Write 0,0234234... in the form m/n where m and n are relatively prime.
Answer:
m=26, n=111
Step-by-step explanation:
Let 0,0234234... be x
Then 100x = 23,4234234...
100x-x=23,4234234...-0.0234234...
99x=23,4
999x=234
111x=26
x=26/111
m=26, n=111
Using a crankshaft, a carpenter drills a 1 cm radius hole through a ball of wood along a diameter. If the radius of the ball is 4 cm, determine the volume of wood remaining.
Answer:263.89cm cubed
Step-by-step explanation:
Volume of A Sphere: 4/3 pi radius cubed
4cubed= 64
64 times pi=201.061
201.061 multiply 4/3= 268.08
1cubed= 1
1 times pi=3.14
3.14 times 4/3= 4.19
268.08-4.19= 263.89cm cubed
What’s the formula for the geometric mean of three numbers?
Answer:
Geometric mean is most commonly represented as:
[tex]\sqrt{abc}[/tex]
Geometric mean formula is represented by [tex]\sqrt[n]{\sf x_1 \cdot x_2 \cdot x_3 \cdot ... x_n}[/tex] where n resembles term position and x₁, x₂, x₃ are numbers and they continue.
The formula for geometric mean of three numbers [n = 3]:
Solution: [tex]\sqrt[3]{\sf x_1 \cdot x_2 \cdot x_3 }[/tex]
Example's:
Geometric mean of 5 numbers [n = 5] : [tex]\sqrt[5]{\sf x_1 \cdot x_2 \cdot x_3 \cdot x_4 \cdot x_5 }[/tex]
Geometric mean of 2 numbers [n = 2] : [tex]\sqrt[2]{\sf x_1 \cdot x_2 }[/tex]
simplify the expression -2v+15d
Answer:
isn't this already fully simplified?
Step-by-step explanation:
Calculate the unit cost per Kg if it costs $16.99 for 454 g package of cooked shrimp.
Answer:
$37.42 / kg
Step-by-step explanation:
Divide 16.99 by 454 to get the unit cost per gram. This equals 0.037422907…
Take this number and multiply it by 1000, while rounding it to the nearest hundredth after.
This equals about $37.42 / kg.
Which is the equation in slope-intercept form for the line that passes through (−2, 15) and is perpendicular to 2x + 3y = 4?
y=−32x+18
y=32x−12
y=23x+18
y=32x+18
The linear equation that respects the given conditions is:
[tex]y = \frac{3}{2}x + [/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When two lines are perpendicular, the multiplication of their slopes is of -1. Hence, considering it is perpendicular to 2x + 3y = 4.
[tex]2x + 3y = 4[/tex]
[tex]3y = -2x + 4[/tex]
[tex]y = -\frac{2x}{3} + \frac{4}{3}[/tex]
Then:
[tex]-\frac{2}{3}m = -1[/tex]
[tex]m = \frac{3}{2}[/tex]
Hence:
[tex]y = \frac{3}{2}x + b[/tex]
It passes through (−2, 15), that is, when x = -2, y = 15, hence:
[tex]y = \frac{3}{2}x + b[/tex]
[tex]15 = \frac{3}{2}(-2) + b[/tex]
15 = -3 + b
b = 18.
So the equation is:
[tex]y = \frac{3}{2}x + [/tex]
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Write the sentence as a proportion.
1(1)/(2) cups of milk is to 10 bagels as (3)/(4) cups of milk is to 5 bagels
Find K such that the number 23K10 is
divisible by 2, 3, and 5
2021
The values of K that will make 23K10 to be divisible by 2, 3 and 5 are; 0, 3, 6 and 9
How to use divisibility rules?We want to find the number K in 23K10 that will make it divisible by 2, 3 and 5.
Now, for the number to be divisible by 2, 3 and 5, then it means it must be divisible by the LCM which is; 2 * 3 * 5 = 30
Now, the divisibility rule for 30 is that it must be divisible by 3 and 10.
If 23K10 is divisible by 3, sum of digits will be multiple of 3.
Thus;
2 + 3 + K + 1 + 0 = K + 6 must be equal to 0, 3, 6, 9, 12, 15, 18....
Thus, K could either be 0, 3, 6 or 9
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What is the simplified form of this expression √-150
Answer: [tex]\boldsymbol{5i\sqrt{6}}[/tex]
where [tex]i = \sqrt{-1}[/tex]
=============================================
Work Shown:
[tex]\sqrt{-150}\\\\\sqrt{-1*25*6}\\\\\sqrt{-1}*\sqrt{25}*\sqrt{6}\\\\i*5*\sqrt{6}\\\\\boldsymbol{5i\sqrt{6}}\\\\[/tex]
The trick with these type of problems is to factor the number into pieces such that we pull out the largest perfect square factor. In this case, that factor is 25. We also pull out the -1.
The rule used is [tex]\sqrt{A*B} = \sqrt{A}*\sqrt{B}[/tex] that lets us break up the root.
A survey found that 10 out of 15 students like pizza. If four students are chosen at random, what is the probability that all the four students like pizza?
Using the hypergeometric distribution, it is found that there is a 0.1539 = 15.39% probability that all the four students like pizza.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, the values of the parameters are given as follows:
N = 15, n = 4, k = 10.
The probability that all the four students like pizza is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,15,4,10) = \frac{C_{10,4}C_{5,0}}{C_{15,4}} = 0.1539[/tex]
0.1539 = 15.39% probability that all the four students like pizza.
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homework! This is a stats problem I’ve been struggling with and need help thanks!!!
A jar contains 2 red marbles numbered 1 to 2 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given event.
The probability that the randomly chosen marble will be red is 1/6 or 0.1667.
What is the probability of an event?The probability of an event is the possibility, chance, or likelihood for an event to take place or occur.
From the given information:
Let us find the probability that if marble is drawn at random from the jar, the given marble will be red:
The total number of marble = 10 + 2 = 12 marbles.
There are 2 red marbles and 10 blue marblesThe probability that the randomly chosen marble will be red is:
P(red) = 2/12
P(red) = 1/6
P(red) = 0.1667
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[tex](4 * 3^x)'[/tex]
Evaluate
Answer:
[tex]\approx 4.39 \cdot 3^x[/tex]
Step-by-step explanation:
Recall a property:
[tex](c\cdot f(x))'=c\cdot f(x)'[/tex], where [tex]c[/tex] is a constant.
Apply the property to the task:
[tex](4\cdot 3^{x})'=4\cdot (3^x)'[/tex]
Recall a property of the derivative of an exponential function:
[tex](a^x)'=a^x \cdot \ln{a}[/tex]
Apply the property to the task:
[tex]4\cdot 3^x \cdot \ln 3[/tex]
Since [tex]\ln 3\approx 1.0986[/tex], it follows:
[tex]4\cdot 3^x \cdot \ln 3 \approx 4\cdot 1.0986 \cdot \ln3[/tex]
Multiply the numbers.
The answer is about [tex]4.39\cdot 3^x[/tex].
Write the range of each function for the given domain:
f(x) = 3 + 2x; Domain = {-8, 4)
Answer:
the range of each function for the given domain are the step of 3+2x are equal the -8,4
You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $160,000. Your bank requires 1/5 of the market value as a down payment.
(a)
What is the amount (in $) of the down payment? $
(b)
What is the amount (in $) of the mortgage for which the Bradys are applying? $
(c)
Your bank offers the Bradys a 30-year mortgage with a rate of 5%. At that rate, the monthly payments for principal and interest on the loan will be $5.37 for every $1,000 financed. What is the amount (in $) of the principal and interest portion of the Bradys' monthly payment? $
(d)
What is the total amount (in $) of interest that will be paid over the life of the loan? $
(e)
Your bank also requires that the monthly mortgage payments include property tax and homeowners insurance payments. If the property tax is $1,710 per year and the property insurance is $1,458 per year, what is the total monthly payment (in $) for PITI (principal, interest, taxes, and insurance)? $
(f)
To qualify for the loan, bank rules state that mortgage payments cannot exceed 14 of the combined monthly income of the family. If the Bradys earn $3,750 per month, will they qualify for this loan?
Yes, they will http://qualify.
No, they will not qualify.
(g)
What monthly income (in $) would be required to qualify for this size mortgage payment? $
a) The amount (in $) of the down payment is $32,000.
b) The amount (in $) of the mortgage for which the Bradys are applying is $128,000.
c) The amount (in $) of the principal and interest portion of the Bradys' monthly payment, at $5.37 for every $1,000 financed, is $687.36.
d) The total amount (in $) of interest that will be paid over the life of the loan is $$119,449.60.
e) The total monthly payment (in $) for PITI (principal, interest, taxes, and insurance) is $951.36.
f) Based on the bank rules that state that mortgage payments cannot exceed 14% of the combined monthly income of $3,750, B. No, they will not qualify.
(g) The monthly income (in $) that would be required to qualify for this size mortgage payment is $4,909.71 ($687.36/0.14).
Data and Calculations:Down payment = 1/5 or 20%
Home Price = $160,000
Down Payment = 20%
Loan Term = 30 years
Interest Rate = 5%
Annual property tax = $1,710 per year
Annual property insurance = $1,458 per year
Monthly taxes and insurance = $264 ($3,168/12)
Monthly PITI (principal, interest, taxes, and insurance) = $951.36 ($264 + $687.36)
14% of $3,750 = $525
Results:
Monthly Pay: $687.36 ($5.37 x $128,000/$1,000)
Loan Amount $128,000 ($160,000 - $32,000)
Down Payment = $32,000 ($160,000 x 20%)
Total of 360 Mortgage Payments = $247,449.60 ($687.36 x 360)
Total Interest = $119,449.60 ($247,449.60 - $128,000)
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Which choice is equivalent to the quotient below?
-/100/-/25
the answer to this equation is 4
Need the answer please anyone!!!
The correct expression is the one in option B.
[tex]P(x) = (x - \sqrt{4} )*(x - 2)*(x + 2)[/tex]
Which is the correct expression?If we know that a polynomial has the known zeros:
{x₁, x₂, ..., xₙ}
Then the factored form is:
[tex]p(x) = a*(x - x_1)*...*(x - x_n)[/tex]
Where a is the leading coefficient, in this case we take a = 1.
Here we also know that the zeros are:
√4, 2, -2.
Then the factored form is just:
[tex]P(x) = (x - \sqrt{4} )*(x - 2)*(x - (-2))\\\\P(x) = (x - \sqrt{4} )*(x - 2)*(x + 2)[/tex]
Then we conclude that the correct option is B.
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Which of these is the quadratic parent function?
A. f(x) = (1/4 x)²
B. f(x)=x²-3
C. f(x) = x² +5
D. f(x) = x²
Answer:
[tex]f(x)=x^2[/tex]
Step-by-step explanation:
The quadratic parent function, has no transformations, and has the vertex at (0, 0). Which is the function: [tex]f(x)=x^2[/tex]. Any other quadratic function, has some form of transformation, whether it be a reflection, translation, compression/stretch, etc...
Two children had 110 marbles between them. After one child had lost half her marbles
and the other had lost 20 they had an equal number. How many marbles did each child
start with and how many did they finish with?
Answer:
1 child - 60 another child - 50
Step-by-step explanation:
we start from the end. they had a equal number.
child A lost half therefore we give them another half having 2 units as shown in the diagram. child B had 1 unit plus 20 because he lost 20 which total adds up to 110. from there you have
3 units + 20 = 110
3 units = 90
1 unit = 30
since A has 2 units,
30 × 2 = 60
child A has 60.
since B has 1 unit plus 20
30 + 20 = 50
Price of article = $315.50
Down payment = $31.55
Monthly payment amount = $16.50
Duration of payments = 20 months
Interest
(
I
)
=
2
y
c
m
(
n
+
1
)
True annual interest rate to the nearest tenth=
The true annual interest rate to the nearest tenth is 16.7%.
How is interest determined?The interest amount for this scenario can be determined by computing the total mortgage payment and subtracting the mortgage amount from the earlier figure.
Since payment was made for 20 months, the interest rate can be annualized using 24 months as below.
Data and Calculations:Price of article = $315.50
Down payment = $31.55
Mortgage amount = $283.95
Monthly payment amount = $16.50
Duration of payments = 20 months
Total payment (mortgage and interest) = $330 (20 x $16.50)
Interest = $46.05 ($330 - $283.95)
Annualized interest rate = 16.7% ($46.05/$330 x 24/20)
Thus, the true annual interest rate to the nearest tenth is 16.7%.
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What is the solution to the equation
1/4x-1/8=7/8+1/2x?
Answer:
x=-1/4
Step-by-step explanation:
1 / 4x-1/8 = 7/8 + 1 / 2x <=> 1/4x - 1/2x = 7/8+1/8 <=> 1/4x-2/4x = 1 <=> -1/4x = 1
<=> x= -1/4
Answer:
2.7 + 8x/8.2
Step-by-step explanation:
1/4x - 1/8 = 7/8 + 1/2x x/4 - 1/8 = 7/8 + x/2
8x + 4 (-1)/4.8 = 2.7 + 8x/8.2
Circle properties can be used to prove that various shapes are polygons.
The question is incomplete. Below you will get the missing part of the question.
Find whether the given statement is true or false ?
True. Circle properties can be used to prove that various shapes are polygons.
With a centre of the circles, sides of an angle with vertex outside the circle, and arcs inside the circle, various shapes can be polygon.
So, from this description, we can say that, circle properties can be used to prove that various shapes are polygons.
Hence, the given statement is true.
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graph absolute value of x-1
It gives magnitude of the number or variables.
It is also known as an absolute value the function.
The result of this modulus function is always positive.
Draw the graph:
f(x) = |x-1|
f(x) = -(x-1) when x-1 is negative
f(x) = (x-1) when x-1 is positive
when x = -2, f(x) = 3
when x = -1, f(x) = 2
when x = 0, f(x) = 1
when x = 1, f(x) = 0
when x = 2, f(x) = 1
Using this values, draw the graph of f(x) = |x-1|
Hence, the required modulus of x-1 graph.
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Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?
The equation perpendicular to the line passing through the points (-4,7) and (1,3) is[tex]y=\frac{5}{4}x-2[/tex]
Equation perpendicular to a lineThe slope of the given line is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{3-7}{1-(-4)} \\\\m=\frac{-4}{5}[/tex]
The equation perpendicular to the given line will be of the form
[tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]
Substitute [tex]x_1=-4, y_1=7, and m=\frac{-4}{5}[/tex]
[tex]y-7=\frac{5}{4}(x+4)\\\\ y=\frac{5}{4}x+5-7\\\\ y=\frac{5}{4}x-2[/tex]
Therefore, the equation perpendicular to the line passing through the points (-4,7) and (1,3) is [tex]y=\frac{5}{4}x-2[/tex]
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Answer: [tex]y = -\frac{5}{4} x - 2[/tex]
Step-by-step explanation:
How many sides does a nonagon have
Solve for x in the diagram below.
Answer:
x=40
Step-by-step explanation:
total sum of angle in a triangle =180
180-100=80
x+x =2x
x= 80/2
x=40
Find the solution, if possible, to the following system of equations using any method.
Give your answer in fraction form if necessary. Show all work. If you use matrices, you MUST write out the augmented matrix you inputted into the calculator.
3 − 4 + = −4
4 − 8 + 7 = 2
−2 + 4 − 3 = 5
Harpreet, Sukhpreet and Komalpreet are three sisters. Sukhpreet is x years old. Harpreet is 3 years older than Sukhpreet. Komalpreet is twice the age of Harpreet. If the average age of the three sisters is 15, how old is Harpreet?
Answer:
12
Step-by-step explanation:
Givens
Harpreet = x + 3
Sukhpreet = x
Komalpreet = 2*(x + 3)
Average Age = 15
Equation
[(x + 3) + x + 2*(x + 3) ] / 3 = 15 Multiply both sides by 3
Solution
3 [(x + 3) + x + 2*(x + 3) ] / 3 = 15 * 3 Combine
[(x + 3) + x + 2*(x + 3) ] = 45 Remove the brackets
x + 3 + x + 2x + 6 = 45 Combine like terms
4x + 9 = 45 Subtract 9 from both sides
4x + 9 - 9 = 45 - 9 Combine
4x = 36 Divide by 4
4x/4 = 36/4
x = 9
Answer
Harpreet is x+ 3 = 9 + 3 = 12
Problem
(a) Find x given that [tex]4x^2=2[/tex]
(b) Let x = 1.1609... be the positive real number such that [tex]4^x=5[/tex]. Prove that x is irrational.
The value of x is ±0.7071 and x is an irrational number
How to solve for x?The equation is given as:
[tex]4x^2 = 2[/tex]
Divide by 4
[tex]x^2 = 0.5[/tex]
Take the square roots
[tex]x = \pm 0.7071[/tex]
Hence, the value of x is ±0.7071
How to prove that x is irrational?The equation is given as:
[tex]4^x = 5[/tex]
Take the logarithm of both sides
[tex]x\log(4) = \log(5)[/tex]
Divide both sides by log(4)
x = 1.16096....
The above number is a non-terminating decimal.
Non-terminating decimals cannot be represented as fractions of two integers
Hence, x is an irrational number
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Use the equations to find the perimeter equation
The perimeter of the park is 3x^2 + 37x - 4
How to determine the perimeter?The side lengths of the triangular park are:
10x + 3x^2 - 8, 12x and 15x + 4
Add these sides to determine the perimeter
P = 10x + 3x^2 - 8 + 12x + 15x + 4
Collect the like terms
P = 3x^2 + 10x + 12x + 15x - 8 + 4
Evaluate the sum
P = 3x^2 + 37x - 4
Hence, the perimeter of the park is 3x^2 + 37x - 4
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