Answer:
The mean is 20.Step-by-step explanation:
To find:
The mean.Given:
The mean is calculated by dividing all the values in a set by their left-to-right numbers.
To begin, add up all the means numbers.
Solve.
Solutions:
[tex]\Longrightarrow: \sf{28+18+19+18+17=100}[/tex]
Five mean numbers are given.
All you have to do is divide them.
[tex]\Longrightarrow: \sf{100\div5=\boxed{\sf{20}}[/tex]
[tex]\Longrightarrow: \boxed{\sf{20}}[/tex]
Therefore, the mean 28, 18, 19, 18, 17 is 20, which is our answer.I hope this helps, let me know if you have any questions.
Good luck with your assignment!
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Consider the equation:
x^2= -8x – 7
1) Rewrite the equation by completing the square.
Your equation should look like (2 + c)2 = dor (x – c)2 = d.
---
-
2) What are the solutions to the equation?
Answer:
Step-by-step explanation:
Question 1:
x² = -8x - 7
x² + 8x = -7
(x + 4)² = 9
So the answer is (x + 4)² = 9
Question 2:
(x + 4)² = 9
So x = -4 ± 3
14.
Case Study - 2 John planned a birthday party for his younger sister with his friends.
ded to make some birthday caps by themselves and to buy a cake from a bakery shop. For these two items, they decided the following dimensions : Cake : Cylindrical shape with diameter 24 cm and height 14 cm. cap: Conical shape with base circumference 44 cm and height 24 cm.
2
Based on the above information, answer the following questions: (a) How many square cm paper would be used to make 4 such caps ?
The bakery shop sells cakes by weight (0-5 kg, 1 kg, 1.5 kg, etc.). To have the required dimensions, how much cake should they order, if 650 cm3 equals 100 g of cake?
-30/3/1
a. The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².
b. For the cake to have the required dimensions, they should order 1 kg of cake.
a.
The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².
To find the number of square cm paper would be used to make 4 caps, we need to find the area of a cone.
Area of a coneThe area of a cone, A = πr² + πr[√(h² + r²)] where
r = radius of cone and h = height of coneNow given that the base circumference of the cone is C = 44 cm. So,
C = 2πr where r = radius of base
So, r = C/2π = 44 cm/2π = 22 cm/3.142 = 7 cm
The height of the cone, h = 24 cm
So, A = πr² + πr[√(h² + r²)]
A = π(7 cm)² + π(7 cm)[√((24 cm)² + (7 cm)²)]
A = π(7 cm)² + π(7 cm)(7)[√((4 cm)² + (1 cm)²)]
A = 49π cm² + 49π cm[√(16 cm² + 1 cm²)]
A = 49π cm² + 49π cm[√(17 cm²)]
A = 49π [1 cm² + 4.123 cm²)]
A = 49π [5.123 cm²)]
A = 251.032π
A = 788.64 cm²
Since the area of one cap is A = 788.64 cm²,
the area of 4 caps is A' = 4A
= 4 × 788.64 cm²
= 3154.56 cm²
So, the number of square cm of paper that would be used to make 4 caps is 3154.56 cm².
b.
For the cake to have the required dimensions, they should order 1 kg of cake.
To find the amount of cake to be ordered, we need to find the volume of a cake since it is the volume of a cylinder.
Volume of a cylinderThe volume of a cylinder is V = πd²h/4 where
d = diameter of cake = 24 cm and h = height of cake = 14 cmSubstituting the values of the variables into the equation, we have
V = πd²h/4
V = π(24 cm)²(14 cm)/4
V = π(576 cm)²(14 cm)/4
V = 8064π cm³/4
V = 2016π cm³
V = 6333.45 cm³
So the volume of the cake is 6333.45 cm³
Since 650 cm³ equals 100 g, 6333.45 cm³ = 6333.45 cm³ × 100 g/650 cm = 974.4 g = 0.974 kg ≅ 1 kg.
So, for the cake to have the required dimensions, they should order 1 kg of cake.
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Sian is going to roll the dice 50 times work out an estimate for the number of times the dice will land on either 5 or 6
Answer:
5
Step-by-step explanation:
5,10,15,20,25,30,35,40,45,50
6,12,18,24,30,36,42,48,54
Find. The unit vector. Multiple choice
Answer:
D
Step-by-step explanation:
6i = 3/5i
8j = 4/5j
3/5i + 4/5j
The circumference of a pipe is 9.24 centimeters. What is the diameter of the pipe? Use 3.14 for ℼ and do not round your answer.
Hi Student!
The first step that we need to take when approaching this problem is to extract the important information that was given in the problem statement. Reading through it, we can see that we are given a circumference of a pipe being 9.24 centimeters. After that, they are asking for us to determine what the diameter of the pipe is and tell us to use 3.14 instead of π.
Now that we have completed the information gathering, we can move onto the part of plugging in our values and solving for the unknown.
Plug in the values
[tex]C=d*\pi[/tex][tex]9.24\ cm=d*3.14[/tex]Divide both sides by 3.14
[tex]\frac{9.24\ cm}{3.14}=\frac{d*3.14}{3.14}[/tex][tex]\frac{9.24\ cm}{3.14}=d[/tex][tex]2.942675\ cm=d[/tex]Therefore, after solving for our unknown being the diameter we were able to determine that it is around 2.942675 centimeters using the Circumference formula.
An industry currently has 100 firms, each of which has fixed cost of $16 and average variable cost as follows: Quantity Average Variable Cost 1 $1 22 33 44 55 66 Compute a firm’s marginal cost and average total cost for each quantity from 1 to 6. The equilibrium price is currently $10. How much does each firm produce? What is the total quantity supplied in the market? In the long run, firms can enter and exit the market, and all entrants have the same costs as above. As this market makes the transition to its long-run equilibrium, will the price rise or fall? Will the quantity demanded rise or fall? Will the quantity supplied by each firm rise or fall? Explain your answers. Graph the long-run supply curve for this market, with specific numbers on the axes as relevant.
The marginal cost is the change in the total cost that arises when the quantity produced is incremented, the cost of producing additional quantity.
a). First construct total variable cost for each level Q -- simply multiply Q by AVC. So
Q TVC
1 1
2 4
3 9
4 16
5 25
6 36
Now calculate marginal cost as the change in TVC for each level Q.
Q MC
1 1
2 3
3 5
4 7
5 9
6 11
b) with price = 10, firm will produce 5 but not 6 units.
c) calculate total profits at Q=5. Total revenue is $50, total costs is $25+$16 = $41. Since there are profits to be made, more firms will enter, shifting the supply curve out, Price will fall, quantity goes up. Each firm will supply the same or less as price falls.
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How many solutions does the following equation have? 4x -6 = 2(2x+3)
Answer:
None
Step-by-step explanation:
[tex]4x-6 = 2(2x+3)\\4x-6 = 4x+6\\0x -12 = 0\\no solutions[/tex]
Answer: There are no solutions for the equation.
Step-by-step explanation:
4x - 6 = 2(2x + 3)
4x - 6 = 4x + 6
-6 = 6
Ashley has finished 7/25 of her homework what percentage of the homework does Ashley still need to finish
Answer:
72 percent
Step-by-step explanation:
7/25, x 4 to get a fraction of 100
28/100
100 - 28 = 72
72 percent
Answer:
Ashley still needs to finish 72 percent of her homework
Step-by-step explanation:
Happy to help!! :D
What is an in-text citation?
A. Providing constructive criticism
B. Using another person's ideas or writing without citing them.
C. Using reliable sources in your paper
D. Providing the author's name and where you found the information.
the first three terms of a G.P is are x+1, x-3 and x-1 find the value of x
[tex]\text{First term,}~ a = x+1\\\\\text{Common ratio,}~ r = \dfrac{x-3}{x+1}= \dfrac{x-1}{x-3}\\\\\text{Now,}\\\\~~~~~~\dfrac{x-3}{x+1} = \dfrac{x-1}{x-3}\\\\\\\implies (x-3)(x-3) = (x-1)(x+1)\\\\\\\implies (x-3)^2 = x^2 -1\\\\\\\implies x^2 -2\cdot 3x +3^2 =x^2 -1\\\\\\\implies -6x+9=-1\\\\\\\implies -6x = -1 -9\\\\\\\implies -6x = -10\\\\\\\implies x =\dfrac{-10}{-6}\\ \\\\\implies x = \dfrac 53[/tex]
can someone please help I pay £100
Answer:
The new points to the triangle will be:
[tex]A(1,4)\\ B(1,1)\\ C(-1,1)[/tex]
Step-by-step explanation:
Because the reflection point is at [tex]x=2[/tex], all x values will subtract their distances from [tex]x=2[/tex] to get their new values. The y values remain the same.
The starting values are:
[tex]A(3,4)\\ B(3,1)\\ C(5 ,1)[/tex]
Point [tex]A[/tex] is 1 unit away from [tex]x=2[/tex], so we'll subtract 1 from 2 to get the new x value: [tex]2 - 1 = 1[/tex], so [tex]A(1,4)[/tex].
Point [tex]B[/tex] is also 1 unit away from [tex]x=2[/tex], so we'll subtract 1 from 2 to get the new x value: [tex]2 - 1 = 1[/tex], so [tex]B(1,1)[/tex].
Point [tex]C[/tex] is 3 units away from [tex]x=2[/tex], so we'll subtract 3 from 2 to get the new x value: [tex]2 - 3 = -1[/tex], so [tex]C(-1,1)[/tex].
Amiya has 8 more stamps than Huiling. Ravi has twice as many stamps as Amiya. Amiya and Ravi have 72 stamps altogether. How many stamps does Huiling have?
Amiya + Ravi = 72
x + 2x = 72
3x = 72
x = 72/3
x = 24
therefore Amiya has 24 stamps
Huiling has 8 more than Amiya = 24 + 8 = 32stamps
hope it helps...!!!
find the circumference of the circle 5cm
Please solve this for me
[tex]6 sin² x + 4 cos²x = Stanx[/tex]
[tex]Correct option is B)
Given, 4cos2x+6sin2x=5
[/tex]
[tex]⇒4cos2x+4sin2x+2sin2x=5
⇒2sin2x=1⇒sin2x=21=(21)2
⇒x=nπ±4π
[/tex]
Solve any question of Trigonometric Functions with:-[tex]~~~~~~6 \sin^2 x + 4 \cos^2 x = 5 \tan x \\\\\implies 3 \cdot 2\sin^2 x + 2 \cdot 2 \cos^2 x = 5 \tan x\\ \\\implies 3(1- \cos 2x ) + 2( 1 + \cos 2x) = 5 \tan x\\\\\implies 3 - 3 \cos 2x +2 +2 \cos 2x = 5 \tan x\\\\\implies 5- \cos 2x = 5 \tan x\\ \\\implies 5 - \left(\dfrac{1- \tan^2 x}{ 1+ \tan^2 x} \right)=5 \tan x\\\\\implies \dfrac{5+5 \tan^2x -1 + \tan^2 x}{1+ \tan^2 x} = 5 \tan x\\\\\implies 4 + 6\tan^2 x = 5( \tan x)(1+ \tan^2 x)\\\\\implies 4 +6\tan^2 x = 5 \tan x + 5 \tan^3 x[/tex]
[tex]\implies 5\tan^3 x -6 \tan^2 x+5 \tan x-4=0\\\\\implies 5 \tan^3 x - 5 \tan^2 x - \tan^2x + \tan x+ 4\tan x -4=0 \\\\\implies 5\tan^2 x(\tan x-1) -\tan x(\tan x-1) +4(\tan x-1)=0\\\\\implies ( \tan x - 1)( 5 \tan^2 x- \tan x +4) =0\\\\\implies \tan x =1\\\\\implies x = n \pi+ \dfrac{\pi}4[/tex]
Aziza has a triangle with two sides measuring 11 in. and 15 in. She claims that the third side can be any length as long as it is greater than 4 in. Which statement about Aziza’s claim is correct?
Aziza’s claim is not correct. The third side must be between 4 in. and 26 in.
Aziza’s claim is not correct. The third side can be any length less than 26 in.
Aziza’s claim is not correct. The third side can be any length.
Aziza’s claim is not correct. The third side must create a scalene triangle.
Answer:
First choice.
Step-by-step explanation:
The third side cannot be 26 or greater ( as 11 + 15 = 26).
Answer:
it is A i think
Step-by-step explanation:
If you make 20 dollars a week how many weeks will it take you to reach the goal Of 700 dollars
Answer:
35
Step-by-step explanation:
it takes 5 weeks to make 100 since 20 x 5 = 100
100 x 7 = 700
5 x 7 = 35
Answer:
It will take 35 weeks.
Express tan j as a fraction in simplest terms
From the figure, the value of tan j is 13/9
How to determine the value of tan j?The tangent of an angle is calculated using:
tan(j) = opposite/adjacent
From the figure, we have:
opposite = 13
adjacent = 9
So, we have:
tan(j) = 13/9
Hence, the value of tan j is 13/9
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Please help me math
Answer:
Diagonal is = 16.97
Step-by-step explanation:
To find the length of a diagonal across a square use this formula
d = √(2×area)Plug in
d = √(2×144)d = √288D = 16 . 97
there are 6 batteries in a small paket ofbatteries. there are 9 batteries in a large paket ofbatteries. chow buys m small pakets of batteries and g large pakets of batteries. write down a formula in terms of m and g for t
Answer:
t = 6m + 9g.
Step-by-step explanation:
Total number of batteries is t.
t = 6m + 9g.
How many different bit strings can be formed using six 1s and eight 0s?
Answer:
The string contains 6 ones and 8 zeros, thus 14 bits in total.
Step-by-step explanation:
Hope this helps.
Write the equation of each line in slope‐intercept form.
F is the function f(×)= 2x+5
Find f(3)
Answer:
f(3)=11
Step-by-step explanation:
f(x) = 2x + 5
to find f(3) we simply plug in 3 where ever x is
So f(3) = 2(3) + 5
==> multiply 2 and 3
f(3) = 6 + 5
==> add 6 and 6
f(3) = 11
help me please.. where does he cut from the board?? i need an answer. please i beg you.
Answer: 6 pieces
Step-by-step explanation:
He is cutting the board into pieces each measuring [tex]\frac{1}{8}[/tex] of a foot. The original board is [tex]\frac{3}{4}[/tex] of a foot long. This means he is dividing, so we will solve the problem by doing the following.
[tex]\displaystyle \frac{3}{4}/\frac{1}{8}[/tex]
[tex]\displaystyle\frac{3}{4}*\frac{8}{1}[/tex]
[tex]\displaystyle\frac{3*8}{4*1}[/tex]
[tex]\displaystyle\frac{24}{4}[/tex]
[tex]\displaystyle6[/tex]
He can cut the board into 6 pieces, each measuring [tex]\frac{1}{8}[/tex] of a foot.
How many triangles can be constructed with sides measuring 6 cm, 2 cm, and 7 cm? more than one none one
Answer:
None
Step-by-step explanation:
By using the equation a^2 +b^2=c^2 we can see if it will work.
Substitute a for 6 and b for 2 to get 6^2+2^2=40
when you [tex]\sqrt{40}[/tex] you don't get 7 therefore you cant make any triangles
A rectangular prism has a
length of 2 1/2yd, a width of 1 1/2yd, and a height
of 1 1/2yd. You use cubes with fractional edge
lengths of 1/2 yd to find the volume. How many
cubes are there for each of the length, width,
and height of the prism? What is the volume of
the prism?
Step-by-step explanation:
we need 2 1/2 × 2 = 5 cubes along the length.
1 1/2 × 2 = 3 cubes along the the width.
and 1 1/2 × 2 = 3 cubes along the height.
altogether we need
5×3×3 = 45 cubes
and the volume is
2 1/2 × 1 1/2 × 1 1/2 = 5/2 × 3/2 × 3/2 = 45/8 = 5 5/8 yd³
There are 96 cubes are there for each of the length, width, and height of the prism.
The volume of a rectangular prism is 12 yd³.
What is the prism?A prism is a three-dimensional solid object in which the two ends are identical. It is the combination of flat faces, identical bases, and equal cross-sections.
A rectangular prism has a length of 2 1/2yd, a width of 1 1/2yd, and a height
of 1 1/2yd.
length 2 1/2 and half yd = 2 1/2+ (1/2) yd = 5/2 + 1/2 = 6/2= 3 yd
Width 1 1/2 and half yd = 1 1/2 + (1/2) yd = 3/2 + 1/2 = (4/2) = 2 yd
Height 1 1/2 and half yd = 1 1/2 + (1/2) yd = 3/2 + 1/2 = (4/2) = 2 yd
Cubes of edge length (1/3) yd are used to fill the rectangular prism.
The length would contain (3) ÷ (1/2) = 6
The width would contain (2) ÷ (1/2) = 4
The height would contain (2) ÷ (1/2) = 4
How many cubes are there for each of the length, width, and height of the prism?
6 × 4 × 4 = 96 cubes
There are 96 cubes are there for each of the length, width, and height of the prism.
What is the volume of the prism?
The volume of rectangular prism = 3 × 2 × 2 = 12
The volume of a rectangular prism is 12 yd³.
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100 POINTS i need help fast!
Answer:
Step-by-step explanation:
you multiple each hight and base
(1.1x10^-3) - (9.6x10^-4)
Answer:
0.00014
Step-by-step explanation:
just use calculator...
(1.1x10^-3) - (9.6x10^-4) = 0.00014
EXPLAIN IN YOUR OWN WORDS PLEASE!!!! ILL GIVE BRAINLIEST!!!
A scale drawing of a kitchen is shown below. The scale is 1 : 20. A rectangle is shown. The length of the rectangle is labeled 4 inches. The width of the rectangle is labeled 5 inches. Show your work to determine the area of the room in square feet.
Answer: 55 [tex]\frac{5}{9}[/tex] feet² or 55.556 feet²
Step-by-step explanation:
The scale means that for ever one in the scale drawing, it is 20 in the actual room. We will convert the dimensions using proportions.
[tex]\frac{5}{x}=\frac{1}{20}[/tex]
100 = x
-> The length is 100 inches
[tex]\frac{4}{x}=\frac{1}{20}[/tex]
80 = x
-> The width is 80 inches
The area of a rectangle can be found by multiplying the length by the width:
A = L * W
A = 100 * 80
A = 8,000 inches²
To get this into square feet, we will divide by 144. Why? There are 12 inches in a foot. 12 times 12 is 144.
8,000 inches² / 144 = 55 [tex]\frac{5}{9}[/tex] feet²
The area of the room, in square feet, is 55 [tex]\frac{5}{9}[/tex] feet².
For -3y+2x=-18 determine the value of y when x = 0, and the value of x when y = 0.
Hello!
We have two different scenarios that we have to solve in the question. We will be solving for both the x and y variable.
We were given the equation: -3y + 2x = -18
To solve for our variables, we will use the values given in our question.
Solve:
Lets solve for the value "y", where our x = 0
Plug in 0 to x and solve:
-3y + 2(0) = -18
-3y = -18
y = 6
Lets now solve for the value "x", where our y = 0
Plug in 0 to y and solve:
-3(0) + 2x = -18
2x = -18
x = -9
Therefore, our answers would be: y = 6, x = -9
Answer:
y = 6
x = -9
HELP ME PLEASSE!!! I WILL MARK AS BRAINLIEST
The turtle’s distance from his starting point is increasing between (blank)
seconds.
0 and 12
0 and 6
6 and 8
8 and 12
The turtle’s distance from his starting point is constant between (blank)
seconds.
0 and 12
0 and 6
6 and 8
8 and 12
The turtle’s distance from his starting point is decreasing between (blank)
seconds.
0 and 12
0 and 6
6 and 8
8 and 12
Answer:
See below
Step-by-step explanation:
The turtle’s distance from his starting point is increasing between 0 and 6
seconds (which means it is getting larger in that time interval)
The turtle’s distance from his starting point is constant between 6 and 8 seconds (which means it is not moving in that time interval!)
The turtle’s distance from his starting point is decreasing between 8 and 12
seconds (which means it is getting smaller in that time interval)
Answer:
0-6, 6-8, 8-12
Step-by-step explanation:
For this, we'll have to use the numbers along the x-axis to measure. The line begins moving in a positive direction (up) from 0 to 6, which at that point, it remains stationary until 8 seconds. It then moves in a negative direction (down) all the way to 12.
If I can explain or elaborate in any way, please let me know.
Hope this helps!
