Answer:
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.
Step-by-step explanation:
Given that,
A box is being created out of a 15 inches by 10 inches sheet of metal.
The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.
The length of the metal box be = (15-2x) inches.
The width of the metal box be =(10-2x) inches
The height of the metal box be =x inches
Then, the volume of the metal box= length×width×height
=(15-2x)(10-2x)x cubic inches
=(150x-50x²+4x³) cubic inches
∴ V= 4x³-50x²+15x
Differentiating with respect to x
V'=12x²-100x+15
Again differentiating with respect to x
V''=24x-100
For maximum or minimum value, V'=0
12x²-100x+15=0
Apply quadratic formula [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex], here a=12, b= -100 and c=15
[tex]x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}[/tex]
[tex]\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}[/tex]
[tex]\Rightarrow x=0.1528,8.18[/tex]
For x= 8.18, The value of (15-2x) and (10-2x) will negative.
∴x=0.1528 .
Now, [tex]V''|_{x=0.1528}=24(0.1528)-100<0[/tex]
∴At x=0.1528 inch, the volume of the metal box will be maximum.
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.
Kaytlyn must build a sand castle in the form of a square pyramid for a project as shown to the left. She bought 3 bags of sand each containing 1200 inches cubed. Will she save enough sand to build the castle?
Answer:
see the explanation
Step-by-step explanation:
The complete question is
The dimensions of the square pyramid are
Base: 40 inches
Height: 12 inches
step 1
Find the volume of the square pyramid
The volume of the square Pyramid is given by the formula
[tex]V=\frac{1}{3}b^2h[/tex]
where
b is the length side of the square base
h is the height of the pyramid
we have
[tex]b=40\ in\\h=12\ in[/tex]
substitute
[tex]V=\frac{1}{3}(40)^2(12)[/tex]
[tex]V=6,400\ in^3[/tex]
step 2
Find the volume of sand
Multiply the number of bags of sand by the volume of each bag
so
[tex]3(1,200)=3,600\ in^3[/tex]
step 3
Compare the volume of the sand with the volume of the square pyramid
3,600 < 6,400
therefore
Kaytlyn has not enough sand to build the castle
in a geometric sequence, the fourth term is 8 times the first term. the sum of the first 10 terms is 2557.5. find the 10th term of this sequence.
Answer: 1280
Step-by-step explanation:
The fourth term is 8 times the first term.
The fourth term = [tex]ar^3[/tex]
[tex]ar^{3} = 8a[/tex]
To find the common ratio:
∴ [tex]\frac{ar^3}{a} = \frac{8a}{a}\\[/tex]
∴ [tex]r^3 = 8\\r = 2\\[/tex]
Common ratio = 2
To find the nth number of terms = [tex]\frac{a(r^n -1)}{r-1\\}[/tex]
∴ [tex]\frac{a(2^{10} -1)}{2-1}[/tex]
∴ [tex]1023a\\[/tex]
The sum of 10 terms = 1023a
The sum of 10 terms = 2557.5
∵ 2557.5 = 1023a
∵ [tex]a = \frac{5}{2}[/tex]
To find the 10th term:
∴ [tex]ar^9\\[/tex]
∴ [tex]\frac{5}{2} *2^9[/tex]
⇒ 1280 ║ answer.
From the question given above, we were told that the fourth term is 8 times the first term. This can be written as:
T₄ = 8a
But
T₄ = ar³
a => is the first term
r => is the common ratio
Thus,
ar³ = 8a
Solving for the common ratio (r):
ar³ = 8a
Divide both side by a
r³ = 8
Take the cube root of both side
r = ³√8
r = 2
Thus, the common ratio (r) is 2
Next, we shall determine the first term (a). This can be obtained as follow:
Sum of 10th term (S₁₀) = 2557.5
Common ratio (r) = 2
Number of term (n) = 10
First term (a) =?Sₙ = a[rⁿ – 1] / r – 1
2557.5 = a[2¹⁰ – 1] / 2 – 1
2557.5 = a[1024 – 1]
2557.5 = 1023a
Divide both side by 1023
a = 2557.5 / 1023
a = 2.5
Thus, the first term is 2.5
Finally, we shall determine the 10th term of the sequence. This can be obtained as follow:
Common ratio (r) = 2
First term (a) = 2.5
10th term (T₁₀) =?T₁₀ = ar⁹
T₁₀ = 2.5 × 2⁹
T₁₀ = 2.5 × 512
T₁₀ = 1280
Therefore, the 10th term of the sequence is 1280
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is 2 and 3/4 greater than 2 and 4/5
Answer:
no it is less then
Step-by-step explanation:
2 3/4 is equal to 2.75 in decimal form and 2 4/5 is 2.80 in decimal form so 2 3/4 is less the 2 4/5
Gertrude made eight more than three times the number of apple pies that Ruth made. If Gertrude made 14 pies, how many did Ruth make?( hint: let p equal the number of pies Ruth made.)
Cement was poured to make two rectangular prism the prism were stacked as shown 4 feet 3 feet 4 feet 3 feet 2 feet what are lengths , width, height in feet of the smaller rectangular prism
Final answer:
Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.
Explanation:
Given:
Lengths of the larger prism: 4 feet, 3 feet, 4 feet
Dimensions of the stacked prisms: 4 feet, 3 feet, 2 feet
Let: The lengths, widths, and heights of the smaller prism be L, W, and H respectively.
Two proportions:
4/L = 4/3
3/W = 3/2
Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.
Which expressions are equivalent to the one below? Check all that apply.
3^4 • 3^X
Answer:
C and D
Step-by-step explanation:
Answer:
its c and d
Step-by-step explanation:
The circle below has center K, and its radius is 3 yd. Given that m 2 LKM = 70°, find the length of the major arc LNM.
Give an exact answer in terms of 71, and be sure to include the correct unit in your answer.
Length of major arc LNM :
The length of the major arc LNM, in terms of pi, is 29π/6 yards.
The circle has a radius of 3 yards and the central angle m∠LKM is 70°. Since the question asks for the length of the major arc LNM, we first need to calculate the angle of the major arc. The angle of a full circle is 360°, so the angle of the major arc will be 360° - 70° = 290°.
To find the arc length, we use the formula for arc length (l) which is: l = rθ (in radians). We must convert the angle from degrees to radians by multiplying by π/180. So, 290° becomes (290π/180) radians.
Now, compute the length of the major arc LNM: l = 3 yd * (290π/180) = (870π/180) yd, which simplifies to: 29π/6 yd. Thus, the length of the major arc LNM, in terms of π, is 29π/6 yards.
What error did Amy make in writing the equation in slope-intercept form for the line shown in the graph?
Amy’s equation:
Answer:
letter C
Step-by-step explanation:
She substitue the X-Intercept, (3,0), for B
#brainliestisthekey
Work out the answers to:
a) 6 × (-3)
b) (-5) × 4
c) (-9) × (-2)
Step-by-step explanation:
a. 6 * (-3) = - 18
b. (-5) * 4 = - 20
c. (-9) * (-2) = 18
The box plots show the average wind speeds, in miles per hour, for various cities in two different countries
Average Wind Speeds of Cities in Country A
D
's
8
9
10 11
Average Wind Speeds of Cities in Country B
Which statement describes the symmetry of the data in the two box plots?
The data in country A are more symmetric than the data in country B.
The data in country B are more symmetric than the data in country A
The data in both countries have about the same symmetry.
The symmetry of the data cannot be determined by looking at the box plots.
What is the answer
Answer:
the answer is b.
Step-by-step explanation:
Finding Coordinates of a Translation
Triangle XYZ has coordinates X(2, 4), Y(-3, 4), and Z(-3,1). If the triangle is translated using the rule
(x, y) → (x - 2, y + 1), what are the coordinates of Y'?
Y'(-5,5)
OY'(0,5)
Y'(-5,2)
Y'(-1,3)
Transformation involves changing the position of a shape
The coordinates of Y' are (-5, 5)
The vertices are given as:
X(2, 4), Y(-3, 4), and Z(-3,1)
The transformation rule is given as:
(x, y) → (x - 2, y + 1)
For vertex Y, we have:
(-3, 4) → (-3 - 2, 4 + 1)
Simplify
(-3, 4) → (-5, 5)
Hence, the coordinates of Y' are (-5, 5)
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Please help!
Two semicircles are placed in a rectangle. The width of the rectangle is 7 cm.
Find the area of the shaded region. Use the value 3.14 for pi , and do not round your answer.
Answer:
Total length of the rectangle = 14+14= 28cm
width= 7 cm
Area of the rectangle = 28×7cm²
= 196 cm²
Area of 2 semicircles = Area of 1 circle
= π(7)² = 3.14×49= 153.86cm²
Area of the shaded region = 196-153.86
= 42.14 cm²
Answer: 42.14 [tex]cm^2[/tex]
Step-by-step explanation:
Assuming that the width of the rectangle is 7 cm, the semi-circle's radius is also 7 cm.
Let's calculate the area of the two semi-circles, which in total makes a whole circle.
The formula for a circle is [tex]a=2\pi r^2[/tex]
Since r = 7, plug it in the formula:
[tex]a=2\pi (7)^2[/tex]
[tex]a=49\pi =153.86 cm^2[/tex]
Now, to figure out the length of the rectangle, look at the semi-circles. Their radius is 7 cm, so their diameter is 14 cm. We have two semi-circles with the diameter (14 cm), so we can say that the width is 28 cm.
Area of a rectangle: [tex]a=lw[/tex]
[tex]a=7*28=196cm^2[/tex]
To find the area of the shaded region, we subtract the area of the semi-circles to the rectangle, which should be:
[tex]196 - 153.86=42.14 cm^2[/tex]
The width of a rectangular rug is 6 feet if the perimeter is 24 feet what is the area of the rug?
Answer:
36 feet squared
Step-by-step explanation:
Finding the perimeter of an object is adding all of the sides together. If the width of the rug is 6 feet then we know that there are two sides that length. Add those together.
6 feet + 6 feet = 12 feet
You would subtract the number you get from the perimeter.
24 feet - 12 feet = 12 feet
And then divide the number by the number of sides left, 2, to get each of their lengths.
12 feet / 2 feet = 6 feet
To find the area of a rectangle you multiply length times width, which in this case both are 6 feets.
6 feet x 6 feet = 36 feet squared
WILL GIVE 1ST RIGHT ANSWER BRAINIEST!
After two numbers are removed from the list 9,13,15,17,19,23,31,49, the average and the median each increase by 2. What is the product of the two numbers that were removed?
Answer:
247
Step-by-step explanation:
Hello!
We can begin by finding the average and median before two numbers are removed.
(9 + 13 + 15 + 17 + 19 + 23 + 31 + 49) / 8 = 22
And the median!
(17 + 19)/ 2 = 18
Since we know that the average and median will increase by 2, we will have the median after removal as 20, and the average, 24.
For the average, we can see that the total must be 144, that's what 24 * 6 is.
19 must have been one of the numbers because (17 + 23) / 2 = 20.
That's 32 less than the original sum of 176.
So if one of the removed numbers is 19, the other must be 13.
13 * 19 = 247
Thus, the product of the removed numbers are [tex]\boxed{247}[/tex].
Hope this helps!
A garden is in the shape of a rectangle 85 m by 50m.
Flowers are grown in 32% of the garden.
The rest of the garden is grass.
Work out the area of the garden that is grass.
Show your working out.
Answer:
2,890 meters^2 is grass
Step-by-step explanation:
First find the area of the garden
Area of a rectangle can be found using:
a=lw
a=85*50
a=4,250 meters^2
We know that 32% of the area is flowers, so we can multiply 32% and 4250
32%*4250
Convert 32% to a decimal by dividing by 100
32%/100=0.32
0.32*4250=1360
So, 1360 meters^2 is flowers.
The rest must be grass, so we can find the difference between the total area and the flowers
4250-1360=2890
So, 2,890 meters^2 is grass
Answer:
The answer to your question is 2890 m²
Step-by-step explanation:
Data
length = 85 m
width = 50 m
32% are flowers
Process
1.- Calculate the area of the garden
Area = length x width
-Substitution
Area = 85 x 50
= 4250 m²
2.- Calculate the area of the garden that are flowers
4250 ----------------- 100%
x ------------------ 32%
x = (32 x 4250) / 100
x = 136000/100
x = 1360 m² are flowers
3.- Calculate the area of the garden that is grass
Area of grass = 4250 - 1360
Area of grass = 2890 m²
Round 44.057 to the nearest hundredth.
Answer:
44.057 to nearest hundredth
44.06
The circus returned home and the animal trainers friend asked how many lions were on the train. The trainer answer "7 times as many lions than other animals (not lions). Then the friend asked about the bears." there were a seventh as many bears as other animals", replied the trainer. Then the friend asked about the elephants. How should the trainer respond to the question?
Answer:
Step-by-step explanation:
Solution:-
- We will denote:
Number of Lions = x
Number of bears = y
Number of elephants = z
Any other animal = T
- Now we will mathematically each statement given by the trainer.
Statement 1:
"7 times as many lions than other animals (not lions)."
- There were 7 times as many lions than any other animals i.e ( bears and elephants). So we can express:
x = 7*( x + y + T) .... E 1
Statement 2:
"there were a seventh as many bears as other animals"
- There were 1/7 as many bears than any other animals i.e ( lions and elephants). So we can express:
y = (x+z+T) / 7 ... E2
- Now combine two decrypted mathematical expressions.
x + y + z = T
7T + T/7 + z = T
What is the value of x in 15x-15=30
Answer: 3
15(3)-15=30
45-15=30
30=30
15x-15=30
15x=45
x=3
Answer:
x=3Step-by-step explanation:
[tex]\sf 15x-15=30[/tex]
[tex]\sf 15x-15+15=30+15[/tex]
[tex]\sf 15x=45[/tex]
[tex]\sf \frac{15x}{15}=\frac{45}{15}[/tex]
[tex]\sf x=3[/tex]
An equation has solutions of m = -5 and m = 9. Which could be the equation?
(m + 5)(m - 9) = 0
(m - 5)(m + 9) = 0
m? - 5m + 9 = 0
m2 + 5m-9=0
Answer:
(m+5) (m-9) = 0
Step-by-step explanation:
An equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given that, the solutions of an equation are m = -5, and m = 9, we need to find the equation,
(m + 5) (m - 9) = 0
One possibility is that of a quadratic equation.
y = (m + 5) (m - 9)
y = m² - 9m + 5m - 45
y = m² - 4m - 45
Hence, an equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.
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please assist me with this problem
Answer:
a) [tex]\sqrt{64+x^2}[/tex]
b) 15
Step-by-step explanation:
a) We know that AB = 8 and BC = x. We can use the Pythagorean Theorem, which states that for a right triangle with sides a, b, and c: [tex]a^2 +b^2=c^2[/tex] , where a and b are the shortest sides and c is the longest.
Here, AB = a = 8 and BC = b = x. So, AC = c. Then:
[tex]AB^2+BC^2=AC^2[/tex]
[tex]8^2+x^2=AC^2[/tex]
[tex]AC=\sqrt{64+x^2}[/tex]
b) We know that AC - AB = 9. Since AB = 8, then AC = 9 + 8 = 17. We also have the expression from above, so set them equal:
[tex]AC=\sqrt{64+x^2}=17[/tex]
[tex]64+x^2=289[/tex]
[tex]x^2=225[/tex]
x = 15
Hope this helps!
Answer:
sqrt(x^2 +64) = AC
x = 15
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2 + b^2 =c^2 a and b are the legs and c is the hypotenuse
We know the legs are x and 8
x^2 + 8^2 = AC^2
x^2 + 64= AC^2
Solving for AC
Take the square root of each side
sqrt(x^2 + 64) = sqrt(AC^2)
sqrt(x^2 +64) = AC
We are given AC - AB = 9
We know AB = 8
AC -8 =9
Add 8 to each side
AC -8+8 = 9+8
AC = 17
AC is the hypotenuse,
x^2 + 64= AC^2
x^2 +64 = 17^2
x^2 +64 = 289
Subtract 64 from each side
x^2 +64-64 = 289-64
x^2 =225
Take the square root
sqrt(x^2) = sqrt(225)
x =15
7. What is the measure of ZE ?
Answer:
70 degrees
Step-by-step explanation:
The adjacent angles in a parallelogram are supplementary and add to 180 degrees
∠CDE+∠DEF=180
We know that ∠CDE is 110 degrees, so we can substitute that in
∠CDE+∠DEF=180
110+∠DEF=180
Subtract 110 from both sides
∠DEF= 70
So, ∠E is 70 degrees
As I was going to St Ives I met a man with 7 wives. Each wife had 7 kids. Each kid had 7 cats. Each cat had 7 kittens. How many were going to St Ives?
Answer:
2401
Step-by-step explanation:
7 * 7 * 7 * 7 = 2401
Wich is the least common multiple of 12 and 8?
Answer: 24
Step-by-step explanation: The first few multiples of 8 are: 8, 16, 24, 32, 40, and 48. The first multiples of 12 are: 12, 24, 36, 48, 60, and 72.
...
Step 1: List the Multiples of Each Number.
How to get the inverse of this problem
Answer:
i think it is g(x)=x^3/8 -1
Step-by-step explanation:
Simplify: 27 : 54 : 9
Answer:
3 : 6 : 1
Step-by-step explanation:
The common multiple between these numbers is 9, so divide everything by nine.
Answer:
3:6:1
Step-by-step explanation:
27/9=3
54/9=6
9/9=1
3:6:1
I hope this helps!
Each lap Jeffery runs is 1 tenth of a mile. He wants to run 3 fifths
of a mile
How many laps does Jeffery need to run?
Answer:
6 laps
Step-by-step explanation:
Jeffery needs to run 3 laps.
Explanation:To find the number of laps that Jeffery needs to run, we can set up a proportion. We know that 1 lap is equal to 1 tenth of a mile, so we can set up the following proportion:
1 lap / 1 tenth mile = x laps / 3 fifths mile
Cross-multiplying and solving for x, we get:
x = (1 lap * 3 fifths mile) / (1 tenth mile)
x = 3 laps / 1 lap
x = 3
Therefore, Jeffery needs to run 3 laps.
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Which sentence signals a major shift in the action of the story?
A "The suns beat down on her neck as she stepped closer to examine the chart
B "She stamped her foot and gave a loud groan."
C Kari suddenly remembered a magic trick she had performed at her little brother's
birthday party.
D
"Then she watched as the pile of snow came falling down to test on the dirt that had
been underneath the grass field."
Answer:
i think, it is option c.
What is 4/24 x 2/3 =
Simplied
Answer:
all work is shown and pictured
Hey, I need help with the questions attached. I need it in 20 minutes, it is last minute homework. Thank you very much.
Answer:
1)
90g strawberry jelly
6 sponge fingers
315ml custard
135g tinned fruit
2) 260 cm²
Step-by-step explanation:
1) 120/4 × 3
90g strawberry jelly
8/4 × 3
6 sponge fingers
420/4 × 3
315ml custard
180/4 × 3
135g tinned fruit
2) area = base × height
= 20 × 13
= 260 cm²
Answers and Step-by-step explanations:
1. Let's find the amount of each ingredient we need for 1 person, and then multiply that by 3 later.
strawberry jelly: we have 120 grams for 4 people, so for 1 person, we need 120/4 = 30 grams
sponge fingers: we have 8 of these for 4 people, so for 1 person, we need 8/4 = 2 sponge fingers
custard: we have 420 mL for 4 people, so for 1 person, we need 420/4 = 105 mL
tinned fruit: we have 180 grams for 4 people, so for 1 person, we need 180/4 = 45 grams
Now, multiply each of these by 3 to find the amount needed for 3 people:
strawberry jelly: 30 grams * 3 = 90 grams
sponge fingers: 2 sponge fingers * 3 = 6 sponge fingers
custard: 105 mL * 3 = 315 mL
tinned fruit: 45 grams * 3 = 135 grams
2. The area of a parallelogram is calculated by the formula: A = Bh, where B is the base length (usually a side length) and h is the height perpendicular to the base. Here, we see that have two potential base lengths: 20 and 15. However, looking at the height, it's only perpendicular to the base with length 20, so we know that B = 20 and h = 13.
Plugging these into the formula, we get: A = 20 * 13 = 260 cm squared.
Hope this helps!
How would you write twelve more than the quotient of a number and five
Answer:
n/5 +12
Step-by-step explanation: