Answer: 13.5
Step-by-step explanation:
Find the total volume of the melted cubes:
V₁ = 6³ V₂ = 8³ V₃ = 12³
= 216 = 512 = 1728
So the new cube will have a volume of 216 + 512 + 1728 = 2456
Volume of the cube = side³
2456 = s³
[tex]\sqrt[3]{2456} = s[/tex]
13.5 = s
Sara needs to pack 108 stalks of roses, 81 stalks of lilies, and 54 stalks of orchids into identical baskets so that each type of flower is equally distributed among the baskets. Find the largest number of the basket that can be packed
Answer:
54
Step-by-step explanation:
There are 108 roses, 81 lilies and 54 orchids.
The problem is asking that every basket contain the same number for that type of flower.
So if I put one of each flower in each basket, I will get 54 baskets at the most.
Sounds correct to you?
a previous analysis of paper boxes showed that the standard deviation of their lengths is 15 millimeters. A packers wishes to find the 95% confidense interval for the average length of a box. How many boxes do he need to measure to be accurate within 1 millimeters
Answer:
864.36 boxes
Step-by-step explanation:
In the question above, we are given the following values,
Confidence interval 95%
Since we know the confidence interval, we can find the score.
Z score = 1.96
σ , Standards deviation = 15mm
Margin of error = 1 mm
The formula to use to solve the above question is given as:
No of boxes =[ (z score × standard deviation)/ margin of error]²
No of boxes = [(1.96 × 15)/1]²
= 864.36 boxes
Based on the options above, we can round it up to 97 boxes.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
[tex]\boxed{F(x)>0}[/tex]
Step-by-step explanation:
The range is the set of possible values of y (the output).
The input value x is all real numbers, because there are no restrictions on x.
When the input x is all real numbers, the output is always greater than 0.
[tex]2^{-15}= 0.00003051757[/tex]
[tex]2^{8}= 256[/tex]
[tex]2^{-4}= 0.0625[/tex]
As mountain climbers know, the higher you go, the cooler the temperature gets. At noon on July 4th last summer, the temperature at the top of Mt. Washington — elevation 6288 feet — was 56◦F. The temperature at base camp in Pinkham Notch — elevation 2041 feet — was 87◦F. It was a clear, still day. At that moment, a group of hikers reached Tuckerman Junction — elevation 5376 feet. To the nearest degree, calculate the temperature the hikers were experiencing at that time and place. When you decided how to model this situation, what assumptions did you make?
Answer:
The temperature at 5376 ft is approximately 63°F
The assumption made was that the temperature varies linearly with elevation
Step-by-step explanation:
The parameters given are;
Temperature at 6288 feet = 56°F = 286.5
Temperature at 2041 feet = 87°F = 303.71
We are to find the temperature at 5376 feet
Let the temperature be the y-coordinate value and the elevation be the x-coordinate value, to find the temperature, we have the temperature gradient given by the relation;
[tex]m = \dfrac{y_2-y_1}{x_2 - x_1} = \dfrac{303.71-286.5}{2041 - 6288}= -4.05 \times 10^{-3} \ K/ft[/tex]
The temperature at 5376 ft will be the temperature at 2041 added to the decrease in temperature from climbing to 5376 ft
The increase in elevation is 5376 - 2041 = 3335 ft
The decrease in temperature = 3335 ft × (-4.05 × 10⁻³) K/ft = -13 .5 K
The temperature at 5376 ft will then be 303.71 - 13.5 = 290.196 K = 62.68°F ≈ 63°F
The assumption made was that the decrease in temperature with elevation is linear.
Find the value of each trigonometric ratio.
SOH CAH TOA
Sin = opp/hyp
Cos = adj/hyp
Tan = opp/adj
7) 21/35 or 3/5
8) 21/20
9) 30/50 or 3/5
10) 40/50 or 4/5
Answer:
[tex]{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
[tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex]
[tex]tan \theta = \frac{opposite }{adjacent }[/tex]
[tex]sinX=\frac{21}{35}[/tex]
[tex]tanX=\frac{21}{20}[/tex]
[tex]sinC=\frac{30}{50}[/tex]
[tex]cosC=\frac{40}{50}[/tex]
Which expression is equivalent to x^2 • x^3?
Answer:
x^5
Step-by-step explanation:
x^2 . x^3
x^(2+3)
x^5
Paul has four paper strips of the same length. He glues two of them together with a 4 cm overlap, and the new strip is 36 cm long. He wants to make a 30 cm long strip with the other two strips. How long should the overlap be?
Answer:
10 cm overlap required to make a 30 cm long strip.
Step-by-step explanation:
Given:
Four paper strips of the same length.
Two of them glued together with a 4 cm overlap to make a new strip which is 36 cm long.
To find:
Overlap required to make a strip which is 30 cm long = ?
Solution:
First of all, let us understand the concept of overlap.
Please refer to the attached image.
Let length of each strip be [tex]x[/tex] cm.
Given that there is 4 cm overlap resulting in new strip of length 36 cm.
The overlapping length is counted only once as clear from the figure attached.
So, Let us try to find the equation:
[tex]x +(x-4) = 36\\\Rightarrow 2x=40\\\Rightarrow x = 20\ cm[/tex]
i.e. each strip length is 20 cm.
Now, let us assume, an overlap of 'y' cm is to be made to make a new strip of 30 cm.
The equation will be:
[tex](20-y)+20 =30\\\Rightarrow y = 40-30\\\Rightarrow y = 10\ cm[/tex]
ANSWER FOR 30 POINTS A 13-foot ladder is leaning against a tree. The bottom of the ladder is 5 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
Answer:
12 feet
Step-by-step explanation:
Use the Pythagorean Theorem to find how high up the tree the top of the ladder reaches.
13 feet - hypotenuse
5 feet - can be a or b
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = √144
b = 12
The top of the ladder reaches 12 feet up the tree.
Hope that helps.
Answer:
12 ft
Step-by-step explanation:
These circumstances describe a triangle with hypotenuse 13 ft and bottom side 5 ft. The vertical side (height above ground to top of ladder) is to be found. According to the Pythagorean Theorem,
5^2 + (vertical side)^2 = 13 ft = 169, and so
(vertical side) = sqrt( 169 - 25 ) = 144 (ft)
The top of the ladder is s 12 ft above the ground.
Can you tell me the answer to (−7c+8d)0.6
Answer:
-4.2c+4.8d
Step-by-step explanation:
(−7c+8d)0.6
Distribute
-7c*.6 + 8d * .6
-4.2c+4.8d
Answer:
-4.2c + 4.8d
Step-by-step explanation:
We would like to distribute the 0.6 in the expression (-7c + 8d) * 0.6.
Remember that when distributing, we multiply the "outside number" (0.6 in this case) by each of the "inside numbers" (-7c and 8d) and then add those products.
So, the first product will be: 0.6 * (-7c) = -4.2c. The second product will be: 0.6 * 8d = 4.8d. Add these together: -4.2c + 4.8d.
The answer is thus -4.2c + 4.8d.
~ an aesthetics lover
Abigail and Liza work as carpenters for different companies. Abigail earns $20
per hour at her company and Liza earns $25 per hour at her company. Last
week, Abigail and Liza worked for a total of 30 hours and together earned atotal of $690. How many hours did Liza work last week?
Answer as detailed as possible. Thanks :)
Answer:
L = 18 = hours worked by Lisa
a = 12 = hours worked by Abigail
Step-by-step explanation:
Given the following :
Abigail's earning = $20
Lisa's earning = $25
Last week :
Let number of hours worked by Abigail = a
Number of hours worked by Lisa = L
Total earning = $690
Total hours worked :
a + L = 30 - - - - (1)
To obtain their total earning:
(Lisa's earning per hour * hours worked) + (Abigail's earning per hour * hours worked)). $690
($25 * L) + ($20 * a) = $690
25L + 20a = 690 - - - - (2)
a + L = 30 - - - - (1)
25L + 20a = 690 - - - - (2)
L = 30 - a
25(30 - a) + 20a = 690
750 - 25a + 20a = 690
-5a = 690 - 750
-5a = - 60
a = 12
From (1)
a + L = 30 - - - - (1)
12 + L = 30
L = 30 - 12
L = 18
L = 18 = hours worked by Lisa
a = 12 = hours worked by Abigail
The length of the room is 2½ times the breadth. The perimeter of the room is 70 m. What are the length and breadth of the room?
Answer:
length=25m
breadth=10m
Step-by-step explanation:
2.5units+2.5units+1unit+1unit=7units
70/7=10
length=10x2.5=25
breadth=10
(sorryy im not really sure but i hope it helps :D)
Answer:
Length = 25 cm
Breadth = 10 cm
Step-by-step explanation:
Let breadth of the room be 'x'
Let length of the room be ''
Perimeter ( P ) = 70 cm
Now, let's find the breadth of the room 'x '
Perimeter of rectangle = 2(l+b)
plug the values
70=2(2.5x+x)
Collect the like terms
70=2x3.5x
Calculate the product
70=7x
Swap the sides of the equation
7x=70
Divide both sides of the equation by 7
7x / 7= 70/7
Calculate
x=10cm
Breadth = 10 cm
Now, Let's find the length of the room ' 2.5x '
Length of the room = 2.5x
Plug the value of X
2.5x10
Calculate the product
25cm
Thus , The length and breadth of the room is 25 cm and 10 cm respectively.
Hope this helps..
Best regards!!
(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the triangle, and (c) determine the area of the triangle. the figure is not drawn to scale.
the length of the unknown side is ____
the perimeter of the triangle is ____
the area of the triangle is ___
Answer/Step-by-step explanation:
a. Unknown side, b, using the Pythagorean theorem is solved as shown below.
[tex] b^2 = c^2 - a^2 [/tex]
[tex] b^2 = 45^2 - 27^2 [/tex]
[tex] b^2 = 1,296 [/tex]
[tex]b = \sqrt{1,296}[/tex]
[tex] b = 36 [/tex]
Unknown side, b, = 36 km
b. Perimeter of the triangle = sum of all the sides of the ∆ = [tex] 36 + 45 + 27 [/tex]
[tex] perimeter = 108 km [/tex]
c. Area of triangle = ½*base*height
where,
Base = 36 km
Height = 27 km
[tex] Area = \frac{1}{2}*36*27 [/tex]
[tex] Area = 18*27 [/tex]
[tex] Area = 486 km^2 [/tex]
Dustin has five hats, five shirts, five pairs of pants, and five pairs of shoes; he has one of each in blue, green, gray, silver, and gold (his five favorite colors). Dustin is picky about what he wears: he insists on his shoes being the same color as at least two other articles of clothing in the outfit. However, he refuses to wear all silver or all gold (because that's tacky). How many possible outfits can Dustin wear?
Answer:
The number of possible outfits Dustin can wear is 73 outfits
Step-by-step explanation:
The information given are;
The number of hats Dustin has = 5
The number of shirts Dustin has = 5
The number of pants Dustin has = 5
The number of shoes Dustin has = 5
The colors of Dustin's clothing are blue, green, gray, silver, and gold
Given that the shoes go with at least two other clothing of the same color, we have;
The number of ways the color of the shoes can be selected = 5 ways
The number of ways of selecting the same color for 2 of the remaining 3 clothing = 3 ways
The number of ways of selecting the color of the fourth clothing = 5 ways
The total number of ways = 5 × 3 × 5 = 75 ways
The number of ways in which all silver can be selected = 1 way
The number of ways in which all gold can be selected = 1 way
Since Dustin refuses to wear all silver and all gold, the total number of ways the outfits can be selected = 75 - 1 - 1 = 73 ways = 73 is the number of possible outfits
Therefore, the number of possible outfits Dustin can wear = 73 outfits.
PLEASE HELP ASAP IM REALLY TRING TO FINISH A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
__♥__♥_____♥__♥___ Put This
_♥_____♥_♥_____♥__ Heart
_♥______♥______♥__ On Your
__♥_____/______♥__ Page If
___♥____\_____♥___ You Had
____♥___/___♥_____ Your Heart
______♥_\_♥_______ Broken
________♥_________…………….
List the first 5 terms of the sequence -3n -2.
Answer:
-5,-8,-11,-14,-17
Step-by-step explanation:
-3n -2
n=1 -3(1) -2 = -3-2 = -5
n=2 -3(2) -2 = -6-2 = -8
n=3 -3(3) -2 = -9-2 = -11
n=4 -3(4) -2 = -12-2 = -14
n=5 -3(5) -2 = -15-2 = -17
We can substitute n with each term in order.
First Term:
-3(1) - 2
-3 - 2
-5
Second Term:
-3(2) - 2
-6 - 2
-8
Third Term:
-3(3) - 2
-9 - 2
-11
Fourth Term:
-3(4) - 2
-12 - 2
-14
Fifth Term:
-3(5) - 2
-15 - 2
-17
Therefore, the sequence is -5, -8, -11, - 14, -17
Best of Luck!
HELLLPPPP ,The value for the missing side is: 25. 4 5. None of these choices are correct.
Answer: The missing side is 5 units.
Step-by-step explanation:
Pythagorean Theorem states that a^2+b^2=c^2. Let the hypotenuse be x.
[tex]4^2+3^2=x^2\\16+9=x^2\\25=x^2\\\sqrt{25}=\sqrt{x^2}\\\left[\begin{array}{c}x=5\end{array}\right][/tex]
Hope it helps <3
KN is perpendicular bisector of MQ identify the value of x
Answer:
x = 6
Step-by-step explanation:
Since KN is the perpendicular bisector, that means ∠KNM = ∠KNQ = 90° and MN = NQ so therefore, since they are right triangles, ΔKNM ≅ ΔKNQ because of HL. Therefore, KM = KQ by CPCTC so:
5x - 3 = 3x + 9
2x = 12
x = 6
If 35%discount is given on a trouser which costs #3,000.00k,how much will a buyer pay for the trouser?
Answer:
1950
Step-by-step explanation:
3000×35/100
=1050
so 3000-1050
=1950
what is angle b in this image
Answer:
Step-by-step explanation:
you have the hypotenuse side and adjacent side, so you would use cosine (adj/hyp). since you are trying to find the angle, you use the inverse operation.
put it in the calculator and you should get 0.98176535657.
Consider the formula F = \dfrac{N\cdot M}{P}F= P N⋅M F, equals, start fraction, N, dot, M, divided by, P, end fraction, where FFF represents the fertility of soil, NNN represents the amount of nutrients in the soil, MMM represents the amount of moisture in the soil, and PPP represents the amount of pollutants in the soil. Select an appropriate measurement unit for fertility of soil.
Answer:
C. Fertility= Nutrients * Moisture / Pollutant
Step-by-step explanation:
F=NM/P
F= Fertility of the soil
N= Amount of nutrients in the soil
M= Amount of moisture in the soil
P= Amount of pollutant in the soil
F=NM/P
Fertility of the soil
= Amount of nutrients in the soil * Amount of moisture in the soil / Amount of pollutant in the soil
Fertility= Nutrients * Moisture / Pollutant
Option C is the correct answer
Solve the equation. 2x + 4 = 3x – 2
Answer:
X=6
Step-by-step explanation:
2x+4=3x-2
-4 -4
2x=3x-6
-3x -3x
-1x=-6
--- ---
-1 -1
X=6
Answer:
6
Step-by-step explanation:
2x+4=3x-2
2x-3x=-2-4
-x=-6
(divide both sides by -1)
X=6
Problem Water boils at 212^\circ212 ∘ 212, degrees Fahrenheit. Write an inequality that is true only for temperatures (t)(t)left parenthesis, t, right parenthesis that are higher than the boiling point of water.
Answer:
t > 212
Step-by-step explanation:
Given
Boiling point = 212°F
Required
Inequality that shows temperature greater than the boiling point
From the question, temperature is represented with t.
The inequality "greater than" is represented with >
So, temperature greater than the boiling point implies that t > 212
Answer: t > 212
Step-by-step explanation:
The question says "Write an inequality that is true only for temperatures that are higher than the boiling point of water."
This means t has to be higher than 212 since it says only for temperatures that are higher than the boiling point.
But since we have to write an inequality the answer would be: t > 212.
I know I did this very late and you probably don't need it but i was bored
If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 2), (negative 1, 2). (–4, –7) (–4, 2) (2, –7) (2, 11)
Answer:
A ( -4, -7)
Step-by-step explanation:
if you translate -1, three units to the left u get -4 and then when u go nine units down u get -7 do it on a grid and u will see wut im talkin about : )
Answer:
A.
Step-by-step explanation:
Sharon is making a large batch of soup. The soup reaches a height of 25 in a cylindrical pot whose diameter is 30cm. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are 7cm, end text long.
Complete question :
Sharon is making a large batch of soup. The soup reaches a height of 25 in a cylindrical pot whose diameter is 30cm. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are 7cm long. How many whole cubes can Sharon make?
Answer:
About 51 ice cubes
Step-by-step explanation:
Given the following :
Height (h) of cylindrical pot = 25
Diameter = 30cm
Edge of ice cube = 7cm long
Volume of cylinder (v) = πr^2h
V = π * (30/2)^2 * 25
V = π * 15^2 * 25
V = 17671.458cm^3
Therefore, the soup occupies 17673.75cm^3
Volume of cubes to store the soup for later:
The volume of a cube is given by the formula:
V = a^3
Where a is the length of it's edge
V = 7^3
V = 343cm^3
Number of cubes required to store soup:
(Volume of cylinder / Volume of ice cube)
17671.458cm^3 / 343cm^3
= 51.520287
This is about 51 whole cubes
These box plots show the prices for two different brands of shoes.
Answer: I’m pretty sure is letter A
Divide both sides of the equation by the coefficient of t to get t by itself how tall is Theresa in inches
p=paul's height
s=steve's height
t=theresa's height
p=s
1 and 1/2=3/2
1 and 1/3=4/3
p=-16+(3/2)t
s=-6+(4/3)t
p=s so
-16+(3/2)t=-6+(4/3)t
add 6 to both sides
-10+(3/2)t=(4/3)t
times both sides by 6 to clear fractions
-60+9t=8t
minus 9t both sides
-60=-t
times -1
60=t
t=60
theresa is 60 inches or 5ft
steve and paul are 84 inches or 7ft (wow!)
A rectangular solid has edges whose lengths are in the ratio 1:2:3. If the volume of the solid is 864 cubic units, what are the lengths of the solid's edges?
Answer: 5.24 units, 10.48 units , 15.72 units
Step-by-step explanation:
Volume of a rectangular solid is given by :-
V = lwh, where l = length , w= width and h = height
Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.
Let lengths of the rectangular solid x , 2 x, 3x.
volume of the solid is 864 cubic units
Then, Volume of rectangle = [tex]x (2x)(3x) =864\ \text{cubic units}[/tex]
[tex]\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24[/tex]
Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units
= 5.24 units, 10.48 units , 15.72 units
find the x intercept x+6y=30
Answer:
x = 30
(30, 0)
Step-by-step explanation:
The x-intercept is when the graph crosses the x-axis when y = 0. In that case, simply plug in 0 for y:
x + 6(0) = 30
x + 0 = 30
x = 30
Answer: (30,0)
Step-by-step explanation:
x-intercept can be found in the form x = my + b, where b is the x-intercept. Thus, simply turn x+6y=30 into x-6y+30, to find that the x-intercept is (30,0)
Hope it helps <3
Determine whether these two functions are inverses. Show your work please. f(x)= 1/x+4-9; g(x)=1/3x+9
Answer: No they are not inverses.
Step-by-step explanation:
If they are inverses, then the inverse of f(x) will equal g(x).
[tex]y=\dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's:}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Solve for y:}\\x+9=\dfrac{1}{y+4}\\\\y+4=\dfrac{1}{x+9}\\\\y=\dfrac{1}{x+9}-4[/tex]
f⁻¹(x) ≠ g(x) so they are not inverses
i will mark brainliest i need help quick
Answer:
x-1
Step-by-step explanation:
| x-1| x> 1
Since x is greater than x, the absolute value will be positive so we can remove it
x-1
Lets use a number to check
Let x = 4
| 4-1| 4>1
3 which is positive
Answer:
x - 1
Step-by-step explanation:
| x - 1 |
x > 1
x is greater than 1. The absolute value is not needed, since the value inside will only be for positive integers.
x - 1
We can check by plugging x as 2.
2 - 1 = 1 (positive)
2 > 1