A blueprint shows an apartment with an area of 15 square inches. If the blueprint's scale is 1 inch : 8 feet. The actual area of the apartment will be 960 square feet.
Dilation:
Inflation is the process of increasing the size of an item without affecting its shape. Depending on the scale factor, the size of the object can increase or decrease. Dilation is a transformation used to change the size of an object. Dilation is used to make objects larger or smaller. This transformation produces an image of the same shape as the original.
The dilation should either stretch or contract the original shape. This transformation is referred to as the "scaling factor".
When zooming in produces a larger image, it is called zooming in.
If dilation produces a smaller image, this is called downscaling.
There is no effect of dilation on the angle.
A blueprint shows an apartment with an area of 15 square inches.
If the blueprint's scale is 1 inch : 8 feet.
Then the scale factor will be 8/1 feet per inch.
Then the actual area square footage of the apartment will be
Actual area = 15 x (scale factor)²
Then the actual area of the footage will be
⇒ Actual area = 15 x (8/1)²
⇒ Actual area = 15 x 64
⇒ Actual area = 960 square feet
Thus, the actual area of the apartment will be 960 square feet.
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Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane. x + 3y + 4z = 9_______.
The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.
To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.
Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.
The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).
Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:
yz + λ = 0
xz + 3λ = 0
x*y + 4λ = 0
x + 3y + 4z - 9 = 0
Solving these equations simultaneously, we get:
x = 1.5, y = 1, z = 2.25, and λ = -0.5625
Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.
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A champion race horse can run 10 000 metres in 60 minutes. What is the average speed in km/h 10,000.show working out.
a champion racehorse runs 10000 metres in 60 minutes what is the average speed in km/h show working out
Answer: We have one km being covered in one minute. So how many km do we cover in one hour? Remember, there are 60 minutes in one hour. Do you think it might be 60 km in one hour? Can you say that a different way, say number of km in one hour? 60 km in one hour. Close. Very good. Now let’s clean up your answer and just say 60 km per hour or 60 ``````````````````````.
Greg sold small boxes of candy for $3 and
large boxes for $5. He sold a total of 21
boxes for $87. How many large boxes did he sell?
Answer:
12 large boxes, 9 small boxes
Step-by-step explanation:
Let s = number of small boxes
l = number of large boxes
We set up and solve this system of equations:
s + l = 21------->3s + 3l = 63
3s + 5l = 87------>3s + 5l = 87
----------------
2l = 24
l = 12, s = 9
What is the answer to this math problem? I can’t seem to figure it out.
Answer:
X
Step-by-step explanation:
We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.
Hope this helps!
Michaela holds her state high school record for the 500-meter freestyle swimming event. She can swim the event in 4 minutes and 50 seconds. At this same rate, how far will she swim in 10 minutes?
Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.
1 minute = 60 seconds
4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds
So, Michaela's rate is:
distance / time = x / 290 seconds
where x is the distance she can swim in 290 seconds.
Simplifying the equation:
x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance
We know that Michaela can swim 500 meters in 290 seconds:
500 meters / 290 seconds = 1.724 meters per second
Therefore, in 10 minutes (600 seconds), she will swim:
distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters
So, Michaela will swim 1034.4 meters in 10 minutes.
Step-by-step explanation:
Mr. Roy captures 15 snapping turtles near some wetland by his house. He marks them with a "math is cool"
label and releases them back into the wild. 6 months later, he captures another 15 snapping turtles - 4 of
which were marked. Estimate the population of snapping turtles in the area to the nearest whole number.
The area's estimated snapping turtIe popuIation, rounded to the cIosest whoIe number, is 56.
WhoIe numbers are aII integers, right?That is correct! As 0 is a whoIe number and aII whoIe numbers were integers, 0 is additionaIIy an integer.
The LincoIn-Petersen index method, which is frequentIy empIoyed to determine the size of a popuIation using a capture-mark-recapture approach, can be utiIized to resoIve this issue.
The estimated popuIation (N) is equaI to (M x C) / R using the foIIowing formuIa:
M is the quantity of peopIe incIuded in the initiaI sampIe (marked turtIes)
C is the second sampIe's size (totaI number of turtIes caught in the second sampIe)
R is the quantity of marked peopIe who were Iocated again in the specimen.
When we enter the specified vaIues into the equation, we obtain:
N = (15 x 15) / 4
N = 56.25
The area's snapping turtIe popuIation is thought to be 56, rounded off to the cIosest whoIe number.
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the pattern continues, on what day will Jackie see a total of 81 clovers?
Jackie would see a total of 81 clovers on the ninth day.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of letters or symbols to represent unknown values or variables, and the use of mathematical operations such as addition, subtraction, multiplication, and division to manipulate these variables and solve equations.
Algebra is used to solve a wide variety of problems in many fields, including science, engineering, economics, and finance. It is also a fundamental tool in mathematics education, providing a basis for higher-level math courses such as calculus and linear algebra.
In algebra, equations are used to represent relationships between variables, and the goal is to find the values of the variables that satisfy the equation. Algebraic expressions, which are made up of variables and mathematical operations, can be simplified using various techniques such as factoring, combining like terms, and using the distributive property.
On the fifth day, Jackie would see nine new clovers (7 + 2) for a total of 25 three-leaf clovers. On the sixth day, she would see 11 new clovers (9 + 2) for a total of 36 three-leaf clovers. On the seventh day, she would see 13 new clovers (11 + 2) for a total of 49 three-leaf clovers. On the eighth day, she would see 15 new clovers (13 + 2) for a total of 64 three-leaf clovers. On the ninth day, she would see 17 new clovers (15 + 2) for a total of 81 three-leaf clovers. Therefore, Jackie would see a total of 81 clovers on the ninth day.
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stuck on this question need some help
Answer:
1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).
2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).
3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).
Is the following an isosceles trapezoid?
A. No, the bases are parallel, but the legs are not congruent.
B. No, the bases are not parallel and the legs are not congruent.
C. Yes, the bases are parallel and the legs are congruent.
D. Yes, all 4 sides are parallel.
The answer is C. Yes, the bases are parallel and the legs are congruent.
What is trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. There are different types of trapezoids, including isosceles trapezoids where the legs are congruent and right trapezoids where one of the angles between a leg and a base is a right angle. A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases, and the non-parallel sides are called the legs. The legs can be either congruent or non-congruent.
There are several types of trapezoids, based on the relationships between their sides and angles:
Isosceles trapezoid: This is a trapezoid where the legs are congruent. The bases may or may not be congruent.
Right trapezoid: This is a trapezoid where one of the angles between a leg and a base is a right angle (90 degrees).
Scalene trapezoid: This is a trapezoid where none of the sides are congruent.
Trapezium: In British English, a trapezium is a quadrilateral with no parallel sides. In American English, this shape is called a general quadrilateral.
Trapezoids are used in many areas of mathematics, including geometry and calculus. In geometry, they can be used to calculate the area and perimeter of various shapes. In calculus, they can be used to calculate integrals over regions with curved boundaries.
Here,
In an isosceles trapezoid, the legs (non-parallel sides) are congruent, and the bases (parallel sides) are also congruent.
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help me fast please I need good grades
A smaller sample size can offer a good estimate of the mean. The expressions population of working adults is not too vast to estimate the mean of the entire group using a sample.
What is expression ?An expression in mathematics is a collection of numbers, variables, and complex mathematical (such as addition, subtraction, multiplied, division, multiplications, and so on) that express a quantity or value.
Expressions might be as basic as [tex]"3 + 4"[/tex] or as complicated as [tex]"(3x2 - 2) / (x + 1)"[/tex] . They may also contain functions like "sin(x)" or "log(y)".
Expressions can indeed be evaluated by swapping values for the variables and performing the algebraic calculations in the order specified.
If [tex]x = 2[/tex] , for example, the formula [tex]"3x + 5"[/tex] equals [tex]3(2) + 5 = 11[/tex] . Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
If Fran chooses a random sample of the working adult population in her town, the mean for that group will most likely be close to the mean for the entire group.
Therefore, A smaller sample size can offer a good estimate of the mean. The population of working adults is not too vast to estimate the mean of the entire group using a sample.
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QUESTION 5
What portion of a whole does two sevenths of five ninths represent?
Answer:
10/63
Step-by-step explanation:
Equation: 2/7 * 5/9
Multiply the numerators: 2*5=10
Multiply the denominators: 7*9=63
Your answer: 10/63
What is result of following operation(4623. 56)10+ (110011. 11)2whare (110011. 11(2 mean that 110011. 11as a number express in base 2
The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].
A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:
System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-
[tex](4623.56)_{10} , (110011.11)_{2}[/tex]
these are in decimal and binary system respectively.
now, we will express them in same system ( here we choose decimal system).
[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]
Now, addition is done below:-
4623.56+51.75= 4675.31.
hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=−6x ^2 +190x−826
As a result, in order to make the most money, the widgets must be sold for $15.83, to the nearest cent.
What are a few selling price examples?The cost that consumers pay for a single piece of a good is known as the price at which it is sold. For instance, if a company produces lamps, the sales unit price is indeed the cost to customers of a single lamp. We must identify the x value that maximizes the profitability function y = -6x² + 190x - 826 in order to estimate the selling price for widgets that will yield the highest profit.
Calculus can be used in this process. The critical points, or maximum and lowest values of the function, can be found by taking the derivatives of a profitability function in relation to x and setting it to zero. The derivative test can then be used to assess if the crucial point is indeed a maximum or even a minimum. If we take the profit function's derivative with regard to x, we get:
y' = -12x + 190
By setting y' to zero and figuring out x, we obtain:
-12x + 190 = 0
x = 15.83
The critical value of x is therefore 15.83.
We must compute the second derivative of a profit function with respect to x to determine if this critical point is indeed a maximum or a minimum:
y'' = -12
The critical point at x = 15.83 corresponds to the greatest value of the money demand function since y" is negative. In order to optimize the profit, the widgets must be sold for $15.83, to the nearest cent.
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Doug is selling his autographed baseball. He bought it for $26 and wants to mark it up 20%. What will the new price be?
Answer:
The answer is $31.20
Step-by-step explanation:
do 20% of 26 and add it to the $26
for the theoretical exponential distribution with a scale of 7, calculate and report the mean, median, standard deviation, and probability of a wheelchair not needing to be serviced for the 16 weeks of the semester.
The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.
What's exponential distributionThe exponential distribution is a continuous probability distribution that describes the time between two consecutive events that occur randomly and independently of each other. This distribution is useful in the fields of reliability, physics, and finance, among others.
The exponential distribution has a single parameter known as the scale parameter, which is denoted by lambda (λ) and is typically expressed in terms of the mean time between failures.The mean, median, and standard deviation are three of the most common summary statistics used to describe a probability distribution.
The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester can also be calculated using the exponential distribution.
Mean: The mean of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143
Therefore, the mean is 1/λ = 1/0.143 = 6.993.
Median: The median of the exponential distribution is equal to ln(2)/λ.λ = 1/7 = 0.143
Therefore, the median is ln(2)/λ = ln(2)/0.143 = 4.837.
Standard deviation: The standard deviation of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143
Therefore, the standard deviation is 1/λ = 1/0.143 = 6.993.
Probability: P(X > 16) = e^(-λx)λ = 1/7 = 0.143X = 16P(X > 16) = e^(-0.143 * 16) = 0.230
Therefore, the probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.
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(a)
A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week? Note that which lunch she orders on which day matters, so the following two selections are considered different.
One possible selection:
Mon: Kung pao chicken
Tues: Beef with broccoli
Wed: Kung pao chicken
Thurs: Moo shu pork
Fri: Beef with broccoli
A different selection:
Mon: Beef with broccoli
Tues: Kung pao chicken
Wed: Kung pao chicken
Thurs: Moo shu pork
Fri: Beef with broccoli
(b)
Now suppose that in addition to selecting her main course, she also selects between water or tea for her drink. How many ways are there for her to select her lunches?
There are 6 ways for the student to select her lunch when she chooses from the given main course selection and chooses between water or tea for her drink selection. 3 × 2 = 6 ways.
The problem is about counting the number of ways that can be possible to select the meal for the student.
The student selects one main course and one drink. The main course consists of one of the following:
beef with broccoli, moo shu pork, or chicken with cashew. She can select water or tea for her drink. Therefore, the total number of ways that can be possible to select her lunch is obtained by multiplying the number of options for each course.For instance, there are three options for main course selection, and two options for drink selection. Therefore, the total number of ways that she can select her lunch
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Look at the inequality.
2x+5<11
Which number line shows the solution to this inequality?
The number line which represents the solution bro the inequality 2x + 5 < 11 is:
An open circle is at positive 3. Everything to the left of the circle is shaded.First, we must solve the inequality so that it looks it's simplest form in order to be represented on a number line.
Solving the inequality is as follows:
2x + 5 < 11y < 6 / 2y < 3.In essence, representation of the inequality, y < 3 on the number line is as follows:
An open circle is at positive 3. Everything to the left of the circle is shaded.
PS: It is only a closed circle if the inequality includes an equal to sign.
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Sophie bikes at the speed of s mph. Her friend rana is slower, her biking speed is only r mph. Today both girls went on 20 mile trip. Each girls was biking at there usual speed. How long did Sophie wait for rana at the finish line
The amount of time Sophie waited for Rana at the finish line can be calculated as 20/r - 20/s, where r is Rana's biking speed in mph and s is Sophie's biking speed in mph.
To find out how long Sophie waited for Rana at the finish line, we need to calculate the time it takes for each of them to complete the 20 mile trip. The time taken can be calculated using the formula: time = distance / speed.
Sophie's time to complete the trip can be calculated as follows:
time taken by Sophie = distance / speed of Sophie
time taken by Sophie = 20 / s
Similarly, Rana's time to complete the trip can be calculated as:
time taken by Rana = distance / speed of Rana
time taken by Rana = 20 / r
Since Sophie waits for Rana at the finish line, she would have to wait for the amount of time it takes for Rana to finish the trip. Therefore, the total waiting time would be the time taken by Rana to complete the trip minus the time taken by Sophie to complete the same trip:
waiting time = time taken by Rana - time taken by Sophie
waiting time = 20/r - 20/s
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Exercise 16.8. Prove Theorem 16.8 following the outline below: Let p be a prime number that is irreducible in Zi]. We wish to show that Z,[i] is a field. Let [c] + [d]i be a nonzero element of Zp[i], with [c] and [d] in Zp. (Thus we may take c and d to be integers representing their congruence classes.) We need to prove that [cl+ Idi is a unit. 1. Notice that [c +(di is a unit if one of [e and [d is [0 and the other is not. 2. Having taken care of the case in which one of [c and [d is the zero congruence class in Zp, suppose now that [cj and [d are both nonzero elements of Zp[i]. Observe that in Zj, the prime p cannot divide c + di (why?), so that p and c+ di are relatively prime. 3. Deduce that in this case, by Theorem 16.7, there exist Gaussian integers r and s such that (c + d)r = 1 + ps. 4. Supposer e fi for integers e and f. Deduce that in Zp[l. 5. Conclude that Zpli] is a field.
The theorem is Every nonzero element in the ring has an inverse, hence we deduce that Z[i]/(p) is a field. For any prime number p that is irreducible in Z[i], as asserted, Z[i]/(p) is a field.
Proof of Theorem is Let p be a prime number that is irreducible in Z[i]. We want to show that Z[i]/(p) is a field, where (p) denotes the ideal generated by p.
Suppose that [c] + [d]i is a nonzero element of [tex]Z[i]/(p)[/tex], where [c] and [d] are congruence classes in Zp.
If one of [c] and [d] is [0], then [c] + [d]i is a unit, since the other element is nonzero. So, suppose that [c] and [d] are both nonzero in Zp.
We observe that p cannot divide c + di in Z[i] since p is irreducible in Z[i] and it cannot divide both c and d. Therefore, p and c + di are relatively prime in Z[i].
By Theorem 16.7, there exist Gaussian integers r and s such that [tex](c + di)r = 1 + ps.[/tex]
Now, suppose that [e] + [f]i is another nonzero element of Z[i]/(p), where [e] and [f] are congruence classes in Zp. We want to show that [e] + [f]i is also a unit.
Since p and c + di are relatively prime, there exist integers u and v such that [tex]pu + (c + di)v = 1[/tex] , by Bezout's identity.
Multiplying both sides by e + fi, we get:
[tex]pue + (c + di)ve + (ce - df) + (cf + de)i = e + fi[/tex]
Therefore, [tex](e + fi)(ue + vi(c + di)) = (e + fi)(1 - (cf + de)i)[/tex]
Multiplying both sides by the conjugate of (e + fi), we get:
[tex](e + fi)(e - fi)(ue + vi(c + di)) = (e^2 + f^2)[/tex]
Since p is irreducible in Z[i], it is also prime. Thus, Z[i]/(p) is an integral domain, which means that the product of two nonzero elements is nonzero. Therefore, [tex]e^2 + f^2[/tex] is nonzero in Zp, and
so [tex](e + fi) (ue + vi(c + di))[/tex] is a unit in Z[i]/(p).
We conclude that Z[i]/(p) is a field since every nonzero element has an inverse in the ring.
Therefore, Z[i]/(p) is a field for any prime number p that is irreducible in Z[i], as claimed
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there are four bacteria in an egg salad that is left out at room temperature. after two hours, how many bacteria will be in the egg salad?
The number of bacteria in an egg salad that is left out at room temperature is 256 option D.
The bacteria would double 4 times in 2 hours, so the total number of bacteria in the egg salad would be 256.
So we have 4 bacteria after 2 hours we have,
4 x 4 x 4 x 4 = 256 bacteria.
Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring.
Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilised in probability distribution, in which you will learn about the possible results of a random experiment. To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.
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Complete question:
There are four bacteria in an egg salad that is left out at room temperature. After two hours, how many bacteria will be in the egg salad?
- 32
- 2048
- 8
- 256
A box shaped like a right rectangular prism measures 8 inches by 6 inches by 5 inches. What is the length of the interior diagonal of the prism to the nearest hundredth
Answer:
Step-by-step explanation:
The diagonal length of a right rectangular prism is given by the formula (l2 + w2 + h2) units. The length of the diagonal of this rectangular box is 5√2 cm.How do you find the length of a diagonal in a rectangular prism?Therefore, the equation for the diagonal length of a right rectangular prism is (l2+w2+h2), where l is the length, b is the breadth, and h is the height.
Question 6(Multiple Choice Worth 2 points)
(Laws of Exponents with Integer Exponents MC)
Which expression is equivalent to
O
O
74
310
74
310
3
74
(7-2.35) ²2
Answer:
7^4/3^10 is the correct answer
How can I use the compound angle formula to write sin 165degrees as surds?
We may approximate the sin 165 angles using trigonometric formulas as: tan 165°/(1 + tan2(165°)) (1-cos2(165°))...
Trigonometric identities enable the expression of sin 165° as,
Sin (15°) = sin(180° - 165°)
(-sin 180 + -sin 165) = -sin 345
cos(-75°) = cos(-90° - 165°)
(90 + 165)/255 = -cos 255
Explanation: We know that cos(165) is negative and sin(165) is positive because 165 is in QII. We will use 330 with in half angle formulae because 165=3302.
165 degrees are somewhere between 90 and 180 degrees. Hence, it has an acute angle.
Hence, the 165° angle's addition is 15°. Q. Below are a few angles' measurements.
525 is a positive number of interactions angle, while 195 is a negative coterminal angle.
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Solve for x to the nearest tenth.
8
3
4
7
Answer:
x=4.9
Step-by-step explanation:
using the Pythagorean theorem to find the leg of tringle A:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]y^{2} +3^{2} =7^{2}[/tex]
[tex]y^{2} +9=49\\y^{2} =40\\\sqrt{y^{2} } =\sqrt{40} \\y=\sqrt{40}[/tex]
we know that the hypotenuse for tringle B is [tex]\sqrt{40}[/tex] so, now we can find the value of x:
using the Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]4^{2} +x^{2} =(\sqrt{40} )^{2}[/tex]
[tex]16+x^{2} =40\\x^{2} =24\\\sqrt{x^{2} } =\sqrt{24} \\x=4.9[/tex]
a market sells five kinds of cups, 4 kinds of saucers, and 2 kinds of spoons. How many ways are there to buy two objects of different types?
There are 84 ways to buy two objects of different types.
How to choose two objects of different types ?To choose two objects of different types, we can choose one type of object first and then choose one object from that type and one object from the other two types.
The number of ways to choose one type of object is 3 (cups, saucers, or spoons). For each type of object, there are different numbers of objects to choose from:
Cups: 5 objectsSaucers: 4 objectsSpoons: 2 objectsSo, the total number of ways to choose two objects of different types is:
3 x (5 x 4 + 5 x 2 + 4 x 2) = 3 x 28 = 84
Therefore, there are 84 ways to buy two objects of different types.
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A.14.5 square inches
B.29 square inches
c.20.5 square inches
d.32 square inches
Answer:
d. 32 in.²
Step-by-step explanation:
Bottom face: 6 in. × 0.5 inch
Side faces: 2 × 5 in. × 0.5 in.
Front and back faces: 2 x 6 in. × 4 in. / 2
surface area = 3 in.² + 5 in.² + 24 in.²
surface area = 32 in.²
Andrew can row his boat downstream 15 miles in the same amount of time as it takes him to row upstream 8 miles. If the current in the river is 2 mph, how fast can Andrew row in still water? (round to the tenth)
hint: t=d/t
The time that Andrew can use to row his boat in still waters would be = 5.75 hrs.
How to calculate the speed of the boat in still water?The speed can be defined as the scalar quantity that shows that amount of distance that is covered with respect to time.
The formula that can be used to calculate speed = distance/time.
The speed of the current in the river = 2 mph
The distance covered downstream = 15miles
The distance covered upstream = 8
average distance = 15+8/2 = 11.5 miles
Given 2 miles = 1 HR
11.5 miles = X
Make X the subject of formula;
X = 11.5×1/2
= 5.75 hrs
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Solve the given differential equation by undetermined coefficients.y" - 8y' +16y = 24x +2
The solution to the differential equation y" - 8y' + 16y = 24x + 2 is y = (c1 + c2 x) e^(4x) - 3x + 1 plus any constants determined by initial or boundary conditions.
To solve the given differential equation y" - 8y' + 16y = 24x + 2 using the method of undetermined coefficients, we first find the complementary solution of the homogeneous equation y" - 8y' + 16y = 0:
The characteristic equation is r^2 - 8r + 16 = 0, which has a double root of r = 4. Therefore, the complementary solution is y_c = (c1 + c2 x) e^(4x).
Next, we need to find a particular solution for the non-homogeneous equation. Since the right-hand side has two terms, we can try a particular solution of the form y_p = Ax + B for the homogeneous term and y_p = C for the constant term.
Substituting this form into the differential equation, we get:
y_p" - 8y_p' + 16y_p = 24x + 2
Taking the derivatives and plugging them back into the equation, we get:
-8A + 16B + 16C = 2
0 + 0 + 16C = 24
Solving for A, B, and C, we get A = -3, B = -1/2, and C = 3/2.
Therefore, the particular solution is y_p = -3x - 1/2 + 3/2 = -3x + 1.
The general solution is then y = y_c + y_p = (c1 + c2 x) e^(4x) - 3x + 1.
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Please help me answer
Stephanie puts thirty cubes in a box. The cubes are 1\2 inches on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?
If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.
To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.
Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:
30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches
The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.
The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.
Now, we can calculate the volume of the box by multiplying its length, width, and height:
Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.
In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.
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