Point of y-intercept is (0,1)
What is y-intercepts?In a graph, the point where the line or curve crosses the axis is called the intercept. If a point crosses the x-axis it is x-intercepts. If a point crosses y-axis it is y-intercepts.
Given the function is [tex]y=2.5^{x}[/tex]
y-intercept is the point where the graph of the function crosses the y-axis.
To find the point of y-intercept put x=0 in the given function, we get
if x=0 then [tex]y=2.5^{0}[/tex] ⇒ y=1.
The function crosses at the point 1 in the y-axis.
Hence, point of y-intercept is (0,1)
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g 28. explain whether a variable can be both a. nominal and ordinal b. interval and categorical c. discrete and interval
A variable can be both Nominal and ordinal as shown in the explanation below.
Nominal data is defined as data that's used for naming or labeling variables, without any quantitative value. It's occasionally called “ named ” data – a meaning chased from the word nominal.
Ordinal data is a type of categorical data with an order. The variables in ordinal data are listed in an ordered manner. The ordinal variables are generally numbered, so as to indicate the order of the list.
Age can be both nominal and ordinal data depending on the question types. I.e “ How old are you ” is used to collect nominal data while “ Are you the firstborn or What position are you in your family ” is used to collect ordinal data.
An interval variable is analogous to an ordinal variable, except that the intervals between the values of the numerical variable are inversely spaced.
A categorical variable( occasionally called a nominal variable) is one that has two or further orders, but there's no natural ordering to the orders.
separate variables are innumerable in a finite quantum of time. For illustration, you can count the change in your fund. You can count the plutocrat in your bank account. You could also count the quantum of plutocrat in everyone’s bank accounts. It might take you a long time to count that last item, but the point is it’s still innumerable.
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2040
3. The main engine alone on a rocket can consume the allotted
fuel supply in two-thirds the time it takes the auxiliary engine
alone. Working together they both consume their allotted fuel
in 36 seconds. Formulate an equation to represent the
situation. How long could each be fired alone?
Using equations, the time for the main engine 14.4 seconds and 21.6 seconds for the auxiliary engine
What is the equation to represent the situationLet's call the time each engine takes to consume its allotted fuel supply as "t₁" for the main engine and "t₂" for the auxiliary engine.
From the first piece of information, we know:
t₁ = (2/3)t₂
From the second piece of information, we know that the combined fuel consumption time for both engines is 36 seconds:
t₁ + t₂ = 36
Now we can substitute the first equation into the second:
t₁ + (2/3)t₂ = 36
Combining like terms:
t₂ = 21.6
Finally, substituting t₂ back into the first equation:
t₁ = (2/3)(21.6) = 14.4
So the main engine alone could be fired for 14.4 seconds and the auxiliary engine alone could be fired for 21.6 seconds.
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Use a technique of integration or a substitution to find an explicit solution of the given differential equation. (squareroot x + x) dy/dx = squareroot y + y y =
The explicit solution of the given differential equation is [tex]& y=[c(1+\sqrt{x})-1]^2[/tex]
Solution of the Differential Equation :
Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable)
[tex]\frac{dy}{dx} =f(x)[/tex]Here, the independent variable "x" and the dependent variable "y" are both present.We employ the approach of variable separation to discover the answer to the differential equation. By splitting the equation into two halves, we can find a solution. We integrate both sides after moving all of the equations involving the y variable to one side and all of the equations involving the x variable to the other side.
∫P(y)dy=∫Q(x)dx⇒[tex](\sqrt{x}+x) \frac{d y}{d x} & =(\sqrt{y}+y) \\[/tex]
⇒[tex]\frac{d y}{\sqrt{y}(1+\sqrt{y})} & =\frac{d x}{\sqrt{x}(1+\sqrt{x})}[/tex]
Put [tex]$\sqrt{y}=u \quad \sqrt{x}=v$[/tex]
⇒[tex]& \frac{1}{2 \sqrt{y}} d y=d u \frac{1}{2 \sqrt{x}} d x=d v \\[/tex]
⇒[tex]& \frac{d y}{\sqrt{y}}=2 d u \frac{d x}{\sqrt{x}}=2 d v[/tex]
By substituting,
⇒[tex]& \int \frac{7 d u}{1+u}=\int \frac{2 d v}{1+v} \\[/tex]
⇒[tex]& \ln (1+u)=\ln (1+v)+\ln c \\[/tex]
⇒[tex]& \ln (1+u)=\ln [c(1+v)] \\[/tex]
⇒[tex]& (1+u)=c(1+v) \\[/tex]
⇒[tex]& (1+\sqrt{y})=c(1+\sqrt{x}) \\[/tex]
⇒[tex]& \sqrt{y}=c(1+\sqrt{x})-1 \\[/tex]
⇒[tex]& y=[c(1+\sqrt{x})-1]^2[/tex]
Therefore, the explicit solution of the given differential equation is [tex]& y=[c(1+\sqrt{x})-1]^2[/tex]
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You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is\sigma=100 If you want the margin of error to be approximately 10, which of the following would be the required minimal sample size?
A) 13
B) 271
C) 26
D) 165
The required minimal sample size would be 26. This is because in order to estimate the mean score with a margin of error of 10 and a confidence level of 90%, the sample size must be large enough for the Central Limit Theorem to apply. Therefore, in this case, the sample size would be (1.96*100)/10 = 19.6, which is approximately 26.
1. Calculate the sample size, n: n = (1.96*σ)/m
2. Plug in the values: n = (1.96*100)/10
3. Calculate: n = 19.6
4. Round up: n = 26
The required minimal sample size of 26 is necessary in order to estimate the mean SAT score for a population of students with a 90% confidence interval and a margin of error of 10. This is because, in order for the Central Limit Theorem to apply, the sample size must be large enough. The formula for the sample size is (1.96*σ)/m, where σ is the population standard deviation and m is the margin of error. Plugging in the values, we get (1.96*100)/10, which is approximately 19.6. Therefore, the required minimal sample size is 26. This sample size is necessary in order to make sure that the estimates have a high degree of accuracy and reliability.
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if it is assumed that all 52 5 poker hands are equally likely, what is the probability of being dealt
The probability of being dealt a flush is 0.001980, probability of being dealt a one pair is 0.422569, probability of being dealt two pairs is 0.04753.
a) First select a suit: 4 choices
then, we can have to select 5 cards out of 13: C(13, 5)
required probability: 4*C(13, 5)/C(52, 5)
= 0.001980
b)- We have to select two cards to make a pair: C(4, 2) choices (we have to select 2 from 4 because a suit can't have 2 cards of same number, so we are selecting 2 suits from 4),
then select a number for the pair: 13 choices,
now for remaining three cards: each card can be of same suit but number must be different, i.e. 4³*C(12, 3)
required probability: 13*C(4, 2) * C(12, 3) *4³ / C(52, 5)
= 0.422569
c)- First, we have to select two numbers for two pairs: C(13, 2) ,
Select suits for both pairs: C(4, 2) * C(4, 2) ,
For the remaining one card: 11 choices for the number and 4 choices for the suit,
required probability: C(13, 2)*C(4, 2)*C(4, 2)*11*4/C(52, 5)
= 0.04753
Probability means possibility. It's a branch of mathematics that deals with the circumstance of a arbitrary event. The value is expressed from zero to one. Probability has been introduced in Maths to prognosticate how likely events are to be. The meaning of probability is principally the extent to which commodity is likely to be.
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Complete question:
If it is assumed that all (52 5) poker hands are equally likely, what is the probability of being dealt (a) a flush? (A hand is said to be a flush if all 5 cards are of the same suit.)
(b) one pair? (This occurs when the cards have denominations a, a, b, c, d, wherea, b, c, and d are all distinct.)
(c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, wherea, b, andc are all distinct.)
fill in the blank. counting 67 colonies on a plate with 1ml of the 1:1,000,000 dilution indicates that___bacteria were present in 1ml of the original sample.
By applying the unitary method, counting 67 colonies on a plate with 1ml of the 1:1,000,000 dilution indicates that 67,000,000 bacteria were present in 1ml of the original sample.
The unitary method is a mathematical technique that involves finding a unit value and using it to solve problems. In this case, we need to determine the number of bacteria present in 1ml of the original sample.
The dilution factor represents the ratio of the volume of the original sample to the volume of the diluted sample. In this case, the dilution factor is 1:1,000,000, which means that 1ml of the original sample was diluted with 1,000,000ml of a diluent solution to obtain 1ml of the diluted sample. Therefore, the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample.
Now, let's use the colony count to determine the number of bacteria in the diluted sample. We are told that 67 colonies were counted on the plate with 1ml of the 1:1,000,000 dilution. This means that each colony represents the growth of a single bacterium in the diluted sample. Therefore, the number of bacteria in the diluted sample is 67.
Using the unitary method, we can now determine the number of bacteria in 1ml of the original sample. We know that the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample. Therefore:
Number of bacteria in original sample = Dilution factor x Number of bacteria in diluted sample
Number of bacteria in original sample = 1,000,000 x 67
Number of bacteria in original sample = 67,000,000
So, the answer is that 67,000,000 bacteria were present in 1ml of the original sample.
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Suppose you and a friend are playing a game that involves flipping a fair coin 3 times. Let X = the number of times that the coin shows heads. The probability distribution of X is shown in the table.
The expected number of heads is ______.
The standard deviation of the number of heads is _____. Round to three decimal places.
Answer:
Step-by-step explanation:
A species with an initial population of 350
is growing in an environment where the
carrying capacity is 7000. After 5 years
the population is up to 900. Find the
logistic function that models this
population as a function of time.
Answer:
the logistic function that models the population of this species as a function of time is P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t)).
Step-by-step explanation:
We can use the logistic growth equation to model the population of this species as a function of time:
P(t) = K / (1 + A * e^(-r * t))
Where:
P(t) is the population at time t
K is the carrying capacity of the environment
A is the initial population as a proportion of the carrying capacity (A = P(0)/K)
r is the growth rate of the population
We are given that the initial population A is 350/7000 = 0.05 (since the carrying capacity is 7000). We are also given that after 5 years the population has grown to 900. So we can use this information to find the growth rate r:
P(5) = 900 = K / (1 + A * e^(-r * 5))
We also know that the carrying capacity K is 7000. Substituting these values, we get:
900 = 7000 / (1 + 0.05 * e^(-r * 5))
Multiplying both sides by the denominator and simplifying, we get:
1 + 0.05 * e^(-r * 5) = 7.777...
Subtracting 1 from both sides, we get:
0.05 * e^(-r * 5) = 6.777...
Dividing both sides by 0.05, we get:
e^(-r * 5) = 135.555...
Taking the natural logarithm of both sides, we get:
-ln(135.555...) = -r * 5
Solving for r, we get:
r = 0.1682...
Now that we have the growth rate r, we can use the logistic growth equation to find the function that models the population as a function of time:
P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t))
Therefore, the logistic function that models the population of this species as a function of time is P(t) = 7000 / (1 + 0.05 * e^(-0.1682 * t)).
Need some help on this problem please
The value of x in this figure is equal to: D. 5.
How to determine the value of x?In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
Sum of interior angles = 180 × (5 - 2)
Sum of interior angles = 180 × 3
Sum of interior angles = 540°.
112 + 7x + 5 + 6x + 2 + 10x - 8 + 4x + 24 = 540°.
27x = 135
x = 135/27
x = 5.
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Solve the system it’s 9th grade work and you have to put one solution no solution or infinite many
The system of equations has only one solution and is the point (1, 1)
How to solve the system of equations?Here we have the graph of a system of equations, where we can see that both of them are linear equations.
Whenw e have a graph of a system, the solutions are all the points where the graphs of the equations intercept.
On the given graph, we can see that the two lines intersept at the point (1, 1)
So we have only one solution and is the point (1, 1)
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What is the answer??? I need help ASAP
Answer: x = 41
Step-by-step explanation:
When you add supplementary angles together, you should have a total of 180 degrees. You can set up and equation like this...
(2x - 25) + 3x = 180
Combine like terms. 5x - 25 = 180
Add 25 to both sides to help isolate x 5x = 205
Divide by 5 to both sides to get x by itself. x = 41
A system may or may not be:
1.) Memoryless
2.) Time Invariant
3.) Linear
4.) Casual
5.) Stable
Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) denotes the system output and x(t) is the system input.
a.) y(t)=x(t-2)=x(2-t)
b.) y(t)=[cos(3t)]x(t)
c.) y(t)=\int2t-infinity(x(?t)dt
d.) y(t)=0 for t<0 & x(t)+x(t-2) for t>or=0
e.) y(t)=0 for x(t)<0 & x(t)+x(t-2) for x(t)>or=0
f.) y(t)=x(t/3)
g.) y(t)=dx(t)/dt
A system may or may not be:
a.) Memoryless: Yes, Time Invariant: Yes, Linear: Yes, Casual: No, Stable: Yes
b.) Memoryless: No, Time Invariant: No, Linear: No, Casual: No, Stable: Yes
c.) Memoryless: No, Time Invariant: No, Linear: No, Casual: Yes, Stable: Yes
d.) Memoryless: Yes, Time Invariant: No, Linear: No, Casual: No, Stable: Yes
e.) Memoryless: Yes, Time Invariant: No, Linear: No, Casual: No, Stable: Yes
f.) Memoryless: No, Time Invariant: Yes, Linear: Yes, Casual: No, Stable: Yes
g.) Memoryless: Yes, Time Invariant: Yes, Linear: No, Casual: Yes, Stable: Yes
A memoryless, time invariant, linear, casual, and stable system is an idealized system in which the output is directly proportional to the input and the output at any given time is independent of the outputs at any other time.
The system is stable in the sense that the output does not grow indefinitely as the input increases, and it is casual in the sense that the output at any given time is only affected by the inputs at previous times.
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Assume Marleen adds security Y to her portfolio that is less than perfectly positively correlated with the portfolio. Security Y has the same standard deviation as the portfolio. What will happen to the standard deviation of the portfolio after she adds security Y?
Select one:
It will remain the same
It will decrease
It will increase
It may increase or decrease, depending on the weightings of the portfolio holdings
The standard deviation of the portfolio may increase or decrease, depending on the weightings of the portfolio holdings. after she adds security Y
The portfolio standard deviation as a result of revealing how reliable an investment's earnings are, mean serves as a risk indicator. Because it reveals that the earnings are extremely unstable and fluctuating, a high standard deviation in a portfolio denotes significant risk.
The statistical measure of market volatility used to determine how widely prices deviate from the average price is called standard deviation. The standard deviation will show a low number, which denotes little volatility if prices move within a small range of prices.
The term "standard deviation" (or " σ") refers to a measurement of the data's dispersion from the mean.
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Chris needs 9 tiles to cover length of floor each tile is 7/8 of an inch what is the total length of tiles
The total length of the tiles that Chris needs to cover the floor is 63/8 inches.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to find the total length of the tiles, we need to multiply the number of tiles by the length of each tile.
The number of tiles Chris needs is 9.
The length of each tile is 7/8 of an inch.
To find the total length of the tiles, we can multiply the number of tiles by the length of each tile as follows:
Total length of tiles = Number of tiles x Length of each tile
Total length of tiles = 9 x (7/8) inches
Total length of tiles = 63/8 inches
Therefore, the total length of the tiles that Chris needs to cover the floor is 63/8 inches.
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Complete question is given below.
Chris needs 9 tiles to cover length of floor, each tile is 7/8 of an inch what is the total length of tiles?
To determine if a sum is reasonable you can round each
number to the nearest whole and compare the
estimated sum to the actual sum.
What key phrases did you use?
Look at the tenths place to round to the nearest
whole number.
Compare the estimated sum to the actual sum.
The estimated answer is close to the actual answer.
Round each number to the nearest whole
Compare the estimated sum to the actual sum
Look at the tenths place to round to the nearest whole number
The estimated answer is close to the actual answer
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The key phrases used are:
Round each number to the nearest whole
Compare the estimated sum to the actual sum
Look at the tenths place to round to the nearest whole number
The estimated answer is close to the actual answer
These phrases are all related to the process of approximating a sum by rounding the addends to the nearest whole number and comparing the resulting estimate to the exact sum.
Hence, Round each number to the nearest whole
Compare the estimated sum to the actual sum
Look at the tenths place to round to the nearest whole number
The estimated answer is close to the actual answer
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The cost of 2 game apps is $3.50; the cost of 5 game apps is $8.75. The graph below represents this linear relationship. Select all true statements about the graph.
The statement (i) and (iv) is true.
What is linear equation?An equation containing variables with its highest power as one is called linear equation.
The cost of 2 game apps is $3.50; the cost of 5 game apps is $8.75.
The graph below represents the linear relationship.
By the graph, the equation of the graph is y=1.75x
And the point (0,0) lies on the graph.
The points (7.3,6) and (31.75,51) is not on the line.
Hence, the statement (i) and (iv) is true.
Question:
The cost of 2 game apps is $3.50; the cost of 5 game apps is $8.75.The graph below represents this linear relationship. Select all true statements about the graph.
(i) The equation of the graph is y=1.75x.
(ii) The point (7.3,6) lies on the line.
(iii) The point (31.75,51) lies on the line.
(iv) The point (0,0) lies on the line.
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determine whether the lines and are parallel, skew, or intersecting. if they intersect, find the point of intersection. stewart, james. essential calculus (p. 579). cengage textbook. kindle edition.
The lines L1 and L2 are not parallel and intersect at a single point. We have also found the point of intersection.
If the direction vectors are parallel, then the lines are parallel. If the direction vectors are not parallel but do not intersect, then the lines are skew. If the direction vectors are not parallel and do intersect, then the lines intersect at a single point.
To determine whether the given lines are parallel, skew, or intersecting, we need to compare their direction vectors. The direction vectors of the lines are the coefficients of the parameters t and s in the respective equations. Thus, the direction vector of L1 is <2,-1,3> and the direction vector of L2 is <4,-2,5>.
To check whether the direction vectors are parallel, we can compute their cross product. If the cross product is the zero vector, then the direction vectors are parallel.
<2,-1,3> × <4,-2,5> = (7,2,-10)
Since the cross product is not zero, the direction vectors are not parallel. Thus, the lines are either skew or intersecting.
To determine whether the lines are intersecting, we can set the parametric equations of the lines equal to each other and solve for t and s. This will give us the point of intersection.
3 + 2t = 1 + 4s
4 - t = 3 - 2s
1 + 3t = 4 + 5s
Rearranging the equations, we get:
2t - 4s = -2
t + 2s = 1
3t - 5s = 3
Using Gaussian elimination or other methods, we can solve for t and s:
t = 11/13
s = 2/13
Substituting these values back into either equation gives us the point of intersection:
x = 3 + 2(11/13) = 37/13
y = 4 - (11/13) = 41/13
z = 1 + 3(11/13) = 40/13
Thus, the lines intersect at the point (37/13, 41/13, 40/13).
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Complete Question:
Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.
L1: x = 3 + 2t, y = 4 – t, z = 1 + 3t
L2: x = 1 + 4s, y = 3 – 2s, z = 4 + 5s
(7+3/2) power of 3 in math
(7+3/2)^3
Answer: 614.125
To round to the nearest whole number it would be 614
hope this helped =)
What is 4/16 in simplest form
Can someone help me find the measure of XY
Answer:
108+x=108 or x=108-108
x=72
x+y=108
y=108
x+88-88=108-88
x=92
88+y=88
if my answer is helpful comment
What are the zeros of the function y = 2x^2+7x+3
x=-1/2 and x=-3 are the zeros of the function y =2x²+7x+3
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given function is y= 2x²+7x+3
Factor out the equation
2x²+6x+x+3
2x(x+3)+(x+3)
(2x+1)(x+3)=0
So the roots we get
2x+1=0
x=-1/2 is one zero and x=-3 is another zero.
Hence, x=-1/2 and x=-3 are the zeros of the function y =2x²+7x+3
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what is the answer to the blanks
The distance between point D and E is 17.89 units
What is distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
d=√((x2 – x1)² + (y2 – y1)²).
d = √ (11-3)² + 13-(-3)²
d = √ 8²+ 16²
d = √ 64 + 256
d = √320
d = 17.89 units
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 7 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?
Answer:
there are 458640 different ways to award the six medals.
Step-by-step explanation:
There are two distinct groups in the competition, boys and girls. The order in which the medals are awarded to the groups does not matter, so we can count the number of ways to award medals to the boys and the girls separately, and then multiply the results.
For the boys, there are 7 possible candidates for the gold medal. Once the gold medalist is chosen, there are 6 remaining candidates for the silver medal, and 5 candidates for the bronze medal. So, there are 7 x 6 x 5 = 210 ways to award medals to the boys.
Similarly, for the girls, there are 14 possible candidates for the gold medal. Once the gold medalist is chosen, there are 13 remaining candidates for the silver medal, and 12 candidates for the bronze medal. So, there are 14 x 13 x 12 = 2184 ways to award medals to the girls.
To get the total number of ways to award the six medals, we multiply the number of ways to award medals to the boys by the number of ways to award medals to the girls:
Total number of ways = 210 x 2184 = 458640
Therefore, there are 458640 different ways to award the six medals.
Solve the system of equations using the linear combination method.
fc+d=17
c-d=-3
Enter your answers in the boxes.
C=
d =
The solution of the system of equations is c = 10 and d = 7.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
Given:
A system of equations,
c+d=17 {equation 1}
c-d=-3 {equation 2}
Adding both the equation,
we get,
c + d + c - d = 17 + 3
2c = 20
Divide by 2,
we get,
c = 10 and d = 7.
Therefore, c = 10 and d = 7.
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Mrs. Goldstein baked 24 cookies. 2 thirds of the cookies were oatmeal. How many oatmeal cookies did Mrs. Goldstein bake?
16 cookies were oatmeal
Oatmeal cookies' shelf lifeHow long do cookies with oats last? The cookies can last up to two weeks when kept in an airtight container. The cookies may be frozen and kept for two months. But, these cookies taste best when they are still warm from the oven!
Where do you keep cookies with oatmeal?Keep crisp cakes in a jar with such a loose-fitting cover for cookies which will be consumed within a day or two; keep soft sweets in a jar with a close cover. Wax paper should be placed between the layers of cookies that are exceptionally soft, delicate, iced, or adorned. Many cookies may be frozen.
To find the number of oatmeal cookies, take the total number of cookies and multiply by the fraction that were oatmeal
24 * 2/3 = 48/3 = 16
16 cookies were oatmeal
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City Donuts
recently sold 14 donuts, of which 4 were cream-filled donuts. Considering this
data, how many of the next 7 donuts sold would you expect to be cream-filled donuts?
cream-filled donuts
The expected value of cream-filled donuts the store City Donuts is selling should be 2.
What is the expected value?We are aware of In the realm of probability theory, the expected value, commonly referred to as the expected average, is a generalization of the weighted average.
Given, City Donuts recently sold 14 donuts, of which 4 were cream-filled donuts.
So, The probability of cream-filled donuts is = 4/14 = 2/7.
Therefore, The expected number of cream-filled donuts is,
= (2/7)×7.
= 2.
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4 A set of data has a normal distribution with a mean of 50 and a standard deviation of 8. What percent of the data should be greater than 34?
The Standard Normal Curve
O
2.5%
97.5%
99%
95%
13.5%
13.5%
34% 34%
13.5% 2.5
Answer: 97.5% ( look at the image for the solution )
Step-by-step explanation:
Two stores are shaped like rectangles. Store A is 125 feet long and 80 feet
wide. Store B is 100 feet long and 60 feet wide. Do the stores form similar rectangles?
Explain your reasoning. If they do not form similar rectangles, change one dimension
so the rectangles are similar.
The stores do not form similar rectangles, as the ratios between the equivalent side lengths are different.
What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.To observe if the rectangles are similar for this problem, we must observe if the side lengths of Store B and of Store A have the same ratio, as follows:
Length: 100/125 = 4/5.Width: 60/80 = 3/4.Different ratios, hence not similar.
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Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that angle A1 is smaller than angle A2).
Givens: b = 126, c = 162, angle B = 43 degrees
The triangle ABC has sides of length a = 106.5, b = 126, and c = 162, and angles A = 83.3, B = 43, and C = 53.7. Additionally, we have A₁ = 32.7, A₂ = 32.7, and C₁ = 8.2.
To solve the triangle ABC, we can use the Law of Cosines and the Law of Sines.
First, we can use the Law of Cosines to find the length of side a, which is opposite angle A:
a² = b² + c² - 2bc cos(B)
a² = (126)² + (162)² - 2(126)(162) cos(43)
a = 106.5
Next, we can use the Law of Sines to find angle A:
sin(A) / a = sin(B) / b
sin(A) = (a sin(B)) / b
A = 83.3
To find angle C, we can use the fact that the angles of a triangle add up to 180:
C = 180 - A - B
C = 53.7
Next, we can use the given relationship between angles A₁ and A₂ to find their values:
A₂ = A₁ = 2C₁
A₁ + A₂ + C₁ = 180
A₁ + 2A₁ + A₁/2 = 180
5.5A1₁ = 180
A₁ = 32.7
A₂ = 32.7
C₁= 8.2
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For the pair of parametric equations below, eliminate the parameter to find its Cartesian equation. Also specify the domain and range of your equation using interval notation.
x(t)=2cos(t)
y(t)=2sin(t)
The Cartesian Equation of the given parametric equation is written below
: x^2 + y^2=4
To eliminate the parameter t and find the Cartesian equation, we can use the trigonometric identity: cos^2(t) + sin^2(t) = 1. We can rearrange the given equations to get:
x(t) = 2cos(t)
y(t) = 2sin(t)
Dividing both sides of each equation by 2, we get:
cos(t) = x/2
sin(t) = y/2
Squaring both equations and adding them, we get:
cos^2(t) + sin^2(t) = (x/2)^2 + (y/2)^2
Using the identity, we can simplify the right-hand side to get:
1 = (x/2)^2 + (y/2)^2
Multiplying both sides by 4, we get the Cartesian equation:
x^2 + y^2 = 4
This is the equation of a circle with radius 2 centered at the origin. The domain of this equation is all real numbers, and the range is from -2 to 2 (inclusive) in both the x and y directions, represented as [-2,2].
In summary, the Cartesian equation of the given parametric equations is x^2 + y^2 = 4, with domain of all real numbers and range of [-2,2].
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