Answer:
x^2 = a/b
Step-by-step explanation:
[tex]\frac{\sqrt{a}}{\sqrt{b} } =x[/tex]
If we have square root at the top and bottom then we take single square root with fraction inside
[tex]\sqrt{\frac{a}{b}} =x[/tex]
To remove square root we take square on both sides because square and square root will get cancelled
[tex]\frac{a}{b}=x^2[/tex]
x^2 = a/b is true
The statement that must be true is:
[tex]x^2 = a/b[/tex]
How to find an equivalent expression?
To find an equivalent expression, we just need to rewrite the given expression.
Here we will use the fact that the square root is distributive with respect to the division, which means that we can rewrite:
[tex]\frac{\sqrt{a} }{\sqrt{b} } = x\\\\\sqrt{\frac{a}{b} } = x[/tex]
Now if we square both sides of that expression, we will get:
[tex]\sqrt{\frac{a}{b} }^2 = x^2\\\\\frac{a}{b} = x^2[/tex]
So we can see that the correct option is A.
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In a crowd, the ratio of men to women is 5 to 6. If there are 90 men, how many women are there?
for every 5 men there are 6 women
90 /5 = 18
18 *6 = 108 women
Answer:
108 women
Step-by-step explanation:
w is partly constant and partly varies inversely as the square of t. when w=24, t=4 and when w=18, t=2.
i. determine the law connecting w and t
ii. find t when w = 46
To find the law connecting w and t, we establish w as partly constant and partly inverse to t squared. Using given values, we find constants k and c and then solve for t when w is 46.
The problem states that w is partly constant and partly varies inversely as the square of t. Given two sets of values for w and t, we can establish the relationship between them. Since the variation is inverse with respect to the square of t, we can write the relationship as:
w = k / t2 + c
where k is a constant of variation and c is the constant part of w. To find these constants, we use the given data points (24, 4) and (18, 2). Substituting these into the equation, we get two simultaneous equations:
24 = k / 42 + c18 = k / 22 + cSolving these will give us the values of k and c, which then allows us to find t when w = 46.
To solve for t when w = 46, we plug this value into our established equation and solve for t. We'll end up with a quadratic equation in terms of t that we need to solve to find the time t.
5/6 is equivalent to a percent that is larger than 100%. True False
y/6-3=-11
What does y equal?
Find all numbers such that a third of a number increased by half that number is at least 3 less than that same number.
Answer:
All the numbers are less than and equal to 18.
Step-by-step explanation:
To find : All numbers such that a third of a number increased by half that number is at least 3 less than that same number ?
Solution :
Let the number be 'x',
A third of a number is [tex]\frac{x}{3}[/tex]
Half that number is [tex]\frac{x}{2}[/tex]
3 less than that same number is [tex]x-3[/tex]
A third of a number increased by half that number is at least 3 less than that same number is written as,
[tex]\frac{x}{3}+\frac{x}{2}\geq x-3[/tex]
[tex]\frac{2x+3x}{6}\geq x-3[/tex]
[tex]\frac{5x}{6}\geq x-3[/tex]
[tex]5x\geq 6x-18[/tex]
[tex]5x-6x\geq -18[/tex]
[tex]-x\geq -18[/tex]
[tex]x\leq 18[/tex]
Therefore, all the numbers are less than and equal to 18.
The set of numbers such that a third of a number increased by half that number is at least 3 less than that same number are given as; x <= 18.
According to the question;
Let the numbers in question be represented as x.
In essence;
[tex] \frac{x}{3} + \frac{x}{2 } \geqslant x - 3[/tex]
[tex] \frac{5x}{6} \geqslant x - 3[/tex]
5x >= 6x - 18-x >= -18x <= 18Therefore, the set of numbers such that a third of a number increased by half that number is at least 3 less than that same number are given as; x <= 18.
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4.Thirty percent of the liquid evaporated. If 560 milliliters remain, how many milliliters evaporated?
Joe’s weekly pay increased from $80 to $100. What is the percent increase in Joe’s weekly pay?
10%
40%
25%
20%
If the marginal propensity to consume is 0.8, (a) what is the value of the multiplier?
Kevin has had a checking account for a month. As he reconciles his account, Kevin notices that the dates on his check register do not match the dates on his account statement. He immediately calls the bank to find out what the problem is. What is the bank's likely response to Kevin?
A- "you obviously made a mistake and you should be careful"
B-"sorry we entered the wrong dates but thanks for telling us, we will fix it immediately"
C-"theres a serious problem with your account, please bring us all your records and info so we can check it"
D-"The date that the check is written is usually a few days before it is cashed. We record when it was cashed and you record when its written"
The bank's likely response to Kevin's concern would be that checks are recorded on the date they are cashed, not on the date they are written, which explains the mismatch in dates Kevin observed. Balancing one's checkbook regularly is important for managing personal finances.
When Kevin has noticed that the dates on his check register do not match the dates on his account statement and contacts the bank, the bank's likely response will be "The date that the check is written is usually a few days before it is cashed. We record when it was cashed and you record when it's written." This is a common situation in personal finance and is related to the cash basis of accounting that most individuals use to manage their finances. The difference in dates arises because checks are processed and cleared by the bank on the date they are cashed, not on the date they are written. It's important for individuals to balance their checkbooks regularly to manage money, keep track of cash flow, and avoid overdraft fees.
3y-5z=-23
4x+2y+3z=7
-2x-y-z=-3
Solve for each variable, please show work if possible!
How do you solve -3x+d=-9
HELP!!!! Which system of Linear inequalities is graphed?
x < -3 and y < -x -2
x < -2 and y ≤ -x +2
x < -2 and y ≤ -x -2
x ≤ -2 and y ≤ x -3
x < -2 and y ≤ -x -2
In how many ways can you place 8 rooks on a 8x8 chessboard so that no row or column contains more than one rook if
82=6482=64choices for that.
Now, for the second one, we can't be in the row or column of that first one, so leaving us with 72=4972=49 choices.
Then so on, we have 62=3662=36 for the third one, 2525 for the fourth one, and so on ……
But, however, we have to remember the rooks are not labeled, thus it doesn't matter specifically about a specific rook's position.
Thus, we have a total of (8!)28!=40320(8!)28!=40320 ways.
How can x-2/3=5/6 be solved for x in one step?
x - 2/3 = 5/6
the only step needed is to add 2/3 to 5/6
2/3 + 5/6 = 1 1/2
x = 1 1/2
Answer:
the value of x is [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
we need to solve value of x for expression [tex]x-\frac{2}{3}=\frac{5}{6}[/tex]
[tex]x-\frac{2}{3}=\frac{5}{6}[/tex]
Add both the sides by [tex]\frac{2}{3}[/tex]
[tex]x-\frac{2}{3}+\frac{2}{3}=\frac{5}{6}+\frac{2}{3}[/tex]
take L.C.M both the side and simplify
[tex]x=\frac{3}{2}[/tex]
Hence, the value of x is [tex]\frac{3}{2}[/tex]
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
a. the number of hits to a website in a daynumber of hits to a website in a day
b. the weight of a upper t dash bone steakweight of a t-bone steak
c. the political party affiliation of adults in the united statespolitical party affiliation of adults in the united states
d. the number of bald eagles in a countrynumber of bald eagles in a country
e. the amount of snowfall in december in city upper aamount of snowfall in december in city a f. the number of textbook authors now sitting at a computer
Evaluate 390mm to 13cm as a ratio in its lowest terms
To evaluate the ratio of 390mm to 13cm, we convert 13cm to 130mm and then simplify the ratio of 390mm to 130mm to its lowest terms, which is 3 : 1.
To evaluate the ratio of 390mm to 13cm, we first need to express these measurements in the same unit. Converting centimeters to millimeters is simple: there are 10 millimeters in 1 centimeter.
Therefore, 13cm is equivalent to 130mm. Now, we can write the ratio as 390mm : 130mm. To simplify this ratio to its lowest terms, we divide both numbers by the greatest common divisor, which is 130 in this case. The simplified ratio is therefore 3 : 1.
The generalized description is as follows: quantity (in old units) imes conversion factor = quantity (in new units). One must remember to simplify the ratio by dividing both the numerator and the denominator by their greatest common divisor, finalizing the answer without the '1' in the denominator when it's the only figure present.
What is the center point of a data set when all of the values are listed in order?
the mean
the median
the mode
the range
The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 3x + 8 and g(x) = x2. Find (f • g)(x).
A. x2 − 3x − 8
B. 3x2 + 8
C. 3x3 + 3x2 + 8
D. 3x3 + 8x2
What method can be used to write the equation of a line in slope-intercept form given two points?
To write the equation of a line in slope-intercept form given two points, calculate the slope from the points, use one point and the slope to find the y-intercept, then write the equation as y = mx + b.
Explanation:To write the equation of a line in slope-intercept form, given two points, follow these steps:
Calculate the slope (m) using the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the coordinates of the two given points.Once you have the slope, choose one of the two points to substitute into the slope-intercept form equation, y = mx + b, along with the slope you calculated. This will allow you to solve for the y-intercept (b).With both the slope and y-intercept, you can write the final equation of the line: y = mx + b.For example, if the two points given are (1, 3) and (4, 11), the slope would be (11 - 3) / (4 - 1) = 8 / 3. Then choosing the point (1, 3), we would substitute to find the y-intercept: 3 = (8/3)(1) + b, resulting in b = 3 - 8/3 = 1/3. So the equation of the line is y = (8/3)x + 1/3.
Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?
A. $197.24 B. $379.97 C. $54.44 D. $201.12
Answer:
b
Step-by-step explanation:
the perimeter of a rectangle that is x units wide and y units long is 24 centimeters.
A.) Write an equation in standard form for the perimeter
B.) Find the x and y units. Does either intercept make sense as a solution for this situation? Explain.
James borrows $300 at an interest rate of 8% and takes 5 years to pay it off. How much does he pay? Question 2 options: $420 $120 $240 $600
What is 0.02% written as a decimal
The value 0.02% written as a decimal is 0.0002
Given the value to be written as a decimal :
0.02%To express as a decimal , divide 0.02 by 100
Now we have ;
0.02/100 = 0.0002Therefore, the value 0.02% written as a decimal is 0.0002
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In what way is a debit card similar to a check? a You must always provide a signature to use either.
b Both always take a few days to clear, so there is some float time until the payment goes through.
c Both pull money directly from a checking or savings account.
d Both charge interest on the purchases you make with them.
A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller. When will the station first give away all three prizes to one caller? PLEASE HELP.
Answer:
The station first give away all three prizes to 300th caller.
Step-by-step explanation:
A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller.
To get the answer we need to calculate L.C.M. of 15, 25, 100.
15 = 3 x 5
25 = 5 x 5
100 = 2 x 2 x 5 x 5
LCM is = 2 x 2 x 3 x 5 x 5 = 300.
Hence, the station first give away all three prizes to 300th caller.
A rock is thrown in the air from the edge of a seaside cliff. Its height in feet is represented by f(x) = –16(x2 – 3x – 18), where x is the number of seconds since the rock was thrown. The height of the rock is 0 feet when it hits the water.How long does it take the rock to hit the water? How many seconds?
The time it takes the rock to hit the water is 6 seconds
Data;
f(x) = -16(x^2 - 3x -18)Time it takes for the rock to hit the ground?To find the time it takes for the rock to hit the ground, we have to use the and assume that the given equation represents the height at which the rock attained.
[tex]f(x) = -16(x^2 - 3x -18)\\0 = -16x^2 + 48x + 288\\16x^2 - 48x - 288 = 0\\x^2 - 3x - 18 = 0[/tex]
Solving the above quadratic equation,
x = - 3 or x = + 6
The time it takes the rock to hit the water is 6 seconds
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There are 4 seats available at a table in the lunch room of an elementary school, and 12 students are looking for seats. In how many ways can the seats at the table be filled with 4 of these 12 students?
Answer with explanation:
Total number of vacant seats = 4 seat
Number of students Looking for Seats = 12 Student
We have to fill the four Seats and there are 12 students.
First Seat can be filled in 12 ways,11 students are left,So, second seat can be filled in 11 ways ,Now,there are 10 students left ,So, third seat can be filled in 10 ways,Now there are 9 students left,so last seat can be filled in 9 ways.
Total number of ways of filling 4 seats if there are 12 number of students
=12 × 11 × 10 × 9
=132 × 90
= 11880 ways
Or ,you can solve it directly by the concept of Permutation.
Total ways of filling 4 vacant seats if there are 12 students in all
[tex]= _{4}^{12}\textrm{P}=\frac{12!}{(12-4)!}=\frac{12\times 11\times 10\times 9\times 8!}{8!}=12\times 11\times 10\times 9=11880[/tex]
PLEASE HELP ME AND SHOW WORK
Write the polynomial in standard form, then identify its leading coefficient and constant term.
6x^2+2x+11x^3
Standard form: 11x^3+6x^2+2x, can you just show the work for this?
Leading coefficient: 11
Constant term: please show me how to find this
Find the maximum rate of change of f(xy)=ln(x2+y2) at the point (-1, -5) and the direction in which it occurs.
Which statement is true about this argument?
Premises:
If a parallelogram has a right angle, then it is a rectangle.
Parallelogram PQRS has a right angle.
Conclusion:
Parallelogram PQRS is a rectangle.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of syllogism.
The argument is not valid because the premises are not true.
The argument is valid by the law of detachment.
The argument is valid by the law of detachment.
Answer:
The argument is valid by the law of detachment.
Step-by-step explanation:
We first verify that the first statement, "if p, then q" is correct. If a parallelogram has a right angle, this means that the angle opposite that angle must also be right; this is because the opposite angles of a parallelogram are congruent.
This also means that the adjacent angle to this right angle must also be right; this is because the adjacent angles in a parallelogram are supplementary.
Thus "if p, then q" is true.
The law of detachment states that if I have two statements, one of the form "if p, then q" and the other "p", then the conclusion, "q," is valid.