nth number [tex]a_n = ar^{n-1][/tex].
For example 1 ,3,9,27,81,.... The sum of the first n terms of such a sequence is equal to [tex]$S_n = \frac{a(r^n-1)}{r-1}$[/tex]. if the absolute value of r, [tex]|r| < 1[/tex], then the sum to infinity is [tex]$S = \frac{a}{1-r}$[/tex].
In our question we are given a geometric sequence whose first term :
[tex]$a = -9x^2\,,\textrm{ and common ratio : r } = 2x^5$[/tex] .
So the 11th term is [tex]$ar^{10} = (-9x^2){(2x^5)}^{10} = (-9x^2)(1024x^{50}) = -9216x^{52}$[/tex]
To know more about geometric sequences, visit:
https://brainly.com/question/13008517
#SPJ1
when sampling from a population with , which of the following sample means is more surprising? why? sample a: a random sample of 9 pell grant recipients with a mean award amount of $2750. sample b: a random sample of 36 pell grant recipients with a mean award amount of $2750.
Sample mean in sample b to be less variable and more representative of population mean than sample mean in sample a.
Standard error measures the variability of sample means around the population mean.
It decreases as sample size increases.
Using the formula for the standard error of the mean,
Calculate the standard errors for each sample,
Standard error of sample a
= s/√(n)
= 850/√(9)
= 283.33
Standard error of sample b
= s/√(n)
= 850/√(36)
= 141.67
Where s is the sample standard deviation
And n is the sample size.
The standard error of sample b is smaller than the standard error of sample a.
Sample mean in sample b is more likely to be closer to true population mean than sample mean in sample a.
Therefore, sample mean b is more surprising as larger sample size makes it more likely and accurately represents population mean.
learn more about sample mean here
brainly.com/question/14727460
#SPJ4
Solve the IVP given by y''+y=t, y(0)=1, y'(0)=-2
The solution to the IVP given by y''+y=t, y(0)=1, y'(0)=-2 is y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
To solve the Initial Value Problem, we can use the method of undetermined coefficients, which involves assuming a particular form for the solution to the non-homogeneous equation y'' + y = t, and then finding the coefficients of the terms in that form by substituting it back into the equation.
First, we find the general solution to the homogeneous equation y'' + y = 0
The characteristic equation is r² + 1 = 0, which has solutions r = ±i. Therefore, the general solution to the homogeneous equation is
y_h(t) = c₁ cos(t) + c₂ sin(t),
where c₁ and c₂ are constants determined by the initial conditions.
Next, we assume a particular form for the non-homogeneous solution, based on the form of the right-hand side t. Since t is a linear function, we assume that the particular solution has the form
y_p(t) = a t + b.
Substituting this into the differential equation, we get
y''_p + y_p = t
2a + (at+b) = t.
Equating coefficients, we get
a = 1/2, b = 0.
Therefore, the particular solution is
y_p(t) = (1/2) t.
The general solution to the non-homogeneous equation is then the sum of the homogeneous and particular solutions
y(t) = y_h(t) + y_p(t)
= c₁ cos(t) + c₂ sin(t) + (1/2) t.
To determine the constants c₁ and c₂, we use the initial conditions:
y(0) = c₁ cos(0) + c₂ sin(0) + (1/2) (0) = c₁ = 1,
y'(0) = -c₁ sin(0) + c₂ cos(0) + (1/2) (1) = c₂ - (1/2) = -2,
so c₂ = -3/2.
Therefore, the solution to the IVP is
y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
Learn more about Initial Value Problem here
brainly.com/question/30547172
#SPJ4