An equation can be defined as a mathematical statement in which two expressions are set equal to each other. In simple words, equations mean equality i.e. the equal sign. Since equations are all about “equating one quantity with another”,they are simply known as equation
Answer:
In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. ... For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
what is the simplified form of the following expression 3 sqrt 4x/5
Answer:
Kindly check the attached picture
Step-by-step explanation:
The solution to the problem has been explicitly solved in the picture attached below :
We need to find a number that makes the denominator a perfect cube in other to simplify the expression which is 25/25.
Kindly check the attached picture for detailed explanation
What is the value of x if 2/ 3 - 2 = -4 ?
Answer:
x= -3
Step-by-step explanation:
(2x/3)-2=-4
Add 2 to both sides
2x/3=-2
multiply both sides by 3
2x=-6
divide both sides by 2
x= -3
Answer:
x = -3
Step-by-step explanation:
2x/3 - 2 = -4
Add 2 to both sides.
2x/3 = -2
Multiply both sides by 3/2.
x = -2 * 3/2
x = -3
The sum of three numbers is 3. The first number minus the second plus the third is -3. The first minus the third is 1 more than the second.
Find the numbers. What is the first number? What is the second number? What is the third number?
Answer: The first number is 2, the second number is 3 and the third number is -2
Step-by-step explanation:
Let the first number be 'x', the second number be 'y' and the third number be 'z'
The equations according to the question becomes:
⇒ x + y + z = 3 ....(1)
⇒ x - y + z = -3 ....(2)
⇒ x - z = 1 + y ....(3)
Rearranging equation 3:
⇒ x - y = 1 + z .....(4)
Putting in equation 2:
⇒ 1 + z + z = -3
⇒ 1 + 2z = -3
⇒ z = -2
Putting this value in equation 4 and equation 1, we get:
⇒ x - y = -1
⇒ x + y = 5
Cancelling 'y' by eliminiation method and equation becomes:
⇒ 2x = 4
⇒ x = 2
Putting value of 'x' and 'z' in equation 1:
⇒ 2 + y - 2 = 3
⇒ y = 3
Hence, the first number is 2, the second number is 3 and the third number is -2
The following data show the number of cars passing through a toll booth during a certain time period over 15 days. 18 19 17 17 24 18 21 18 19 15 22 19 23 17 21 Identify the corresponding dotplot.
Answer: third from the top
Step-by-step explanation:
The correct answer is third from the top.
Arranging numbers in ascending order:
15 17 17 17 18 18 18 19 19 19 21 21 22 23 24
Let's count how many times each number occurs in this series of numbers.
row of numbers
15 +
16 not
17 + + +
18 + + +
19 + + +
20 not
21 + +
22 +
23 +
24 +
25 not
Jerry leaves home driving at 50 miles per hour. Ten minutes later, Jenny drives after him at the speed 65 miles per hour. When will she overtake him?
Hi there!
[tex]\large\boxed{\approx 43.33 min}}[/tex]
Recall:
d = st, where:
d = distance
s = speed
t = time
We can set up an expression where the extra ten minutes is taken into account:
50x = 65(x - 10) <--- because J left 10 minutes after, we must subtract from the time variable, or "x".
Solve for x:
50x = 65x - 650
Subtract 65x from both sides:
-15x = -650
Divide both sides by -15:
x ≈ 130/3 or 43.33 min
What is the meaning proportion between 3 and 27?
Answer:
you mean the mean not the meaning right?
The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.
Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. Write the formula for this sequence in the form an = a1 ⋅ rn−1. Explain how you arrived at your answer.
Answer:
[tex]a_n = 4.5 * 3^{n-1}[/tex]
Step-by-step explanation:
Given
[tex]a_4 = 121.5[/tex]
[tex]r = 3[/tex]
Required
[tex]a_n = a_1 * r^{n -1}[/tex]
Substitute 4 for n in [tex]a_n = a_1 * r^{n -1}[/tex]
[tex]a_4 = a_1 * r^{4 -1}[/tex]
[tex]a_4 = a_1 * r^3[/tex]
Substitute 121.5 for [tex]a_4[/tex]
[tex]121.5 = a_1 * 3^3[/tex]
[tex]121.5 = a_1 * 27[/tex]
Solve for a1
[tex]a_1 = \frac{121.5}{27}[/tex]
[tex]a_1 = 4.5[/tex]
So, we have:
[tex]a_n = a_1 * r^{n -1}[/tex]
[tex]a_n = 4.5 * 3^{n-1}[/tex]
Answer:
First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.
Step-by-step explanation:
sample answer on edge ;)
Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years and the standard deviation was years. If a sample of people from this region is selected, find the probability that the mean life expectancy will be less than years. Round intermediate -value calculations to decimal places and round the final answer to at least decimal places.
Answer:
The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
We have:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].
Sample of size n:
This means that the z-score is now, by the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Find the probability that the mean life expectancy will be less than years.
The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Use reduction of order to find a second linearly independent solution
(2x+5)y′′−4(x+3)y′+4y=0,x>−52,y1=e2x
Given that exp(2x) is a solution, we assume another solution of the form
y(x) = v(x) exp(2x) = v exp(2x)
with derivatives
y' = v' exp(2x) + 2v exp(2x)
y'' = v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)
Substitute these into the equation:
(2x + 5) (v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)) - 4 (x + 3) (v' exp(2x) + 2v exp(2x)) + 4v exp(2x) = 0
Each term contains a factor of exp(2x) that can be divided out:
(2x + 5) (v'' + 4v' + 4v) - 4 (x + 3) (v' + 2v) + 4v = 0
Expanding and simplifying eliminates the v term:
(2x + 5) v'' + (4x + 8) v' = 0
Substitute w(x) = v'(x) to reduce the order of the equation, and you're left with a linear ODE:
(2x + 5) w' + (4x + 8) w = 0
w' + (4x + 8)/(2x + 5) w = 0
I'll use the integrating factor method. The IF is
µ(x) = exp( ∫ (4x + 8)/(2x + 5) dx ) = exp(2x - log|2x + 5|) = exp(2x)/(2x + 5)
Multiply through the ODE in w by µ :
µw' + µ (4x + 8)/(2x + 5) w = 0
The left side is the derivative of a product:
[µw]' = 0
Integrate both sides:
∫ [µw]' dx = ∫ 0 dx
µw = C
Replace w with v', then integrate to solve for v :
exp(2x)/(2x + 5) v' = C
v' = C (2x + 5) exp(-2x)
∫ v' dx = ∫ C (2x + 5) exp(-2x) dx
v = C₁ (x + 3) exp(-2x) + C₂
Replace v with y exp(-2x) and solve for y :
y exp(-2x) = C₁ (x + 3) exp(-2x) + C₂
y = C₁ (x + 3) + C₂ exp(2x)
It follows that the second fundamental solution is y = x + 3. (The exp(2x) here is already accounted for as the first solution.)
Match the graph with the correct equation.
A. Y-1 = -1/4(x+5)
B. Y+1= -1/4(x+5)
C. Y-1= -4(x+5)
D. Y-1 =-1/4 (x-5)
Answer:
y - 1 = -1/4(x+5)
Step-by-step explanation:
what is true for f (x) = 4 times 2x
Answer:
f(x) = 8x
Explanation:
4 x 2 =8
What is the inverse of function f? f(x)=10/9+11
Answer:
Option D is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = 10/9 X + 11
Let f(X) be "y".
y = (10/9) X + 11
Interchange "X" and "y".
x = (10/9) y + 11
or, 9x = 10y + 99
or, y = (9x-99)/10
Therefore, f'(X) = (9x-99)/10.
Hope it helps!
Four cups of pure water are added to a 20-cup bowl of punch that is 75% juice. What percentage of the new punch is juice?
Amount of Juice
15
0
Amount of Punch
20
4
27%
37.5%
62.5%
75%
Answer:
62.5%
Step-by-step explanation:
Given that :
20 cup bowl of punch = 75% Juice
We can infer that :
The number of cups of JUICE is :
75% * 20 = 0.75 * 20 = 15 cups
Adding 4 cups of water to the 20 cups, we have = 24 cups
With 15 cups of JUICE ;
The percentage of the new punch that is juice will be x
x% of 24 cups = 15 cups
x/100 * 24 = 15
0.01x * 24 = 15
0.24x = 15
x = 15 / 0.24
x = 62.5
x = 62.5%
Answer:
It's C
62.5% btw
Step-by-step explanation:
Did the quiz lol
The marked price of a bicycle is Rs 2000. If the shopkeeper allows some discount and a customer
bought it for Rs 1921 including 13% VAT, how much amount was given as the discount?
Answer:
Discount amount = $328.73
Step-by-step explanation:
Below is the calculation for the discount amount:
The marked price of bicycle = 2000
Purchase price = Rs 1921
VAT = 13%
First find the purchase price excluding VAT = 1921 - (13% of 1921) = 1671.27
Discount amount = 2000 - 1671.27
Discount amount = $328.73
16. Risa wants to order business cards. A print-
ing company determines the cost (C) to
the customer using the following function,
where b the number of boxes of cards and
n= the number of ink colors.
C= $25.60b + $14.00b(n - 1)
If Risa orders 4 boxes of cards printed in 3
colors, how much will the cards cost?
OA. $214.40
OB. $168.00
C. $144.40
OD. $102.40
Answer:
A - $214.40
Step-by-step explanation:
Since b is the number of boxes of cards and n is the number of ink colors, and we're given the number of boxes of cards, and number of ink colors, we plug in:
4= b
and
3 = n
into the given equation to solve for C.
Using the order of operations we start inside our parentheses and work from there:
C= $25.60*4 + $14.00*4(3 - 1)
C= $25.60*4 + $14.00*4(2)
C= $102.40 + $112
C= $214.40
At what x value does the function given below have a hole?
f(x)=x+3/x2−9
Answer:
hole at x=-3
Step-by-step explanation:
The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)
The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.
So anyways we have (x+3)/(x^2-9)
= (x+3)/((x-3)(x+3))
Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.
There are four different colored balls in a bag. There is equal probability of selecting the red, black, green, or blue ball.What is the expected value of getting a green ball out of 20 experiments with replacement?
Answer:
The expected value is of 5 green balls.
Step-by-step explanation:
For each experiment, there are only two possible outcomes. Either it is a green ball, or it is not. Since there is replacement, the probability of a green ball being taken in an experiment is independent of any other experiments, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
20 experiments
This means that [tex]n = 20[/tex]
There is equal probability of selecting the red, black, green, or blue ball.
This means that 1 in 4 are green, so [tex]p = \frac{1}{4} = 0.25[/tex]
What is the expected value of getting a green ball out of 20 experiments with replacement?
[tex]E(X) = np = 20*0.25 = 5[/tex]
The expected value is of 5 green balls.
The expected value of getting a green ball out of 20 experiments with replacement is 5.
What is a binomial distribution?The binomial probability distribution of the number of successes in a sequence of n independent experiments is the binomial distribution with parameters n and p.
As it is given that the probability of all the balls coming out of the bag is equal. Therefore, the probability of a green ball coming can be written as,
[tex]\text{Probability of Green Ball} = 0.25[/tex]
Also, we can write the probability of not getting a green ball can also be written as,
[tex]\rm Probability(\text{Not coming Green Ball}) = P(Red\ ball)+P(Black\ ball)+P(Blue\ ball)[/tex]
[tex]=0.25+0.25+0.25\\\\=0.75[/tex]
Now, as there are only two outcomes possible, therefore, the distribution of the probability is a binomial distribution. And we know that the expected value of a binomial distribution is given as,
[tex]\rm Expected\ Value, E(x) = np[/tex]
where n is the number of trials while p represents the probability.
Now, substituting the values, we will get the expected value,
[tex]\rm Expected\ Value, E(Green\ ball) = 20 \times 0.25 = 5[/tex]
Hence, the expected value of getting a green ball out of 20 experiments with replacement is 5.
Learn more about Binomial Distribution:
https://brainly.com/question/12734585
Need answer urgently
Answer:
x = -2; y = 1
Step-by-step explanation:
See picture below.
We are told matrices B is the inverse of matrix A.
The product of a matrix and its inverse is the identity matrix.
An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed?
Answer:
262.5 miles
Step-by-step explanation:
Correct me if I am wrong
There are 48 students o the school bus, 28 girls and 20 boys. what is the ratio of boys ad girls on the bus ?
Step-by-step explanation:
28:20
Once simplified its 7:5
Which of the following is the result of the equation below after completing the square and factoring? x^2-4x+2=10
A. (x-2)^2=14
B. (x-2)^2=12
C. (x+2)^2=14
D. (x+2)^2=8
9514 1404 393
Answer:
B. (x-2)^2=12
Step-by-step explanation:
The constant that completes the square is the square of half the coefficient of the x-term. That value is (-4/2)^2 = 4.
There is already a constant of 2 on the left side of the equal sign, so we need to add 2 to both sides to bring that constant value up to 4.
x^2 -4x +2 = 10 . . . . . . . given
x^2 -4x +2 +2 = 10 +2 . . . . complete the square (add 2 to both sides)
(x -2)^2 = 12 . . . . . . . . . write as a square
Sam works at a shoe store. He earns $300 every week plus $15 for every pair of shoes that he sells. How many pairs of shoes would he need to sell to make $500 in a week?
Answer:
300 + 15x = 500
15x = 200
x = 200/15
x=13.333
14 pair of shoes
Step-by-step explanation:
Sita and Ram divided Rs. 250 into 2:3 ratio. Find their shares.
Answer:
Rs. 100 and Rs. 150
Step-by-step explanation:
the ratio = 2:3 => the sum = 2+3=5
Sita gets = 2/5 × 250 = 100
Ram gets = 3/5 × 250 = 150
write an equation rectangular room 3 meters longer than it is wide and its perimeter is 18 meters
width = x
length = 3 + x
perimeter = x + x + ( 3 + x ) + (3+x)
18 = x + x + ( 3 + x ) + (3+x)
x + x + ( 3 + x ) + (3+x) = 18
6 + 4x = 18
4x = 12
x = 3
NEED HELP
The average amount of money spent for lunch per person in the college cafeteria is $6.75 and the standard deviation is $2.28. Suppose that 18 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
C. For a single randomly selected lunch patron, find the probability that this
patron's lunch cost is between $7.0039 and $7.8026.
D. For the group of 18 patrons, find the probability that the average lunch cost is between $7.0039 and $7.8026.
Answer:
C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]
Step-by-step explanation:
We are given that
n=18
Mean, [tex]\mu=6.75[/tex]
Standard deviation, [tex]\sigma=2.28[/tex]
c.
[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]
[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Using the formula
[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]
[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]
[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]
Find the indicated side of the
right triangle.
45
у
9
45
х
x = [?]
Enter
Answer:
9
Step-by-step explanation:
: Find absolute minimum and maximum values of (, ) = 2
2 +
4 + 4
On the close triangular region R bounded by the lines = −2, = 0, = 2
in a school project you need to provide a blueprint of the schools rectangular playground .the blueprint dimensions of the playground are 23/147 yd x 3/14 yd after reducing them by the factor of 2/147 what are the original dimensions if the playground in yards
Answer:
L = 0.16 yd, W = 0.22 yd
Step-by-step explanation:
Dimensions of play ground 23/147 yd x 3/14 yd
reducing factor 2/147
Let the original length is L.
[tex]L - \frac{2L}{147} = \frac{23}{147}\\\\L\frac{143}{147} = \frac{23}{147}\\\\L=\frac{23}{143} yd[/tex]
L = 0.16 yd
Let the width is W.
[tex]W - \frac{2W}{147} = \frac{3}{14}\\\\W\frac{143}{147} = \frac{3}{14}\\\\W=0.22 yd[/tex]
What is the next three-term of the geometric sequence? 60, 30, 15...?
Answer:
7.5
Step-by-step explanation:
it is feometeic progression
r=0.5
Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she had the disease. the probability is approximately?
Answer:
[tex]P(Negative | Yes) = 0.0486[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{} & {Yes} & {No} & {Positive} & {137} & {24} & {Negative} & {7} & {132} \ \end{array}[/tex]
Required
[tex]P(Negative | Yes)[/tex]
This is calculated as:
[tex]P(Negative | Yes) = \frac{n(Negative\ n\ Yes)}{n(Yes)}[/tex]
So, we have:
[tex]P(Negative | Yes) = \frac{7}{137+7}[/tex]
[tex]P(Negative | Yes) = \frac{7}{144}[/tex]
[tex]P(Negative | Yes) = 0.0486[/tex]
