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
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
[tex]\frac{10}{27}[/tex]
Step-by-step explanation:
[tex]-\frac{2}{9} (-\frac{5}{3})=[/tex]
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Answer:
[tex]\frac{10}{27}[/tex]
Step-by-step explanation:
[tex]\frac{-2}{9} *\frac{-5}{3}[/tex]
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[tex]\frac{10}{27}[/tex]in a fruit basket , there are 6 apples and 3 oranges . what fraction of the basket are apples ?
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Answer:
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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!
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
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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
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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.
__
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__
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__
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)
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?
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Laura uses 3 yards of fabric to make 2 skirts. She uses the same amount of
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Answer:
9 yards
Step-by-step explanation:
3 yards make 2 skirts
2x3=6
3x3=9
9 yards make 6 skirts
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The sum of two numbers is 12 . Their difference is 2 what are two numbers ?
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Step-by-step explanation:
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Answer:
7 and 5
Step-by-step explanation:
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Answer:
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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
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Answer:
answer is
Step-by-step explanation:
Use a table of values to find the solution to the equation f(x)=h(x) where
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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
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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.
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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.
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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
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Answer:
x=8
Step-by-step explanation:
-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
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
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(6x-4)°
(3x+4)°
Answers
Answer:
6x-4+3x+4=180{ straight angel}
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Answer:
true
Step-by-step explanation:
your answer is correct
Find one value of x that is a solution to the equation:
(x2 – 6)2 = -3x2 + 18
Answers
Plsss help me
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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]
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:
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
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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'.
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
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.