Answer:
p = 10.8
Step-by-step explanation:
Given that p is directly proportional to (p-1)² and p is always positive, then;
q = k (p-1)²
If q = 30 and p = 7
30 = k(7-1)²
30 = 6²k
30 = 36k
5 = 6k
k = 5/6
To get p when q = 80
q =k (p-1)²
80 = 5/6((p-1)²
480 = 5(p-1)²
480/5 = (p-1)²
(p-1)² = 96
p-1 = √96
p-1 = 9.8
p = 9.8 + 1
p = 10.8
B) 6
Ch 10.82
Find the Area of the shaded region. Round your answer to the nearest tenth.
Answer:
610 m^2
Step-by-step explanation:
Area of the shaded region = area of the outer rectangle - area of the inner rectangle
Area of the outer rectangle
l = 42
b = 25
a = l*b = 42*25 = 1050m^2
Area of the inner rectangle
l = 22
b = 20
a = l*b = 22*20 = 440m^2
Therefore, the area of the shaded region is = 1050 - 440
= 610m^2
Thank You
Hope u understood
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the area of a carpeted closet is 20 square feet . if the width of the closet is 3/2 feet , what is the width ?
Answer:
Length = 40/3 or 13.33 feet
Step-by-step explanation:
Given the following data;
Area of carpet = 20 feet
Width = 3/2 feet
To find the length of the carpet
Assuming that the shape of a carpeted closet is rectangular.
Area of rectangle = length * width
20 = length * 3/2
Multiplying both sides by 2/3
2/3 * 20 = length * 3/2 * 2/3
40/3 = length
Length = 40/3 or 13.33 feet
Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
(a) If the order of the choices is relevant, how many ways can this be done?
(b) If the order of the choices is not relevant, how many ways can this be done?
Answers:
(a) 73440(b) 3060=====================================================
Explanation for part (a)
Consider four slots labeled A,B,C,D.
We have
18 choices for slot A17 choices for slot B16 choices for slot C15 choices for slot DWe started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440
You can use the nPr permutation formula as an alternative method
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
in this case n = 18 and r = 4. The exclamation marks indicate factorial.
-----------------------------------
Explanation for part (b)
Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.
Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.
There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)
73440/24 = 3060
You could use the nCr combination formula to get the same result
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
where n = 18 and r = 4 are the same from last time.
The connection between nPr and nCr is this
[tex]_nC_r = \frac{_nP_r}{r!}[/tex]
which can be rearranged into
[tex]_nP_r = r!*\left( _nC_r \right)[/tex]
these formulas are handy to help us go back and forth between nCr or nPr.
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
What are combination and permutation?Combination is a way of selecting items from a collection where the order of arrangement is not relevant.
It is given by:
[tex]^nC_r[/tex] = n! / r! (n-r)!
Permutation is a way of selecting items from a collection where the order of the arrangement is relevant.
It is given as:
[tex]^nP_r[/tex] = n! / (n-r)1
We have,
Number of distinct colors = 18
Number of colors to be chosen = 4
The number of ways the four colors be chosen when the order is not relevant:
= [tex]^{18}C_4[/tex]
= 18! / 4! 14!
= 18 x 17 x 16 x 15 / 4 x 3 x 2
= 3060
The number of ways the four colors be chosen when the order is relevant:
= [tex]^{18}P_4[/tex]
= 18! / 14!
= 18 x 17 x 16 x 15
= 73440
Thus,
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
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the graph of f(x)=x^2 will be translated 5 up and 2 units to the right .which function describe the graph produced by the translation
help please!!!!!!!!!!!!!!!!
Answer:
D
The X Axis is the time, the Y Axis is the amount of pages being read.
2x^+7x - 15= 0 If r and s are two solutions of the equation above and r > s which of the following is the value of r-s?
Answer:
6.5
Step-by-step explanation:
You failed to include the choices
What needs to be done before you can add or subtract in this equation?
X - 3/4 = 1/2
A)multiply by the reciprocal of 3/4
B)multiply by the reciprocal of 1/2
C)Find the LCD between 1/2 and 3/4
Answer:
A)
Step-by-step explanation:
I need the answer I will mark brainlist pls
Answer:
8 I belive is C and 9 I think is D :)
Right triangles 1, 2,
and 3 are given with all their angle measures and approximate side lengths.
35
8.2
120
10
9.4
10
2
70
55
5.7
3.4
6.4
7.7
3
50
40
10
Answer:
2.2
Step-by-step explanation:
I did it on khan
Right triangles have the measure of one of its angles to be 90 degrees
The ratio WY/WX is 0.36
From the triangle (see attachment), one of the angles of triangle WXY is 70 degrees.
This means that, the triangle is similar to triangle 1.
Similar triangles may or may not have congruent side lengthsSimilar triangles have equivalent ratiosSo, by comparing the side lengths, we have:
[tex]WY = 3.4[/tex]
[tex]WX = 9.4[/tex]
The ratio is then calculated as:
[tex]\frac{WY}{WX}= \frac{3.4}{9.4}[/tex]
[tex]\frac{WY}{WX}= 0.36[/tex]
Hence, the ratio WY/WX is 0.36
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Please I need it now
A rational number is terminating decimal, if its denominator has
no prime factor other than:
A. 2 and 3 B. 3 and 5 C. 2 and 5 D. 2 and 7
Answer:
it's C. 2 and 5...
Step-by-step explanation:
If the denominator of rational number contains no prime factors other then 2 or 5 or both, then this rational number can be expressed as terminating decimal. So the correct answer is option is C
Find the volume of the box.
3 ft
4 ft
5 ft
The volume of the box is
cubic feet________
Answer:
60 ft³
Step-by-step explanation:
GIVEN :-
Length of cube = 5 ftWidth of cube = 4 ftHeight of cube = 3 ftTO FIND :-
Volume of cubeFACTS TO KNOW BEFORE SOLVING :-
Volume of a cube = Length × Width × Height
SOLUTION :-
In the question , all the dimensions of the cube is given. So,
Volume of the cube = 5 × 4 × 3 = 60 ft³
Based on the calculation, the volume of the box is 60 cubic feet.
How to calculate the volumeTo find the volume of a box, you need to multiply its length, width, and height. In this case, the dimensions of the box are given as:
Length = 3 ft
Width = 4 ft
Height = 5 ft
To calculate the volume, multiply these dimensions together:
Volume = Length × Width × Height
Volume = 3 ft × 4 ft × 5 ft
Volume = 60 cubic ft
Therefore, the volume of the box is 60 cubic feet.
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Factorise as fully as possible:
[tex]8x^{2} -4x[/tex]
Please help me! Got a big test tomorrow and I really want to make sure I have every skill under my belt.
Answer:
[tex]4x(2x−1)[/tex]
Step-by-step explanation:
[tex] {8x}^{2} - 4x[/tex]
[tex]4x(2x) - 4x[/tex]
[tex]4x(2x)+4x(−1)[/tex]
[tex]4x(2x−1)[/tex]
Hope it is helpful....Which expression has the same value as the one below? 87 + (-12)
Answer:
75
Step-by-step explanation:
Given data
First term= 87
Second term= -12
Hence,
87 + (-12)
open bracket
+*-= -
= 87 -12
=75
Therefore the equivalent is 75
Suppose that you have the option to buy an itern with either cash or credit?Under which condition would you use credit?
A if you don't want to pay interest
B if you want to build a good credit history
C if you like carrying a lot of cash on you
Answer:
Step-by-step explanation:
B. You build credit by using credit cards so b is the answer.
A local pizza parlor is selling two different shapes of cheese pizza for the same price. You can get two small square pizza that have sides of 7 inches or a large round pizza with a diameter of 12 inches. Which choice gives you more pizza
Answer:
It is a good idea to buy the round pizza, since it has a total of 113.04 square inches of pizza, while the two square slices together bring together 98 square inches.
Step-by-step explanation:
Since a local pizza parlor is selling two different shapes of cheese pizza for the same price, and you can get two small square pizza that have sides of 7 inches or a large round pizza with a diameter of 12 inches, to determine which choice gives you more pizza the following calculations must be carried out, knowing that the area of a square is equal to pi multiplied by the radius squared, and that the area of a square is equal to its side squared:
Round pizza:
Radius = Half the diameter
3.14 x 6 ^ 2 = X
3.14 x 36 = X
113.04 = X
Square pizzas:
(7x7) x 2 = X
49 x 2 = X
98 = X
Therefore, it is a good idea to buy the round pizza, since it has a total of 113.04 square inches of pizza, while the two square slices together bring together 98 square inches.
A basketball player made 135 of the 225
foul shots he took in 4
games.
How many shots will he make in his next game if he attempts 30 foul shots?
135/225=3/5
3/5 times 6 on both sides=18/30
so he will make 18 shots
Which equation is true for the value a=7
A. a+2(a-3)= 15
B. 4a-4(14)-a=24
C. 2a+47=105
D.3a+2(a-3)=34
E. 4a-2a=18
Answer:
The answer is just re look at the question A
Answer
THE ANSWER IS A
Step-by-step explanation:
Subtract the sum of -6 and -2 from -18. *
Answer:
-26
Step-by-step explanation:
Because -6+ -2= -8
-18- 8= -26
Ahmad deposits $3000 into an account that pays simple interest at a rate of 3% per year. How much interest will he be paid in the first 4 years?
Answer:
.......
Step-by-step explanation:
Jahlan, simple interest means that interest is paid every year on the original $4000.
To find 2% of 4000, you multiply 4000(.02) = $80.
Since the interest is the same, 3(80) = $240.
PLEASE ANSWER IMMEDIATELY!!!
Answer:
w
Step-by-step explanation:
The inputs (x) have the different variables in order for it to be a function.
A class spends 1 hour 15 minutes on
English Language each school day. If
the total time spent in school each day
is 5 hour. What fraction of the time is
spent on English Language
Answer:
1/4
this is fraction of time spent on English language...
Nuts Berry Farm sells nuts for $60 for 4 pounds. Today, and just for today only, Nuts Berry Farm is giving a 30% discount to all those who will buy nuts today. Enter how much, in dollars, is a pound of nuts today after the discount.
-1/2+(3/4x419) =
A. 1/9
B. 5/6
C. -1/5
D. -1/6
9514 1404 393
Answer:
D. -1/6
Step-by-step explanation:
Your calculator can tell you the answer to this.
[tex]-\dfrac{1}{2}+\left(\dfrac{3}{4}\cdot\dfrac{4}{9}\right)=-1/2+\dfrac{4\cdot3}{4\cdot9}=-\dfrac{1}{2}+\dfrac{3}{9}\\\\=-\dfrac{1}{2}+\dfrac{1}{3}=-\dfrac{3}{6}+\dfrac{2}{6}=\boxed{-\dfrac{1}{6}}[/tex]
Any help would be greatly appreciated!
Answer:
the answer for that question is sqrt(49)
What is 5 / 7 ÷ ½ ?
step by step pls
Answer:
1 3/7
Step-by-step explanation:
5 / 7 ÷ ½
Copy dot flip
5/7 * 2/1
10 /7
Changing from an improper fraction
7/7 + 3/7
1 3/7
68 - 4 × (6 - 4)4
pls help o-o
Answer:
Here you go!, hope it helped. 68-32x
Answer:
36 is the answer I think :D
Choose all the expressions that show this statement is true.
Answer:
F. or C.
Step-by-step explanation:
A cylinder has a radius of 8 cm and a height of 4 cm what is the approximate value of the surface area of the cylinder
Area of cylinder = curved area + 2 x base circle
Circles = 2 x π(8)² = 128π cm²
Curved area = circumference of circle x height of cylinder
Circumference of circle = 2πr = 2π(8) = 16π cm
Curved area = 16π x 4 = 64π cm²
Total surface area = 128π + 64π = 192π cm² = 603.19cm² (5sf)
help asap will mark branniest thx
Answer:
[tex](\pi)r ^{2} h \div 3[/tex]
Volume = 3.14 × 5² ×6 ÷ 3
volume = 157 cm³ B
Find the volume of this cylinder.
Round to the nearest tenth.
16cm
4 cm
[?] cm3
The volume of the given cylinder with a diameter of 4 cm and the height of the cylinder is 16cm is 201.062 cm².
What is the volume of a right circular cylinder?The right circular cylinder is the cylinder in which the line joining the centre of the top circle of the cylinder to the centre of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Suppose that the radius of the considered right circular cylinder is 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
The volume of the given cylinder is,
Volume of the cylinder = (π/4) × (4cm)² × 16cm
= 201.062 cm²
Hence, the volume of the given cylinder is 201.062 cm².
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