The diagram shows a cubeAh=11.3cn correct to the nearest millimetre calculate the lower bound for the length of an edge of the cub you must show all your working
Answers
Answer:
Lower bound for the length of the edge = 42.5 cm
Step-by-step explanation:
From the picture attached,
FH is the diagonal of square EFGH.
Therefore, length of diagonal FH = [tex]\sqrt{FG^2+HG^2}[/tex]
(By applying Pythagoras theorem)
In triangle AFH,
AH² = AF² + FH²
= AF² + [tex](\sqrt{FG^2+HG^2})^2[/tex]
= AF² + FG² + HG²
AH² = 3HG²
(11.3)² = 3(HG²)
HG = [tex]\sqrt{\frac{127.69}{3}}[/tex]
HG = 42.563 cm
For distance correct to the nearest mm, lower bound for the length of the edge = 42.5 cm
And upper bound for the length of the edge = 43.6 cm
The side lengths of a cu be are congruent, so the edge length of the cu be is 65 mm
The length of diagonal A H is given as:
[tex]\mathbf{AH = 11.3cm}[/tex]
Considering triangle A FH, we have:
[tex]\mathbf{AH^2 = A\ F^2 + FH^2}[/tex]
So, we have:
[tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]
Considering triangle HE F, we have:
[tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex]
Substitute [tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex] in [tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]
[tex]\mathbf{11.3^2 = A\ F^2 + EF^2 + EH^2}[/tex]
The side lengths of a cu be are congruent.
This means that: A F = EF = EH
So, we have:
[tex]\mathbf{11.3^2 = A\ F^2 + A\ F^2 + A\ F^2}[/tex]
Evaluate like terms
[tex]\mathbf{11.3^2 = 3A\ F^2}[/tex]
Evaluate squares
[tex]\mathbf{127.69 = 3A\ F^2}[/tex]
Divide both sides by 3
[tex]\mathbf{42.563= A\ F^2}[/tex]
Take square roots
[tex]\mathbf{6.52= A\ F}[/tex]
Rewrite as:
[tex]\mathbf{A\ F = 6.52cm}[/tex]
Convert to m m
[tex]\mathbf{A\ F = 6.52 \times 10mm}[/tex]
[tex]\mathbf{A\ F = 65.2\ mm}[/tex]
Approximate
[tex]\mathbf{A\ F = 65\ mm}[/tex]
Hence, the edge length is 65 mm
Read more about cu bes at:
https://brainly.com/question/23261883
Related Questions
solve all of them for brianiest
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Answer:
1.x= 3/-4-2 = x = 11/4
2.1.5x /1.5 = x
6/1.5=4
x=4
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Answer:
answer is
Step-by-step explanation:
5/8 is the fraction that if added to 3/8 gives you the sum of 1 whole
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Answer:
true
Step-by-step explanation:
your answer is correct
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what is 1 1/2 divided by 2/5? Show your work.
Answers
Answer:
3.75 or 3 3/4
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
1.5/.4=3.75
Answer:
[tex]3 \frac{3}{4}[/tex]
Step-by-step explanation:
[tex]1 \frac{1}{2} / \frac{2}{5} = \frac{3}{2} / \frac{2}{5}[/tex]
[tex]\frac{3}{2}[/tex] × [tex]\frac{5}{2}[/tex]
[tex]\frac{3 times 5 }{2 times 2}[/tex]
[tex]\frac{15}{4} = 3 \frac{3}{4}[/tex]
An opaque bag contains 5 blu marbles, 4 green marbles, and 3 red marbles. If two consecutive marbles are drawn without replacement what is the probability that the first one will be red and the second one will be blue?
Answers
Answer:
Probability[Choosing red and blue consecutive] = 5/44
Step-by-step explanation:
Given:
Number of blue marble = 5
Number of green marble = 4
Number of red marble = 3
Find:
Probability[Choosing red and blue consecutive]
Computation:
Probability of red marble = Number of red marble / Total marble
Probability of red marble = 3 / [5 + 4 + 3]
Probability of red marble = 3 / 12
Probability of red marble = 1/4
Probability of next blue marble = Number of blue marble / [Total marble - 1]
Probability of next blue marble = 5 / [Total marble - 1]
Probability of next blue marble = 5 / [12 - 1]
Probability of next blue marble = 5 / 11
Probability[Choosing red and blue consecutive] = Probability of red marble x Probability of next blue marble
Probability[Choosing red and blue consecutive] = [1/4][5/11]
Probability[Choosing red and blue consecutive] = 5/44
PLEASE HELP ASAP!!!!
Answers
Answer:
yes the answer is 456
Step-by-step explanation:
in a study of 225 adults the average heart rate was 72 beats per minute assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute what does a margin of error of 1.1 for the 90% confidence interval of the average beats per minute mean
Answers
Answer:
There Is A 90% Chance That The Population Mean Is Between 70.9 And 73.1 Beats Per Minute. There Is A 90% Chance That The Population Mean Is Between 62 And 82 Beats Per Minute. There Is A 10% Chance That The Population Mean Is Less Than 72 Beats Per Minute
Hope it helps
-21. A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately normally distributed and has a standard deviation of 20 mm. The company wishes to test mm versus mm, using the results of n 10 samples. (a) Find the P-value
Answers
Answer:
0.057
Step-by-step explanation:
To obtain the p value, we need to obtain the test statistic :
For a one sample test :
Test statistic is given by :
(xbar - μ) ÷ (σ/√(n))
(185 - 175) ÷ (20/√(10))
10 ÷ 6.3245553
Test statistic = 1.581
Qe used the Z distribution because we are working with the population standard deviation.
Using the Pvalue from test statistic calculator :
Pvalue obtained using the Pvalue from Z statistic calculator, we obtain ;
Pvalue = 0.0569
Find the area of The Polygon. 12 points.
will give * branliest *
Answers
Answer:
A = 1/2 × b × h
A = 1/2 × 60 × 30
A = 1/2 x 900
A = 450
--------
A = 1/2 x 6 x 18
A= 1/2 x 54
A = 27
----------
27 + 450 = 477
=477
Step-by-step explanation:
The sum of two numbers is 12 . Their difference is 2 what are two numbers ?
Answers
Answer: 7 and 5
Step-by-step explanation:
I HOPE THIS HELPS
STAY SAFE!!!
Answer:
7 and 5
Step-by-step explanation:
7+5=12
7-5=2
Consider the sequence {3,6,9,12,15,…}. Find n if an = 735. Show all steps including the formulas used to calculate your answer.
Will mark brainliest!
Answers
Answer:
n = 245
Step-by-step explanation:
The given sequence is 3,6,9,12,15,…
nth term of the AP is 735
We know that, the nth term of an AP is given by :
[tex]a_n=a+(n-1)d[/tex]
d is common difference, d = 6-3 = 3
Put all the values to find n.
[tex]735=3+(n-1)3\\\\732=(n-1)3\\\\\dfrac{732}{3}=n-1\\\\n=244+1\\\\n=245[/tex]
So, there are 245 terms in the sequence.
~Help please and ty~ ✨Brainilist✨
Answers
Answer:
[tex]\frac{10}{27}[/tex]
Step-by-step explanation:
[tex]-\frac{2}{9} (-\frac{5}{3})=[/tex]
-2 · 5/ -9 · 3 =
10/27 =
[tex]\frac{10}{27}[/tex]
Answer:
[tex]\frac{10}{27}[/tex]
Step-by-step explanation:
[tex]\frac{-2}{9} *\frac{-5}{3}[/tex]
multiply numerator with the other numerator
-2 × -5 = 10 (numerator)
multiply denominator with the other denominator
9 × 3 = 27 (denominator)
put it in its correct order
[tex]\frac{10}{27}[/tex]A farmer had some chickens and some cows. She counted 40 total heads and 126 total legs. How many cows did she have?
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The profit function of a manufacturer, in dollars, when x units of a certain commodity are produced and sold is given by
P(x)=200x−x2.
(a) The maximum profit is
dollars.
(b) The number of units produced and sold to get the maximum profit is
units.
Answers
Answer:
Derivative: P’(x) = 200 - 2x
If P’(x) = 0 , x = 100
Therefore P’ is positive and P increases until x = 100
So the maximum units to maximize profits is 100 units
And for 100 units the profit in dollar is:
20000 - 10000 = 10000
10000 dollars
Given m|n, find the value of x.
(6x-4)°
(3x+4)°
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Answer:
6x-4+3x+4=180{ straight angel}
9x=180x=180/9x=20°stay safe healthy and happy.....I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current rate is $129.00 per month."
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Find one value of x that is a solution to the equation:
(x2 – 6)2 = -3x2 + 18
Answers
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and d are integers.
1. x2 - 6x + 8 = (ax + b)(cx + d)
2.3x3 - 6x2 - 24x = 3x(ax + b)(cx + d)
3. 2x2 - 2x - 24 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
Answers
9514 1404 393
Answer:
(a, b, c, d) = (1, -4, 1, -2)(a, b, c, d) = (1, -4, 1, 2)(a, b, c, d) = (1, -4, 2, 6)Step-by-step explanation:
Once you remove the common factor from the terms, you are looking for factors of the remaining constant term that have a sum equal to the coefficient of the linear term. These factors are the constants in the binomial factors.
__
1. 8 = (-4)(-2) ⇒ x^2 -6x +8 = (x -4)(x -2)
(a, b, c, d) = (1, -4, 1, -2)
__
2. -8 = (-4)(+2) ⇒ 3x^3 -6x^2 -24x = 3x(x -4)(x +2)
(a, b, c, d) = (1, -4, 1, 2)
__
3. -12 = (-4)(3) ⇒ 2x^2 -2x -24 = 2(x -4)(x +3) = (x -4)(2x +6)
(a, b, c, d) = (1, -4, 2, 6) or (2, -8, 1, 3)
Use a table of values to find the solution to the equation f(x)=h(x) where
f (x) = 2/3-x and
h(x)= 3- 2x
Show your work
Answers
9514 1404 393
Answer:
x = 2 1/3
Step-by-step explanation:
We can examine the equations to see where the solution lies.
f(x) = (2/3) -x
This has an x-intercept where y=0, at x=2/3. It has a y-intercept where x=0, at y=2/3. Its slope is -1.
h(x) = 3 -2x
This has an x-intercept where y=0, at x=3/2. It has a y-intercept where x=0, at y=3. Its slope is -2.
__
In the first quadrant, the graph of h(x) is farther from the origin and steeper than the graph of f(x). The lines must cross in the 4th quadrant at some value of x that is greater than 3/2. The fraction in the definition of f(x) suggests that the solution will be a multiple of 1/3.
The attached table shows a couple of guesses at values of x that would make f(x) = h(x). We find that x = 7/3 is the solution we're looking for.
_____
Additional comment
Repetitive function evaluations are done conveniently and with fewer errors by a calculator or spreadsheet that can work with tables of values. Here, we have used a graphing calculator. These tools are readily available for free on almost any phone, tablet, or desktop computer platform.
PLEASEEEE HELPPPPPPP
Answers
Answer:
the scale factor of RSTU to R'S'T'U' is 1/3
Step-by-step explanation:
look at the graph and count how many squares are needed for the line RS (3) and how many for the line R'S' (9).
this is 1:3 or 1/3
all other sides follow the same ratio.
the point P is diagonally one square down from S and 3 squares down from S'.
100 POINTS!!! For which value of b will the quadratic equation x^2-bx+16=0 have exactly two different integer solutions? Select all that apply.
Answers
The value of b for which the quadratic equation x² - bx + 16 = 0 have exactly two different integer solutions is b > 8
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
A quadratic equation is in the form:
y = ax² + bx + c
Where a, b and c are constants.
If b² - 4ac > 0, then the equation have exactly two different integer solutions.
Given the equation:
x² - bx + 16 = 0, to have exactly two different integer solutions:
(-b)² - 4(1)(16) > 0
b > 8
The value of b for which the quadratic equation x² - bx + 16 = 0 have exactly two different integer solutions is b > 8
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Answer:
x=8
Step-by-step explanation:
Students were asked to choose their favorite sport. If 1/8 of the students chose soccer and 2/8 chose basketball, what fraction chose either soccer or basketball?
Answers
Renaldo has a spinner with 10 equal sectors with labels from 1 to 10. He spins the spinner once. What is the probability that he gets a number that is a multiple of 3, or a 5?
Answers
Answer:
2/5
Step-by-step explanation:
3, 6, 9, 5 is four options
4/10 = 2/5
The area of a triangle is 12 square units. The base of the triangle is 4 units. What is the height of the triangle in units?
Answers
Answer:
6 =h
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
12 = 1/2 (4) h
12 =2h
Divide each side by 2
12/2 = 2h/2
6 =h
Write the equation in slope intercept form. -2x-8y= 24
- please help
Answers
Answer:
y= -2/8x + 3
Step-by-step explanation:
Step-by-step explanation:
The slope-intercept form of the equation is :
y = mx+b
The given equation is :
-2x-8y= 24
Taking x term to RHS.
-8y = 24 +2x
Dividing both sides by -8
[tex]\dfrac{-8y}{-8} = \dfrac{24}{-8} +\dfrac{2x}{-8}\\\\y=-3-\dfrac{x}{4}\\\\or\\\\y=\dfrac{-1}{4}x+(-3)[/tex]
Hence, this is the required solution.
if a bag of rice weighs 55 kg find the weight of 123 bags of rice
Answers
Answer:
6765
Step-by-step explanation:
the answer is 6765
Answer: 6,765 kg
Step-by-step explanation:
55 x 123 = 6,765kg of Rice
in a fruit basket , there are 6 apples and 3 oranges . what fraction of the basket are apples ?
Answers
Answer:
6/9=2/3
hope this helps
have a good day :)
Step-by-step explanation:
Answer: 6/9
Step-by-step explanation:
btw can you please help me with my latest question in my profile? Would really appreciate it!
Lana earns $7.95 per hour . How much does she earn in 8 ?
Answers
What she earns in 8 hours= 7.95 x 8
=$63.9
Answer:
$63.6
Step-by-step explanation:
$7.95=1 hr
$7.95×8=$63.6
Laura uses 3 yards of fabric to make 2 skirts. She uses the same amount of
fabric to make each skirt. At this rate, what is the total amount of fabric, in
yards, she needs to make 6 skirts?
Answers
Answer:
9 yards
Step-by-step explanation:
3 yards make 2 skirts
2x3=6
3x3=9
9 yards make 6 skirts
I need help asap thanks
Answers
Answer:
Square root of 0.028
Step-by-step explanation:
17% = 0.17
1/7 = 0.142
1/8 = 0.125 so it isnt in the inequality
1.7 is outside of the inequality
0.091 is out of the inequality
Square root of 0.028 = 0.167 (So it's in the inequality)
Feel free to mark it as brainliest :D