Pi (π) is an irrational number that can be found by dividing the radius of a circumference by its diameter.
The digits of π considering the first 1,000 digital places are:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989
help ................
Percentage of a number
Find a number which
its a 100% percentage
henW
When 232 is 290%
Then find
X = (100%/290)• 232
Divide 232/29 = 10% = 8 exactly
Now multiply by 10 = 10• 8 = 80
Then 100% = 80
Which equation demonstrates the distributive property? Responses A 36 + 9 = 4536 + 9 = 45 B 36 + 9 = 3(12 + 3)36 + 9 = 3(12 + 3) C 36 x 9 = 9 x 3636 x 9 = 9 x 36 D (12 + 3)3 = 3(12 + 3)
The correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.
What is distributive property ?
Distributive property states that the outcomes are the same whether the numbers in parenthesis are added before or after multiplication.
We know that according to the distributive property both sides must be equal such that the outcomes are same whether the numbers in parenthesis are added before or after multiplication. The expression for distributive property is given as : a(b + c) = ab + ac
So , checking the options one by one :
A) 36 + 9 = 45 ; is not an equation representing distributive property as it doesn't satisfy the criteria of a distributive property.
B) 36 + 9 = 3(12 + 3) is an equation representing distributive property as it satisfies the criteria mentioned above i.e.,
36 + 9 = 3 × 12 + 3 × 3
36 + 9 = 36 + 9
45 = 45
C) 36 x 9 = 9 x 36 is not an equation representing distributive property.
D) (12 + 3) × 3 = 3 × (12 + 3) is not an equation representing distributive property because both sides are written in the same way.
Therefore , correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.
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Given the equation of a curve is y=5/x²The value of dy/dx= -10/27Hence, estimate the value of 5/(2.98)²
The given equation is:
[tex]y=\frac{5}{x^2}[/tex]a. Find the value of dy/dx when x=3
Start by finding the derivative:
[tex]\frac{dy}{dx}=\frac{d(\frac{5}{x^2})}{dx}[/tex]You also can express 5/x^2 as 5*x^(-2):
[tex]\frac{5}{x^2}=5x^{-2}[/tex]You know the derivative of a power is:
[tex]\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]Apply it to your case:
[tex]\frac{d}{dx}5x^{-2}=(-2)\cdot5\cdot x^{-2-1}=-10\cdot x^{-3}[/tex]And finally:
[tex]\begin{gathered} x^{-n}=\frac{1}{x^n} \\ \text{Apply it to your equation} \\ \frac{dy}{dx}=\frac{-10}{x^3} \end{gathered}[/tex][tex]\begin{gathered} \text{When x=3} \\ \frac{dy}{dx}=\frac{-10}{3^3}=\frac{-10}{27} \end{gathered}[/tex]b. Estimate the value of 5/(2.98)^2:
[tex]\begin{gathered} y=\frac{5}{x^2}=\frac{5}{2.98^2}=0.563 \\ \text{Which also means x=2.98} \\ \text{Let's find the derivative when x=2.98} \\ \frac{dy}{dx}=\frac{-10}{2.98^3}=\frac{-10}{26.46}=-0.377 \end{gathered}[/tex]Please help me solve: Part CA sign in a freight elevator states that the maximum capacity of the elevator is 2,500 pounds. Use the average weight of a box as 75 pounds and the average weight of a crate as 160 pounds to complete the following parts.If there are 13 average-weight boxes on the elevator, what is the maximum number of average-weight crates that can also be on the elevator given its maximum capacity? Please explain.
Let
x ----> number of average-weight crates
so
we have that
[tex]75(13)+160x\leq2,500[/tex]solve for x
[tex]\begin{gathered} 975+160x\leq2,500 \\ 160x\leq2,500-975 \\ 160x\leq1,525 \\ x\leq9.53 \end{gathered}[/tex]therefore
the maximum number of average-weight crates is 9Simplify the following rational expression to determine if thegiven simplification is correct. If it is correct, select TRUE. If it isnot correct, select FALSE.6x48x556x47
The question asks us to confirm the simplification of the expression:
[tex]-\frac{48x^5}{56x^4}[/tex]Step 1: Factor the numbers
[tex]\begin{gathered} 48=8\times6 \\ 56=8\times7 \end{gathered}[/tex]Therefore, the expression becomes:
[tex]-\frac{48x^5}{56x^4}=-\frac{8\times6x^5}{8\times7x^4}[/tex]Step 2: Cancel out the common terms from the expression
[tex]-\frac{8\times6x^5}{8\times7x^4}=-\frac{6x^5}{7x^4}[/tex]Step 3: Apply the rule of exponents
[tex]\frac{x^n}{x^n}=x^{m-n}[/tex]Therefore, we have:
[tex]-\frac{6x^5}{7x^4}=\frac{6}{7}x^{5-4}=-\frac{6x}{7}[/tex]CONCLUSION
The expression simplifies to give:
[tex]-\frac{48x^5}{56x^4}=-\frac{6x}{7}[/tex]The answer is TRUE.
Need help with problems
You can write the relation between distance and time, as follow:
y = kx
where y is the distance, x is the time and k is the constant of proportionality.
k can be obtained with the given information, as follow:
k = 90/30 = 3
Then, the equation of the relationship is:
y = 3x,
for a time of 10 seconds, the distance traveled is:
y = 3(10) = 30
Hence, the answer is:
y = 3x , 30 feet
For each graph below, state whether it represents a function.
I need help with graph 2
Answer: No
Step-by-step explanation:
The graph fails the vertical line test, and thus the graph does not represent a function.
Mr. Thomatos thinks that {3, 8} and [3, 8] represent the same set of values Is Mr. Thomatos correct? Why or why not? Explain. (giving brainliest)
Answer: its not correct because the got different perenties or groupings and they mean different meaning
Step-by-step explanation:
What kind of transformation converts the graph of f(x) = -x - 10 into the graph of g(x)
-9x - 10?
horizontal stretch
vertical stretch
vertical shrink
horizontal shrink
=
Answer:
zeroay horizontal stretch vertical shrink
Step-by-step explanation:
1+1=2
Ms. Banks divides 18 basketballs evenly among 3 bags. For class, she takes 2 basketballs from each bag. How many basketballs are left in one of the bags?
4 basketballs
Explanation
Step 1
Ms. Banks divides 18 basketballs evenly among 3 bag
divide the 18 basketballs by 3 bags
[tex]\frac{18\text{ basketball}}{3\text{ bags}}=6\text{ basketaball per bag}[/tex]Step 2
now, she takes 2 from each bag, so
[tex]\begin{gathered} \text{total basketball per bag=6-2} \\ \text{total basketball per bag =4} \end{gathered}[/tex]Hence, the answer is 4 basketballs.
I hope this helps you
Jae created a painting with an area of 48 square inches and a length of 6 inches. They create a second painting with an area of 64 square inches. It has the same width as the first painting. What is the length of the second painting?
FIRST PERSON TO ANSWER THIS GETS BRAINILEST.
Determine if the two expressions in each pair are equivalent.If they are equivalent,select the property that is illustrated.
Answer:
The second one is the Multiplicative Property of Zero.
The fourth one is the Commutative property.
Answer:
The second and third one
Step-by-step explanation:
2. Zandile invests her Christmas bonus for R 875.00 in a bank that offers
interest rates of 9% p.a. compounded half-yearly. How much interest will she
have earned after 6 years? I want the interest
After 6 years, Zandile earns an interest of rupees 608.9 after investing her Christmas bonus for R 875.00 in a bank that offers interest rates of 9% p.a. compounded half-yearly.
What is interest?The simplest way to calculate interest is as a percentage of the principal. For instance, if you agreed to borrow $100 from a friend with 5% interest, the interest you would pay would only be 5% of $100: $100(0.05) = $5.
What is compound interest?Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The principal (original) sum and the interest that has already accrued over the course of previous periods are used to calculate compound interest.
Here,
Principal amount= 875
Rate of interest= 9% pa
Compounding= half-yearly (2/year)
Time= 6 years
A = P(1 + r/n)ⁿᵇ
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
b=number of time periods elapsed
A=875(1+9/6)⁶*²
A=₹1,483.90
Zandile invests her Christmas bonus of R 875.00 in a bank that offers interest rates of 9% per year compounded semi-annually, and after 6 years, she earns an interest of Rs 608.99.
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Factor: x^6-5x^4-5+x
The value of the expression x^6 -5x^4 - 5 + x when simplified is x^4(x^2 - 5) - (5 + x)
How to factor the expression?The statement is given as
Factor: x^6 -5x^4 - 5 + x
From the above expression, we have
x^6 -5x^4 - 5 + x
Group the expression in two'2
So, we have
x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)
Factorize each group of the expression
So, we have
x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)
The above expression cannot be further simplified
Hence, the value of x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)
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On the graph below, which dotted line represents a reflection across the x-axis of the red-solid-line graph?5 stars for quicknessplease look at png 1 is question 2 is answer
Hello!
The rule for a reflection across the x-axis is:
[tex](x,y)=(x,-y)[/tex]Knowing it, let's write some points that the red line passes through:
(-2, 0) and (0, 4).
Now, let's use this rule and change the sign of the y coordinate:
• (-2, 0) → (-2, 0) because +0 or -0 doesn't exist.
,• (0, 4) → (0, -4)
Let's analyze it and find a line that passes through these two points:
(-2, 0) and (0, -4)
It will be the blue line.
continued - calculating gross payRemember, this is money round to the nearest Penny/hundredths place. Take OT rate as 1.5 times the regular pay rate.Take the regular working hours per week as 40 hours.
Given Data:
Total working hours is = 51 hours.
Pay rate=$8.45.
OT rate=1.5 times the regular pay rate.
Regular working hours is 40 hours.
Regular pay can be determined as,
[tex]RP=40\text{ hours}\times8.45\text{ USD=338 USD}[/tex]Thus, the regular pay is $338.
The OT rate can be determined as,
[tex]\begin{gathered} OT=1.5\times8.45\text{ USD} \\ =12.675\text{ USD} \end{gathered}[/tex]Thus, the overtime rate is $ 12.68.
The overtime pay can be determined as,
[tex]\begin{gathered} OT\text{ Pay=(51-40) hours}\times12.675\text{ USD} \\ =139.425\text{ USD} \end{gathered}[/tex]Thus, the overtime pay is $139.43.
The gross pay can be determined as,
[tex]\begin{gathered} GP=RP+OT\text{ Pay} \\ =338\text{ USD+139.425 USD} \\ =447.425\text{ USD} \end{gathered}[/tex]Thus, the gross pay is $ 447.425.
Write a quadratic function in standard form whose graph passes through (-5,0),(0,-8),(4,0)
[tex]y = -1.25 x^{2}+ 5[/tex] is the needed quadratic function in standard form.
What is a quadratic equation?A quadratic equation is one with a single degree 2-variable and has the general form [tex]a x^{2} + bx + c = 0.[/tex] a, b, and c is the constant value, and x consists of a variable.
The quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).
f(x) = a (x + 5) (x - 0) (x - 0)
= ax+5a
f(x) = [tex]ax^{2} +5x[/tex]
The quadratic equation's graph goes through (4, 0). Therefore, we must change equation 1 to read x = 4 and f(x) = 0.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
a = [tex]\frac{-20}{16}[/tex]
=-1.25
The quadratic equation is known to have the form ax² + bx + c = 0.
f(x) = -1.25[tex]x^{2}[/tex] + 5x
Consider y= F(x)
∴ The required quadratic equation of function in the standard form is Y = -1.25 x² + 5x.
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3300 dollars is placed in an account with an annual interest rate of 6.75%. To
the nearest tenth of a year, how long will it take for the account value to reach
10700 dollars?
The simple interest formula is A = P(1+r t) then the value of t =33.2210 years.
What is meant by simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The simple interest formula is equal to
A = P(1+r t)
where, A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
P = $ 3300
A = $ 10700
r = 6.75 % = 6.75 / 100 = 0.0675
substitute in the formula above
$10700 = 3300(1+0.0675 t)
simplifying the above equation, we get
Divide both sides by 3300
[tex]$\frac{3300(1+0.0675 t)}{3300}=\frac{10700}{3300}$$[/tex]
Simplifying the above equation, we get
[tex]$1+0.0675 t=\frac{107}{33}$$[/tex]
Subtract 1 from both sides
[tex]$1+0.0675 t-1=\frac{107}{33}-1$$[/tex]
Simplifying the above equation, we get
[tex]$0.0675 t=\frac{74}{33}$$[/tex]
Divide both sides by 0.0675
[tex]$\frac{0.0675 t}{0.0675}=\frac{\frac{74}{33}}{0.0675}[/tex]
[tex]$t=\frac{74}{2.2275}$[/tex]
t = 33.2210 years
Therefore, the value of t exists 33.2210 years.
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An item is regularly priced at $50. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?Amount discounted: sX5?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
regular price = $50
discount = 40% = 0.4
Step 02:
amount discounted:
amount discounted = regular price * discount
amount discounted = $50 * 0.4 = $20
The answer is:
$20
Let x be a continuous random variable that has a normal distribution with μ = 48 and 6 = 8. Assuming -
≤0.05, find the
probability that the sample mean, x, for a random sample of 16 taken from this population will be between 49.60 and 52.20.
Round your answer to four decimal places.
The probability of the sample mean is 0.2008.
What is probability?
Probability is the quality or state of being probable the extent to which something is likely to happen or be the case.
Sol-Let x be a continuous random variable that has a normal distribution with
μ=48 and σ=8
Thus,
X~N(48,8^2/16)
The standardized value of x is obtained by :
Z= X-48/√8^2/16~N(0,1)
The probability that the sample mean x for a random sample of 16 taken from this population will be between 49.62 and 52.80 can be obtained as:
P(49.62<x<52.80)
P=(49.62-48/√8^2/16<x-48/√8^2/16<52.80-48/√8^2/16)
=P(0.81<Z<2.4)
=P(Z<2.4)-P(Z<0.81)
=0.9918-0.7910
=0.2008
There for the probability is 0.2008.
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calculate the perimeter of kite ABCD where AB = 29 cm and CD = 47 cm
Answer:
152 cm
Step-by-step explanation:
Perimeter of kite= 2(a+b)
P= 2(AB+CD) = 2(29+47) = 2 *(76) = 152 cm.
If something remains unclear, be free to ask questions!
graph the system below2x-3y=-183x+y=-5
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 2x-3y=-18 \\ \\ 3x+y=-5 \end{gathered}[/tex]To graph, we calculate the intercepts in each equation to then draw the straight line corresponding to each equation, like this:
[tex]\begin{gathered} \text{ For }2x-3y=-18 \\ \\ \text{The x-intercept} \\ \\ \:2x-3\cdot 0=-18 \\ \\ x=-9\rightarrow(-9,0) \\ \\ \text{The y -intercept} \\ \\ 2\cdot0-3y=-18 \\ \\ y=6\rightarrow(0,6) \\ \\ \\ \text{For }3x+y=-5 \\ \\ \text{The x-intercept} \\ \\ 3x+0=-5 \\ \\ x=-\frac{5}{3}\rightarrow\left(-\frac{3}{5},0\right) \\ \\ \text{The y- intercept} \\ \\ \:3\cdot 0+y=-5\: \\ \\ y=-5\rightarrow(0,-5) \end{gathered}[/tex]Now we graph:
Make x the subject of h = 4(x + 3y) + 2
Answer:
x=\frac{1}{4}(h-12y-2)x=4
Step-by-step explanation:x=\frac{1}{4}(h-12y-2)x=
4
1
(h−12y−2)
Step-by-step explanation:
We are given the equation h=4(x+3y)+2h=4(x+3y)+2 .
Simplifying for x, we get,
h=4(x+3y)+2h=4(x+3y)+2
i.e. h=4x+12y+2h=4x+12y+2
i.e. 4x=h-12y-24x=h−12y−2
i.e. x=\frac{1}{4}(h-12y-2)x=
4
1
(h−12y−2)
Thus, the equation for x is x=\frac{1}{4}(h-12y-2)x=
4
1
Find the x-intercept and y- intercept of the function f(x) = (2x + 3)/(x ^ 2 + 3)can u draw the function of f(x) = (2x + 3)/(x ^ 2 + 3)?Need solution ^^
Answer:
• x-intercept: (-1.5, 0).
,• y-intercept: (0, 1).
Explanation:
Given the function:
[tex]f(x)=\frac{2x+3}{x^2+3}[/tex](a)x-intercept
The x-intercept is the value of x at which f(x)=0.
When f(x)=0
[tex]\begin{gathered} \frac{2x+3}{x^2+3}=0 \\ \text{ Cross multiply} \\ 2x+3=0 \\ \text{ Subtract 3 from both sides of the equation} \\ 2x+3-3=0-3 \\ 2x=-3 \\ \text{ Divide both sides of the equation by 2} \\ \frac{2x}{2}=-\frac{3}{2} \\ x=-1.5 \end{gathered}[/tex]The x-intercept is located at (-1.5, 0).
(b)y-intercept
The y-intercept is the value of f(x) at which x=0.
When x=0
[tex]\begin{gathered} f(x)=\frac{2x+3}{x^2+3} \\ f(x)=\frac{3}{3} \\ f(x)=1 \end{gathered}[/tex]The y-intercept is at (0, 1).
(c)Graph
The graph of f(x) is given below:
Simplify the expression 2^5 +5^4
Therefore
[tex]2^5+5^4=657[/tex]Red Lobster charges $30 per person plus a $100 set up fee to cater an event. Olive Garden charges $25 per person plus a $200 set up fee. PART A: How many guests, g, would both restaurants cost the SAME
There would be 20 guests for the restaurants to cost the same
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the number of guests?From the question, we have the following parameters:
Red Lobster
Rate per person = $30
Set up fee = $100
Olive Garden
Rate per person = $25
Set up fee = $200
So, the equations of the restaurants are
Red Lobster = 30g + 100
Olive Garden = 25g + 200
Where the number of guests is g
When the restaurants cost the same amount, we have
Red Lobster = Olive Garden
Substitute the known values in the above equation
So, we have
30g + 100 = 25g +200
Evaluate the like terms
5g = 100
Divide by 5
g = 20
Hence, the number of guests is 20
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Solve the quadratic equation X^2+5x+6=0 using the completing the square method. Be sure to explain each step.
To complete the perfect trinomial, we add (5/2)² to the given equation and get:
[tex]x^2+5x+(\frac{5}{2})^2+6=(\frac{5}{2})^2.[/tex]Subtracting 6 we get:
[tex]x^2+5x+(\frac{5}{2})^2=\frac{25}{4}-6=\frac{1}{4}.[/tex]Therefore:
[tex](x+\frac{5}{2})^2=\frac{1}{4}.[/tex]Finally, we get:
[tex]\begin{gathered} x+\frac{5}{2}=\pm\sqrt{\frac{1}{4}}, \\ x=\pm\frac{1}{2}-\frac{5}{2}. \end{gathered}[/tex]Answer: [tex]\begin{gathered} x_=-3,\text{ or x=-2.} \\ \end{gathered}[/tex]Mr. Lombardo took his two children to a water park. He used the coupon shown below to buy one adult ticket. The price of admission for all three family members was $76. What was the price of each child's ticket? WORLD OF WATER | This coupon is good | for one adult ticket | to World of Water | at a price of $28.00. YOU SAVE $4.00! Use the math you already know to solve the problem. a. What ticket price do you know? How much is that ticket? Explain.
Data Input
1 Adult + 2 children
The price for all three family members
$76
Procedure
Adult ticket = $28
1 Adult + 2 children = $76
2 children = 76 - 1 adult
2 children = 76 - 28
2 children = 48
children = 48/2
children = 24
how would I answer and what would be the answer?
Answer: (-1, 0)
The interval of decreasing refers to the interval of x-values where the graph is decreasing or going down.
If we look at the graph:
We can see that the graph starts to decrease or "go down" at values x = -1 and x=0. With this, we can conclude that the interval of decrease for the given graph is (-1, 0)
find 11/3÷2/3
The quotient is 5 and ___.
After conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.
What are mathematical operations?A function in mathematics known as an operation is one that transforms zero or more input values into a clearly defined output value. The operation's complexity is determined by its operand count. A mathematical operation is a procedure. A mathematical operation can be anything from addition to subtraction to multiplication to division to finding the root.So, 11/3÷2/3:
We need to perform the division of the given fractions as follows:(Refer to the image attached below for calculations)11/3÷2/3 = 5½Therefore, after conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.
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