The required length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
What is diagonal?A diagonal is a straight line that connects two non-adjacent corners of a polygon, such as a square, rectangle, or any other shape with four or more sides. For a given quesiton, the diagonal of a cube with side length s is given by the formula d = s√3.
Here,
As mentioned in the question, we have given a cube with a length of its side is 5 cm.
We know that the diagonal of a cube with side length s is given by the formula d = s√3.
Substituting s=5 into this formula, we get:
d = s√3.
d = 5√3
Rounding to the nearest tenth, we get d = 8.7 cm.
Therefore, the length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
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A chi-square test involves a comparison between what is observed and what would be expected by _______.
Simplify the expression: -3(4a-5b)
parallel lines r and s are cut by two transversals, parallel lines t and u
In triangle DEF, DG = 10 cm. What is CG?
Answer:
5 cm is the correct answer it would be half of DG
Step-by-step explanation:
Solve △ABC if B=120°, a=10, c=18
write the square root of 23 in exponential form
Can you check my work please!! And don't joke about it! Thanks
Has 320 yards of fencing to enclose a rectangular area. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area
The dimensions of the rectangle that maximize the enclosed area are L = 80 yards and W = 80 yards. The maximum area is A = 80 * 80 = 6400 square yards.
To find the dimensions of the rectangle that maximize the enclosed area using 320 yards of fencing, we'll use the concept of optimization. Let's solve it step by step:
Let's assume the length of the rectangle is L and the width is W.
Perimeter constraint:
The perimeter of the rectangle is given as 2L + 2W, which must equal 320 yards:
2L + 2W = 320
Simplify the perimeter equation:
Divide both sides by 2 to get:
L + W = 160
Express one variable in terms of the other:
Solve the equation for L:
L = 160 - W
Area equation:
The area of the rectangle is given by A = L * W.
Substitute the value of L from the previous step into the area equation:
A = (160 - W) * W
A = 160W - W^2
Maximize the area:
To find the maximum area, we need to maximize the function A = 160W - W^2. This is achieved when the derivative is zero.
Take the derivative of A with respect to W:
dA/dW = 160 - 2W
Set dA/dW = 0 and solve for W:
160 - 2W = 0
2W = 160
W = 80
Substitute the value of W back into the perimeter equation to find the corresponding value of L:
L = 160 - W = 160 - 80 = 80
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The optimization problem involves finding the dimensions of a rectangle to maximize its area using a fixed amount of fencing. The dimensions that maximize the area are both 80 yards, making the maximum area 6400 square yards.
Explanation:The subject of this question is Mathematics, specifically a problem about optimization in the field of Calculus. In the given problem, we wish to find a rectangular area that can be enclosed by 320 yards of fencing that maximizes the area.
Let's designate the rectangular area's width and length as x and y respectively. The problem can now be rephrased. With the total length of fencing equal to 320 yards, you can express this as 2x + 2y = 320. Simplifying this equation, we get x + y = 160, or y = 160 - x.
The area of a rectangle is computed as width times length, or in this case, x(160 - x). This is a quadratic function, and its maximum value happens at the vertex of the parabola defined by this function. For a quadratic in standard form like y = ax^2 + bx + c, the x-coordinate of the vertex is at -b/2a. In this case, the maximum area happens when x = 160/2 = 80.
Substituting this value back into the equation for the rectangle's dimensions gives y = 160 - 80 = 80. So, the dimensions that maximize the area for a rectangle with a parameter of 320 yards are both 80 yards. Therefore, the maximum area possible is 80*80 = 6400 square yards.
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17. Evaluate. Show your work.
a. 6!
b. 6P5
c. 12C3
Can someone please help me with math for college readiness
Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2
***PLEASE HELP**
Rita made $221 for 17 hours of work.At the same rate, how much would she make for 12
hours of work?
Using the concept of proportion, Rita would make $156 for 12 hours of work at the same rate.
We have,
We can use proportions to solve this problem.
Let x be the amount of money Rita would make for 12 hours of work.
We know that Rita made $221 for 17 hours of work,
which can be written as:
221/17 = x/12
To solve for x, we can cross-multiply and simplify:
221(12) = 17x
2652 = 17x
x = 156
Therefore,
Rita would make $156 for 12 hours of work at the same rate.
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A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
It doesn't matter which of the two points on a line you choose to call (x1, y1) and which you choose to call (x2, y2) to calculate the slope of the line.
A. True
B. False
Answer:
the answer is true
Step-by-step explanation:
it's what I got
In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials? a. 0.0554
For two successes in seven binomial trials with a success probability of 0.06, use the binomial probability formula. Calculate (7 choose 2) * (0.06^2) * (0.94^5) to get the probability of 0.0554.
Explanation:To calculate the probability of two successes in seven trials with a success probability of 0.06, you can use the binomial probability formula, which is P(X = k) = (n choose k) * p^k * q^(n-k), where 'n' is the number of trials (7), 'k' is the number of successes (2), 'p' is the probability of success (0.06), and 'q' is the probability of failure (q = 1 - p = 0.94).
First, calculate the binomial coefficient using 'n choose k', which is (7 choose 2). Then, raise the probability of success to the power of the number of successes (0.06^2) and the probability of failure to the power of the number of failures (0.94^5). Lastly, multiply these values together to get the probability.
The calculation is as follows:
(7 choose 2) * (0.06^2) * (0.94^5) = 21 * 0.0036 * 0.7339 = 0.0554
I am confused about this question in trigonometry:
use AE and CE to find the angle
AE = 20, CE = 6
so the angle FOR CAE = tan^-1(6/20) = 16.7 degrees
to Find DF
a^2 = b^2 +c^2-2abcos(A)
a^2 = 10^2 + 14^2 -2(14)(10)cos(16.7)
a^2 = 30
sqrt((30)=5.47 rounded to 5.5
EF =
a^2 = b^2 +c^2-2abcos(A)
a^2 = 20^2 + 14^2 -2(14)(20)cos(16.7)
a^2 = 64
sqrt(64)=8
A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function? graph of function t of x is a curve which joins the ordered pair 0, 1 and 1, 3 and 3, 27. Graph of function p of x is a curve which joins the ordered pair 0, 2 and 1, 3 and 3, 11 and 5, 27 and 6, 38
Final answer:
The function t(x) with ordered pairs (0, 1), (1, 3), and (3, 27) most likely represents the exponential function because it shows rapidly increasing growth rates, which is a defining feature of exponential behavior.
Explanation:
The function that most likely represents the exponential function is the one whose growth rate increases significantly for larger values of x. Examining the ordered pairs, the function t(x), which passes through the points (0, 1), (1, 3), and (3, 27), clearly demonstrates this behavior as the increase between the y-values gets dramatically larger as x increases.
This is a classic characteristic of exponential growth. In contrast, the function p(x) that passes through (0, 2), (1, 3), (3, 11), (5, 27), and (6, 38) shows a more consistent increase in y-values as x increases, indicative of a quadratic function.
Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.
I'm having trouble finding the answer to this question
Karen is trying to determine how long her 4-year-old daughter should sit in time-out for deliberately pouring her juice on the floor. if she uses the suggested estimate, her daughter will be in time-out for:
A good rule of thumb is one minute per year of your child's age. So Karen’s child is 4 years old, she would get four minutes of time-out. If you find that the shorter time-outs aren't having the wanted result, increase the length by half the time (so your 4-year-old would get an extra two minutes, for a total of six minutes).
The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?
multiply 4 by the cos(45)
4 x cos(45) = 2sqrt(2) approximately 2.828cm
so depending how you are supposed to answer, either 2 sqrt(2) or approximately 2.83 cm
Write the total population of india and china.estimate the total population by rounding off each population to nearest 100000
As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of China is 1,388,979,446.
China’s population is equivalent to 18.47% of the total world population.
18.47% of
the total world population is composed by China’s population.
China is ranked number 1 in the list of countries by population.
Rounding that number off to the nearest 100,000, it would be 1,388,980,000.
As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of India is 1,344,431,890.
17.86% of the total world population is composed by India’s population.
India is ranked number 2 in the list of countries by population.
Rounding that number off to the nearest 100,000, it would be 1,344,400,000.
PLEASE HELP!!!! Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
x = _____ or _____
Answer:
-3
Step-by-step explanation:
What is the vertex of the graph of y + 2x + 3 = –(x + 2)2 + 1?
Suppose you are thinking about buying one of two cars. Car A will cost $17,655. You can expect to pay an average of $1230 per year for fuel, maintenance and repairs. Car B will cost about $15,900. Fuel maintenance and repairs for it will average about $1425 per year. After how many years are the total costs for the cars the same? a. 5 years c. 9 years b. 7 years d. 11 years
After 9 years many years are the total costs for the cars the same.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
Given that:-
Car A will cost $17,655. You can expect to pay an average of $1230 per year for fuel, maintenance and repairs. Car B will cost about $15,900. Fuel maintenance and repairs for it will average about $1425 per year. After how many years are the total costs for the cars the same?We can form two-equation for the total cost of the two cars:-
A = 17655 + 1230y,
B = 15900 + 1425y
We wish to know when the cost will become the same for both the cars.
A = B
15900 + 1425y = 17655 + 1230y
Now subtract 15900 from both sides
1425y = 1230y + 1755
Now subtract 1230y from both sides
195y = 1755
Now divide both sides by 195
y = 9 years
Therefore After 9 years, many years are the total costs for the cars the same.
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The volumes of two similar figures 27mm^3 and 1331mm^3. If the surface area of the smaller figure is 18mm^2, what is the surface area of the larger figure
A country population in 1991 was 231 million in 1999 it was 233 million . Estimate the population in 2003 using the exponential growth formula. Round you answer to the nearest million
Answer:
population in 2003 is 234 million.
Step-by-step explanation:
A country's population in 1991 was 231 million
In 1999 it was 233 million.
We have to calculate the population in 2003.
Since population growth is always represented by exponential function.
It is represented by [tex]P(t)=P_{0}e^{kt}[/tex]
Here t is time in years, k is the growth constant, and is initial population.
For year 1991 ⇒
233 = [tex]P_{0}e^{8k}[/tex] = 231 [tex]e^{8k}[/tex]
[tex]\frac{231}{233}= e^{8k}[/tex]
Taking ln on both the sides ⇒
[tex]ln(\frac{233}{231})=lne^{8k}[/tex]
ln 233 - ln 231 = 8k [since ln e = 1 ]
5.451 - 5.4424 = 8k
k = [tex]\frac{0.0086}{8}=0.001075[/tex]
For year 2003 ⇒
[tex]P(t)=P_{0}e^{kt}[/tex]
P (t) = 231 × [tex]e^{(0.001075)(12)}[/tex]
= 231 × [tex]e^{0.0129}[/tex]
= 231 × 1.0129
= 233.9 ≈ 234 million
Therefore, population in 2003 is 234 million.
What is the area for this problem?
C = 2* pi *r = 36 pi
r = 36pi/2pi = 18
We know that A= r^2 * pi
A = 18^2 * pi = 324 pi
the area would be 324PI square units
Find the difference- (ab+3a+7)- (-5ab-2)
Where does the normal line to the parabola, given below, at the given point, intersect the parabola a second time? illustrate with a sketch. (round the answers to three decimal places.) y = 4 x - 2 x^ 2 p = (2, 0)?