Answer:
30.7 ft
Step-by-step explanation:
An equilateral triangle with area 43.5 has a height of 8.68 not 8.5
I will do the problem as written even though it is not a possible equilateral triangle
---------------------------------------------
a = (1/2)bh
43.5 = (1/2)b(8.5)
43.5 = 4.25b
b = 43.5/4.25
b = 10.2352941176
-----------------------
p = 3b
p = 3 * 10.2352941176
p = 30.7058823528
~ 30.7 ft
A box with a square base and open top must have a volume of 171500 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x .] Simplify your formula as much as possible.
Answer:
The dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm
Step-by-step explanation:
The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.
Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are
A = 2lh + lw + 2wh
Now for a box of square base, l = w = x.
So, A = 2xh + x² + 2xh
A = x² + 4xh
Since V = x²h and V = 171500 cm³,
h = V/x² = 171500/x²
substituting h into A, we have
A = x² + 4xh
A = x² + 4x(171500 cm³/x²)
A = x² + 4 × 171500 cm³/x
A = x² + 686000 cm³/x
To find the value of x that minimizes A, we differentiate A with respect to x
So, dA/dx = d[x² + 686000 cm³/x]/dx
dA/dx = 2x - 686000 cm³/x²
equating this to zero, we have
2x - 686000 cm³/x² = 0
2x = 686000 cm³/x²
2x³ = 686000
x³ = 686000 cm³/2
x = ∛(343000 cm³)
x = 70 cm
To determine if this in a minimum dimension for A, we differentiate dA/dx and insert x = 70 cm
So, d²A/dx² = d[2x - 686000 cm³/x²]/dx
d²A/dx² = 2 + 3 × 686000 cm³/x³
d²A/dx² = 2 + 2058000 cm³/x³
with x = 70 cm, we have
d²A/dx² = 2 + 2058000 cm³/(70 cm)³
d²A/dx² = 2 + 2058000 cm³/343000 cm³
d²A/dx² = 2 + 6
d²A/dx² = 8 > 0
So, x = 70 is a minimum value for the dimension
Since h = 171500 cm³/x²
h = 171500 cm³/(70 cm)²
h = 171500 cm³/4900 cm²
h = 35 cm
So, the dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm
What is the MINIMUM of the data set: 35, 20, 30,25, 20?"
a. 15
b. 20
c. 35
d. 25
Answer:
B) 20
The minimum of a data set is the smallest term of that set.
We arrange the terms in ascending order
→ 20,20,25,30,35
So, the minimum is 20
--------------------------------
hope it helps...
have a great day!!
Examine the triangle below. Use it to answer question 31.
Question 3
What type of trangle is shown?
Acute Equilateral Triangle
Acute Scalen Triangle
C. Obuse Scalene Triangle
D. Right Isosedes Triangle
Answer:
It’s blurry but I think it’s an obtuse triangle
Step-by-step explanation:
Maybe a right triangle
Point M is located at (3,-2) on the coordinate plane. Point M is reflected over the
x-axis to create point M'. What ordered pair describes the location of M'?
The answer would be (3,2) because you would do (x,-y)
If 3^2x+1 = 3^x+5, what is the value of x?
Answer:
4
Step-by-step explanation:
Since the bases are equal the powers also are equal
so
2x + 1 = x + 5
2x - x = 5 - 1
x = 4
If the height of the pyramid were increased to 512 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase
Complete question:
The base of a pyramid covers an area of 14.0 acres (1 acre = 43, 560 ft² ) and has a height of 481 ft. If the volume of a pyramid is given by the expression V = bh/3, where b is the area of the base and h is the height. If the height of the pyramid were increased to 512 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase
Answer:
The percentage increase of the volume is 6.45 %
Step-by-step explanation:
The volume of pyramid is calculated as;
V = bh/3
The initial volume of the pyramid is calculated as follows;
[tex]V = \frac{bh}{3} \\\\V_0 = (\frac{1}{3} ) \times (14 \ acres \ \times \frac{43,560 \ ft^2}{1 \ acre} ) \times (481 \ ft)\\\\V_0 = 97,777,680 \ ft^3[/tex]
The final volume of the pyramid when the height is increased to 512 ft.
[tex]V_1 = (\frac{1}{3} ) \times (14 \ acres \ \times \frac{43,560 \ ft^2}{1 \ acre} ) \times (512 \ ft)\\\\V_1 = 104,079,360 \ ft^3[/tex]
The percentage increase of the volume;
[tex]= \frac{104,079,360 - 97,777,680}{97,777,680} \times 100\%\\\\= 6.45 \ \%[/tex]
The volume of the pyramid will increase by 11.79%
The volume of a Pyramid is calculated using:
[tex]V = \frac{Bh}3[/tex]
Where:
B represents the base areah represents the heightWhen the height is increased from 458 to 512, then the initial and the final volumes are:
[tex]V_1 = \frac{458}{3}b[/tex]
[tex]V_2 = \frac{512}{3}b[/tex]
The percentage change is then calculated as:
[tex]\% Change = \frac{V_2 -V_1}{V_1} \times 100\%[/tex]
This gives
[tex]\% Change = \frac{512b/3 -458b/3}{458b/3} \times 100\%[/tex]
Simplify the numerator
[tex]\% Change = \frac{54b/3}{458b/3} \times 100\%[/tex]
Evaluate the quotient
[tex]\% Change = 0.1179 \times 100\%[/tex]
Express as percentage
[tex]\% Change = 11.79 \%[/tex]
Hence, the volume of the pyramid will increase by 11.79%
Read more about volumes at:
https://brainly.com/question/1972490
PLEASE help me out, I COULD REALLY USE THE HELP RN
Answer:
4.2
Step-by-step explanation:
2.1+2.1=4.2
what is the image of point 0,6 after a dilation of 1/3
Answer:
(0,4)
Step-by-step explanation:
3
Solve for x.
X =
8
20
35
Answer:
x=00
Step-by-step explanation:l
nnm
Which represent like terms in the model of the equation?
1
O
II-
and
X X and
XX
х
and
and 1
Answer:
Option 2
Step-by-step explanation:
Like terms are terms with the same variable and the same power.
Let's analysis and write the equation of each model to see if which of them has like terms:
Option 1:
We have x x => 2x
1 1 1 => 3
Equation of model=> 2x + 3
2x and 3 are unlike terms
Option 2:
We have x x => 2x
x x x => 3x
Equation of model=> 2x + 3x
2x and 3x are like terms
Option 3:
We have x x x => 3x
1 1 1 => 3
Equation of model=> 3x + 3 (contains unlike terms)
Option 4:
We have x => x
1 => 1
Equation of model=> x + 1 (unlike terms)
✔️The second option is the answer
Find the value of 'x
Answer:
x = 16
Step-by-step explanation:
The sum of the angles of a triangle are 180
128+ 2x-3 +23 = 180
Combine like terms
2x+148=180
Subtract 148 from each side
2x+148 -148 = 180-148
2x = 32
Divide by 2
2x/2 = 32/2
x =16
According to the fundamental theorem of algebra, how many zeros does the function f(x)= 3x^4 + x + 2 have?
Answer:
4
Step-by-step explanation:
Any polynomial of degree n has n roots
but we may need to use complex numbers
This is a 4th degree polynomial therefor:
4 roots
2(5j + 2 + 4j) as a verbal expression
Answer:
theres a few ways to go about this...
ten j plus, four, plus eightj SIMPLIFY eighteen j's plus four
orrrr
2 times 5j+2 times2+2times4j and combine like terms to get the above expression
What is the value of a?
Answer:
a = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]c^{2}[/tex] = [tex]18^{2}[/tex] (pythagoras theorem)
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]4^{2}[/tex] (pythagoras theorem)
[tex]c^{2}[/tex] + [tex]b^{2}[/tex] = [tex]22^{2}[/tex] (pythagoras theorem)
From these 3 equations we can find the value of a
please yelp me find the area
Which temperature is warmer, -8 degrees Celsius, or -20 degrees Celsius?
Answer:
-8 degrees Celsius is warmer
Answer:
-8 degrees C.
Step-by-step explanation:
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
Answer:
I guess it would go
Ben did:+10
Gail:-8
Nathaniel:0
Step-by-step explanation:
hope this was what you wanted
best of luck
A business consultant wanted to investigate if providing day-care facilities on premises by companies reduces the absentee rate of working mothers with children under six years old. She took a sample of 45 such mothers from companies that provide day-care facilities on premises. These mothers missed an average of 6.4 days from work last year with a standard deviation of 1.20 days. Another sample of 50 such mothers taken from companies that do not provide day-care facilities on premises showed that these mothers missed an average of 9.3 days last year with a standard deviation of 1.85 days.
a. Using a 2.5% significance level, can you conclude that the mean number of days missed per year by mothers working for companies that provide day-care facilities on premises is less than the mean number of days missed per year by mothers working for companies that do not provide day-care facilities on premises?
b. Construct a 98% confidence interval for the difference between the two population means.
i. State the hypothesis
ii. State the rejection or nor rejection region
iii. Calculate the test statistics
iv. State the conclusion
Answer:
Part a:
The null and alternate hypotheses are
i) H0: ud ≥ u vs Ha: ud < u
ii) As the significance level is ∝= 0.025 and it is one tailed test then the critical region R < - 1.96
iii) The test statistics is =−9.15
iv) We accept the alternate hypothesis.
Part b: CI = (−3.637,−2.163)
Step-by-step explanation:
AS the sample sizes are sufficiently large (n1,n2> 30) we can use the sample standard deviations in place of population standard deviations.
Part a:
The null and alternate hypotheses are
i) H0: ud ≥ u vs Ha: ud < u
where
ud is the mean of the days missed per year by mothers working for companies that provide day-care facilities on premises
and
u is the mean number of days missed per year by mothers working for companies that do not provide day-care facilities on premises
ii) As the significance level is ∝= 0.025 and it is one tailed test then the critical region R < - 1.96
iii) The test statistics is
z= xˉ1 − xˉ2/√ s 1² /n 1 +s 2² /n 2
= 6.4−9.3/ √1.2 ² /45+ 1.85² /50
=−9.15
iv) The calculated z = −9.15 values lies in the critical region= R < - 1.96 and the null hypothesis is rejected. Hence the mean of absentees for companies that provide day-care facilities on premises is less than the
the mean number of absentees for companies that do not provide day-care facilities on premises.
We accept the alternate hypothesis.
Part b:
The confidence interval can be calculated using the formula
CI = ( xˉ1 − xˉ2) ± z∝/2 √ s 1² /n 1 +s 2² /n 2
CI = (6.4−9.3) ± 2.326 * √1.2 ² /45+ 1.85² /50
CI = (−3.637,−2.163)
missing coordinates to complete the following ordered pair y+4x=7
Answer:
(1,3)
Step-by-step explanation:
This might be wrong, sorry.
y+4x=7
I would think the pair is
(1,3)
approximate 10.56 to the nearest whole number
Answer:
11.
Step-by-step explanation:
As the first decimal place is 5 we round up the whole number.
Answer:
11
Step-by-step explanation:
See image below:)
The ratio of three angles of a triangle is 1:2:3. Find the measurement of the angles
Answer:
all the angles add up to 180 degrees
So 180÷6=30
(i got 6 cuz 1+2+3)
so 1=30
2=30*2=60
3=30*3=90
Please help me no links!!
Answer:
Slope is -3
y-intercept is -3 and equation is y=-3x-3
Answer:
Slope: -3
y-intercept: -3
Equation: y = -3x - 3
Step-by-step explanation:
1. To get the slope (m):
m = rise / run = -3 / 1 --> it's negative 3 since the slope is going downwards
2. the y-intercept is the point that crosses the y-axis or when the x point is 0, so (0, -3)
3. Put is all together: y = -3x - 3
solve for x:
-x/3 = 2
Answer:
x = -6
Step-by-step explanation:
-x/3 = 2
Multiply each side by -3 to isolate x
-x/3 * -3= 2*-3
x = -6
Answer:
x= -6
Step-by-step explanation:
you want to issolate x.
Start by getting rid of that divison by inversing it. The inverse of division is multiplication, so we multiply 2 by 3 to get 6.
Now -x= 6
in order for it to be truely isolated, we must inverse the negative sign.
its x= -6
if m<1 = 23^ and m<2 = 32^, find the measures of all other angles
Step-by-step explanation:
given,
m1=23°
m2=32°
m3=m1+m2+m3=180°{straight angle}23+32+m3=180°m3=180-55°m3=125°m3=m6{vertically opposite angle r equal}m6=125°m2+m3+m4=180°(straight angle)m4=180-157°m4=23°m3+m4+m5=180°{straight angle}m5=180-148°m5=32°hope it helps
stay safe healthy and happy....If the measure of angle 1 is 78 degrees and the measure of angle 3 is (5x-2)degrees, what is the value of x ?
Answer:
16
Step-by-step explanation:
Vertical Angles are congruent (equal)
78 = 5x - 2
80 = 5x
16 = x
How many plants are taller than 14 inches?
835×79 with formula and all
Please help I need help asap!!! please show work <3
Step-by-step explanation:
(5x⁴y⁵).(2x²y‐⁵)
5×2=10
x⁴×x²= x⁶
y⁵×y-⁵=y⁰
so the answer is 10x⁶y⁰
Please help! I need done ASAP
Answer:
17
Step-by-step explanation:
Find the solution of the system of equation shown on the graph
9514 1404 393
Answer:
(-7, -6)
Step-by-step explanation:
The solution to the system of equations is the point that is on both lines: their point of intersection. That point is (-7, -6).
