5x>25
x>5
Hope it helps!
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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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:
[tex]212 \times 5 + 5222 \div 45 + 63 - 34[/tex]
this question i want
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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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answer:
Step-by-step explanation:
Question
64^m
--------
4^2m
Solution
(64)^m = (4^3)^m = 4^3m
4^3m/4^2m = 4^(3m - 2m) = 4^m
Answer
2^2m = (2^2)^m = 4^m Equivalent
16^0.5m = (16^0.4) ^m = 4^m Equivalent
4^m Equivalent
All three of these are equivalent. The catch is in splitting the powers apart. In this top one (2^2m) you move the brackets so that the right bracket is after the two which gives (2^2)^m = 4m
You do the same thing with (16^0.5)^m. 16^0.5 = 4 So the answer is 4^m
The last one is 4^m which is the answer you got from the division.
Given expression: [tex]64^{m} /{4^{2m} }[/tex]
We can rewrite the expression (in the numerator and the denominator) as the product of multiple fours. Then, we can apply the exponent rule to simplify the expression to its simplest form. The simplest form will be the required simplified expression (solution to the provided expression).
[tex]\implies (4^{3}) ^{m} /{4^{2m} } \\[/tex][tex]\implies 4^{3m} /{4^{2m} }[/tex]We can apply the following exponent rule to simplify the expression:
[tex]\boxed{\text{Exponent rule:} \ 4^{m} /4^{n} = 4^{m - n}}[/tex]
The exponent rule states that the "base" must be the same when subtracting exponents. If we divide a term with same bases, we can reduce work time by subtracting the exponent to simplify the expression.
[tex]\implies 4^{3m} /{4^{2m} }[/tex][tex]\implies 4^{3m - 2m} = 4^{m}[/tex]Step-2) Equivalent or Non-equivalent?Now, let us look at all the options to verify which term matches our simplified term, and which expressions do not match our simplified term.
First option:Given term: [tex]2^{2m} \\[/tex]
Can be re-written as:
[tex]=2^{2m} \\[/tex][tex]= [2^{(2)}]^{m}[/tex]Simplifying the expression inside the long brackets:
[tex]\\= [4]^{m}[/tex][tex]\\= 4^{m} \ ( \text{matches})[/tex]Therefore, the first option is equivalent to our simplified term.
Second option:Given term: [tex]16^{0.5m}[/tex]
Can be re-written as:
[tex]= 16^{0.5m}[/tex][tex]\\= (4^{2}) ^{0.5m}[/tex]Exponent Rule: (xᵃ)ᵇ = xᵃᵇ
[tex]= (4^{1}) ^m[/tex][tex]= (4^{1m})[/tex][tex]= 4^m[/tex]Therefore, the second option is equivalent to our simplified term.
Third option:Given term: [tex]4^{m}[/tex]
This term already matches our simplified term.
Therefore, the third option is equivalent to our simplified term.
Step-3) Conclude/verify your answerWe can conclude that all the options provided are equivalent to the given expression. We proved it by applying exponent rules and formulas.
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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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 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
homework! This is a stats problem I’ve been struggling with and need help thanks!!!
Please help me. NO LINKS!!
The domain (input values) of the cosine function is all negative and positive angle measures.
Let the function be f(x) = cos(x)
The domain of cos(x) is -∞ < x < ∞
The range is -1 ≤ f(x) ≤ 1
Hence, domain of cos(x) is all (+) and (-) angle measures.
Same goes with sine function as well
For function f(x) = sin(x)
The domain is -∞ < x < ∞ and range -1 ≤ f(x) ≤ 1
However for f(x) = tan(x) the same is not applicable.
Answer:
A. all negative and positive angle measures.
Step-by-step explanation:
The domain of a function is the set of input values (x-values).
The cosine function is a continuous function, and therefore has no restrictions throughout its domain.
Therefore, its domain is all real numbers.
Set notation: { x | x ∈ R }
Interval notation: (-∞, ∞)
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]
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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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
AADF, AB = 16,
mZB = 59° mZD = [?]
Answer:
59°
Step-by-step explanation:
ABC and ADF are congruent (that is the meaning of that symbol).
that means all their associated angles and side lengths are the same.
it is relatively clear to see that
A corresponds to A.
D corresponds to B.
F corresponds to C.
therefore, the angle D = angle B = 59°.
FYI - it also means that AD = AB = 16. but this information was actually irrelevant for this question.
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
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
How many sides does a nonagon have
Which choice is equivalent to the quotient below?
-/100/-/25
the answer to this equation is 4
I need to know The value of f(1/2)
[tex]\huge\boxed{\textsf{a.)}\ 10}[/tex]
Substitute [tex]\frac{1}{2}[/tex] for [tex]x[/tex].
[tex]f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}[/tex]
Use [tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex].
[tex]\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}[/tex]
simplify the expression -2v+15d
Answer:
isn't this already fully simplified?
Step-by-step explanation:
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...
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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A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.
Based on the data set given in the frequency table, the number of values that are less than or equal to 6 is 18.
How many values are less than or equal to 6?The value that will be less than or equal to 6 are those that are valued at 6 or below.
The sum of these values are:
= 2 + 3 + 6 + 4 + 3
= 18
In conclusion, 18 values are less than or equal to 6.
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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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Brian has earned 65%, 80% and 92% on his three pre-final exams. These exams are not weighed equally: the lowest counts for only 20% of his overall grade, while the other two count for 25% each. If the final exam is the remainder of the overall grade and there are no opportunities for extra credit, what is the highest grade Brian can earn in the class? Express your answer to the nearest whole percent.
Answer:
89.25%
Step-by-step explanation:
65 is the lowest so it only counts for 20% of the grade
65*0.2=16.25
80*0.25=20
92*0.25=23
There is 30% left and 100% is the highest score
100*0.3=30
16.25+20+23+30=89.25
Answer:
86%
Step-by-step explanation:
From the information give:
Exam 1
Exam result = 65%
Overall grade weighting = 20%
⇒ Credit = 65% of 20% = 0.65 × 0.2 = 0.13 = 13%
Exam 2
Exam result = 80%
Overall grade weighting = 25%
⇒ Credit = 80% of 25% = 0.8 × 0.25 = 0.2 = 20%
Exam 3
Exam result = 92%
Overall grade weighting = 25%
⇒ Credit = 92% of 25% = 0.92 × 0.25 = 0.23 = 23%
Final Exam
The highest grade Brian can earn = 100%
Overall grade weighting = 100% - 20% - 25% - 25% = 30%
⇒ Credit = 100% of 30% = 1 × 30% = 30%
Highest potential class grade
Sum of each exam credit:
⇒ 13% + 20% + 23% + 30% = 86%
Therefore, the highest grade possible that Brian can earn in the class is 86%.
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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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
[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].
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.
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