The approximated value of π using the integer digits 1 2 3 4 5 6 7 8 is is 3.142857
How to approximate the value of π?The integers are given as:
1 2 3 4 5 6 7 8
The value of π is:
π = 22/7
Evaluate the quotient
π = 3.14285714286
From the question, the digits 1 to 8 have to appear just once.
So, we approximate the number up to the point where any of the given digits has more than one occurrence.
So, we have:
π = 3.142857
Hence, the approximated value of π is 3.142857
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A diagonal of a cube measures 15 cm and the length of an edge of the cube is startroot 75 endroot cm. what is the length of the diagonal of a face of the cube? round to the nearest tenth. 7.1 cm 12.2 cm 13 cm 15 cm
A cube is a three-dimensional solid object having six square faces. The measure of the length of the diagonal of the face of the cube is 12.2 cm.
What is a cube?A cube is a three-dimensional solid object having six square faces, facets, or sides, three of which meet at each vertex. The cube is one of the five Platonic solids and the only regular hexahedron.
Given the length of an edge of the cube is √75 cm, therefore, the length of the diagonal of the face of the cube will be √2 times the length of an edge of the cube. Thus, the measure of the length of the diagonal of the face of the cube is,
Length of the diagonal of the face = √2 × √75 = 12.2 cm
Hence, the measure of the length of the diagonal of the face of the cube is 12.2 cm.
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Answer: ITS B (12.2)
Step-by-step explanation:
I am the lizard king, I can do anything.
What is the solution of x = 2 startroot x minus 2 endroot?
The solution to the function [tex]f(x) = 2\sqrt{x - 2}[/tex] when x = 2 is 0
How to determine the solution?The equation of the function is given as:
[tex]f(x) = 2\sqrt{x - 2}[/tex]
When x = 2, we have:
[tex]f(x) = 2\sqrt{2 - 2}[/tex]
Evaluate the difference
[tex]f(x) = 2\sqrt{0}[/tex]
Evaluate the exponent of 0
f(x) = 2 * 0
Evaluate the product
f(x) = 0
Hence, the solution to the function when x = 2 is 0
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PLEASE HELP ASAP, WOULD APPRECIATE IF YOU SHOWED STEPS
Answer:
abbbcab(a) [tex]7^{4}[/tex] (b) [tex](\frac{4}{9}) ^{17}[/tex] (c) [tex]4^{-4}[/tex] (d) [tex]8^{-3}[/tex]Step-by-step explanation:
1. The moment he started: 3 bacteria
1st hour: 3*2 bacteria = 3*[tex]2^{1}[/tex] bacteria
2nd hour: 3*2*2 bacteria = 3*[tex]2^{2}[/tex] bacteria
3rd hour: 3*2*2*2 bacteria = 3*[tex]2^{3}[/tex] bacteria
etc.
Each hour the number of bacteria multiplies by 2 (the power of 2 is increased by 1), therefore, [tex]B=3*(2)^{n}[/tex]
2. Exponential function has the form of [tex]f(x)=ab^{x}[/tex]
if a is greater than 0 and b is greater than 1, then it's exponential growth.
The answer is:
[tex]y=4^{x}[/tex] (4 > 1)
3. If smth increases by 2.5% each time, that means that at first you had 100% and then it became 100%+2.5% = 102.5%. So each time we multiply the value by 1.025 (100*1.025=102.5).
4. Linear equation form: [tex]y=ax+b[/tex]
Quadratic equation form: [tex]y=ax^{2} + bx + c[/tex]
Exponential equation form: [tex]y=ab^{x}[/tex]
In this case, a = 3.8, b = -5.5, c = -4.8
5. (a) square root
(b) linear
(c) exponential
(d) quadratic
6. Each year the car's worth is multiplied by 0.82 (82%). Therefore, after n years, the value will be: V = 27 500 * [tex]0.82^{n}[/tex]
7. Neither first, nor second differences are constant in case of an exponential relation, because we do not add but multiply.
Ex. [tex]y=2^{x}[/tex]
values: 1 2 4 8 16 32...
1st diff: 1 2 4 8 16...
2nd diff: 1 2 4 8...
8. (a) [tex]7^{11} / 7^{7} = 7^{11-7} = 7^{4}[/tex]
(b) [tex](\frac{4}{9})^{12} *(\frac{4}{9})^{5} =(\frac{4}{9} )^{12+5}=(\frac{4}{9})^{17}[/tex]
(c) [tex]4^{11} / (4^{5})^{3} =4^{11} / 4^{5*3}=4^{11} /4^{15}=4^{11-15}=4^{-4}[/tex]
(d) [tex]8^{-6}*8^{3}=8^{-6+3}=8^{-3}[/tex]
For what value of n does startfraction 216 superscript n minus 2 baseline over (startfraction 1 over 36 endfraction superscript 3 n?
They are written in term of power to the base of a function. The value of n that will make both expression equal is 2/9
Exponential expressionThey are written in term of power to the base of a function. Given the expression below:
[tex]216^{n-2}=\frac{1}{36}^{3n}[/tex]
This can be further simplified as:
[tex]6^3^{n-2}=(6^{-2})^{3n}\\6^{3n-2}=6^{-6n}[/tex]
Cancel the base to have:
3n-2 = -6n
3n+6n = 2
9n = 2
n = 2/9
Hence the value of n that will make both expression equal is 2/9
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Question 1 (10 points)
07.01 MC)
Part A: Explain why x = 5 makes 4x-1 s 19 true but not 4x-1 <19. (5 points)
Part B: What value from the set (6, 7, 8, 9, 10) makes the equation 5x+2=47 true? Show your work. (5 points)
GIVE EXPLANATION PLEASE ALONG WITH THE ANSWER
Answer:
7.4,000
8.23,000
9.1,000
Step-by-step explanation:
I'm teacher
For which shape is 180 degrees the smallest angle of rotational symmetry?
Answer:
the sun
Step-by-step explanation:
hope this helps
4 Suppose AABC = AXYZ. Which
coordinates are a possible location
of Z?
у
у
7
7
6
6
5
5
4
3
С
4
3
2
2
Х
Y
1
1
A
B
0 1 2 3 4 5 6
0 1 2 3 4 5 6
J (4,4)
K (4,2)
L (3, 4)
M (3, 3)
M 3,3
Step-by-step explanation:
the coordinates are in the y 3
Help, what do I do here?
Answer:
draw the 2 lines
Step-by-step explanation:
take the first equation, start with X =1 and calculate y , then plot the point. repeat for other X values. join the points up with a ruler you can extent beyond the first and last points
repeat for second equation
where the lines cross is your intersection, the coordinates of this point is the answer.
good luck
What digit makes this statement true?
Divisibility
answer
1. 864,960
is the answer
Step-by-step explanation:
I'm correct because I'm a teacher
Using the digits 9,8,7,0,5,4,6 without repetition, the greatest 7 digit number is
Answer:
9876540
Step-by-step explanation:
it’s the biggest number because it has the numbers in order from least to greatest! Please tell me if you need help with another question similar to this I will help you.
Answer:
9876540
Step-by-step explanation:
saying the digit number you count the big number
A class made a line plot of the weight of each science book in pounds. a line plot. short description, a line plot. ,long description,
the line plot is entitled weight of science books in pounds. it goes from 2 pounds to 3 pounds with marks at some numbers:
one mark is at two and one eighth. two marks are at two and one fourth. one mark is at two and three eighths. two marks are at two and one half. three marks are at two and three fourths. one mark is at two and seven eighths. question
sonya carried ,begin emphasis,all,end emphasis, the books weighing 2 and one-fourth pounds and 2 and three-eighths pounds to the library. how many pounds of books did sonya carry?
The total pounds of science books that sanya carried is; 6⁷/₈ pounds
How to Interpret Line Plots?
From the attached Line Plot, we can see the book weights.
Now, we are told that Sanya carried all the books weighing 2¹/₄ pounds and 2³/₈ pounds.
From the line plot we see that;
Number of books weighing 2¹/₄ pounds are 2 books
Number of books weighing 2³/₈ pounds is 1 book
Thus;
Total weight of books carried by Sanya = 2(2¹/₄) + 1(2³/₈)
Total weight = 4¹/₂ + 2³/₈
Total Weight = 6⁷/₈ pounds
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121. How much sand is needed to fill a sandbox
8 feet by 6 feet to a depth of 18 inches?
A. 64 cu
B. 62 cu ft.
C. 74 cu ft.
D. 72 cu ft.
E. 68 cu ft.
Answer: The answer is D. 72 cu ft.
Step-by-step explanation:
Find the surface area of a basketball with a diameter of 24 cm. Answers are in terms of pi.
if it has a diameter of 24, then its radius must be half that, or 12.
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies SA=4\pi (12)^2\implies SA=576\pi[/tex]
Rachel's nails grow at a rate of 1/8 inch per week. How long will take her nails to grow 6 inches?
Answer:
48 weeks
Step-by-step explanation:
This is a division problem.
6 / (1/8) = 6/1 × 8/1 = 48
Answer: 48 weeks
No 1 a b c d
PLS fast
a) a= 2×40 = 160°
b) b = 60/2 = 30°
c) c = 40°
d) d = 115°
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
I "turly" know the answer is 1/3, its quite easy actually
Step-by-step explanation:
please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
======================================================
Explanation:
See the diagram below.
The diagram shows we have a right triangle with these side lengths:
a = 8 metersb = 5.5 metersc = unknown hypotenuseWe'll use the pythagorean theorem to find c
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\c = \sqrt{(8)^2 + (5.5)^2}\\\\c = \sqrt{94.25}\\\\c \approx 9.7082\\\\c \approx 9.7\\\\[/tex]
Mrs. Durham and Brett are about 9.7 meters apart.
Ram has two plots in two different places. Both are square in shapes. The side of the first field is 350m and the side of the other field is 220m. Find the total area of the fields that Ram has?
The total area of the fields that Ram has is 170,900 square meters ( 170900 m²)
Calculating the areas of squaresFrom the question, we are to determine the total area of the fields that Ram has
Since the fields are square in shapes, we will use the formula for calculating the area of a square
The area of a square can be calculated by using the formula,
A = s²
Where A is the area
and s is the side
For the first field
s = 350 m
∴ A = 350²
A = 122500 m²
For the second field
s = 220 m
∴ A = 220²
A = 48400 m²
Then,
The total area of the fields = 122500 m² + 48400 m²
The total area of the fields = 170900 m²
Hence, the total area of the fields that Ram has is 170,900 square meters ( 170900 m²)
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Sally has just finished her thirty-fifth year with her company and is getting ready to retire. during her thirty-five years, sally’s average annual salary was $45,603. how much can sally expect to receive from social security annually if she were to retire today? (assume she will receive 42% of her average annual salary.) a. $191.53 b. $1,915.33 c. $19,153.26 d. $191,532.60
Using proportions, the amount that Sally can expect to receive from social security annually is given by:
c. $19,153.26.
What is a proportion?A proportion is a fraction of a total amount, and this fraction can also represent a percentage of the total amount.
She is expected to receive 42% of her average annual salary of $45,603, hence, considering 0.42 is equivalent to 42%:
A = 0.42 x 45603 = $19,153.26.
Which means that option C is correct.
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x^2 - 3xb - 40b^2 factor the trinomi
Answer:
− (8b − x) (5b + x)
Step-by-step explanation:
Graph the inequality m > –2.2.
Step-by-step explanation:
I think the question should be m<-2.2 according to your number line
the answer is graphed. I hope it helps
Answer:B
Step-by-step explanation: this is because when it is greater than, it goes right, and if there is no "equal to" it is closed circle and B has a closed circle going to the right of -2.2
Work out the equation of the line which has a gradient of 1/2 and passes through the point (2, -5)
Answer:
y=½x-6
Step-by-step explanation:
m= ½
equation of the line: y-y1=m(x-x1)
y+5=½(x-2)
y=½x-6
Answer:
[tex]y =\dfrac{1}{2}x-6[/tex]
Step-by-step explanation:
Point-slope formula
[tex]y-y_1=m(x-x_1)[/tex]
where:
[tex]m[/tex] = slope (gradient)[tex](x_1,y_1)[/tex] = point on the lineGiven:
Gradient (m) = ¹/₂Point = (2, -5)Substitute the given values into the formula:
[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\\\implies y-(-5) & =\dfrac{1}{2}(x-2)\\\\y+5 & =\dfrac{1}{2}x-1\\\\y & =\dfrac{1}{2}x-1-5\\\\y & =\dfrac{1}{2}x-6\end{aligned}[/tex]
PLS HELP eixosixosdkkzk
The value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.
What is the formula of sum of sin (a+b)?The formula of sum of sin (a+b) is the trigonometry identity which is used to solve and simplify the problem based on trigonometry equation.
The formula of sum of sin (a+b),
Sin(A+B)=(sin A)(cos B)+(cos A)(sin B)
Here, (A and B) are the measure of angles.
The trigonometry equation given in the problem is,
(sin 60)(cos 30)+(cos 60)(sin 30)
Compare this expression with the above formula we get,
A=60
B=30
Thus, the value of the given expression is,
(sin 60)(cos 30)+(cos 60)(sin 30)=sin (60+30)
Thus, the value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.
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If an event is very likely to occur, the probability is between ____ and ____ on the probability spectrum
If an event is likely to occur, the probability that the event will occur is between 3/4 and 1.
What is the probability?Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
If the probability lies between 0 and 1/5, it is likely that the event would not occur. If the probability lies between 1/5 and 1, it is likely that the event would occur.
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Answer:
75% and 100%
Step-by-step explanation:
The probability spectrum is (the spaces are supposed to be equal):
|----------------------|--------------------|--------------------|---------------------|
0% 25% 50% 75% 100%
impossible unlikely equal likely certain
Determine sin(S) and sin(T).
Question 10
There are boys and girls in a class in the ratio 11 : 16
There are 256 girls.
How many boys are there?
Answer:
There are 176 boys
Step-by-step explanation:
256/16=16
11x16=176
Which of the following shows the interval of the domain where
the function f(x)=x2 - 2x+5 is decreasing?
The domain of the function where the function is decreasing is (-∞, 1). Then the correct option is D.
What are domain and range?The domain means all the possible values of the x and the range means all the possible values of the y.
The function is given below.
f(x) = x² - 2x + 5
The equation can be written as
f(x) = x² - 2x + 1 + 4
f(x) = (x - 1)² + 4
Then the domain of the function where the function is decreasing will be (-∞, 1).
Then the correct option is D.
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If 6 hotdogs cost $ 18, then what is the cost for each hotdog
Answer:
each hot dog costs $3
Step-by-step explanation:
$18÷6 hotdogs=$3 or $3×6 hotdogs=$18
PLEASE HELP MI AMOR ILL LOVE YOU FORVER I SWEAR
Answer:
x = 8
z = 65
Step-by-step explanation:
Through various rules, we are able to assert: (6x + 67)° = 115°.
Now, we want to solve for x:
6x + 67 = 115
6x = 48
x = 8
We know that z° is equal to the complement of (6x + 67)°, and together these must sum to 180°. Therefore, we can simply take 180° - 115° to find that z° = 65°.
AM I CORRECT
A school is having a canned food drive. Each class is challenged to collect 190 cans. If there are c classes in the school, which equation could be used to find the total number of cans, T, the school will collect if each class meets the challenge?
This answer does look right to me.
The number of cans the school will collect is T = 190 c.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given:
Each class is challenged to collect 190 cans.
If there are c classes in the school.
Then, the number of Cans can be collected is:
= Number of classes x number of cans each class collect
= c x 190
= 190 c
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