Answer:
Option B is the correct answer.
Step-by-step explanation:
We have one side = 27.6 cm
Hypotenuse = 30 cm
Length of remaining side [tex]=\sqrt{30^2-27.6^2}=11.76cm[/tex]
Area of right angled triangle [tex]=\frac{1}{2}\times \texttt{Product of lengths of 2 sides other than hypotenuse}[/tex]
Area [tex]=\frac{1}{2}\times 27.6\times 11.76=161.7cm^2[/tex]
Option B is the correct answer.
find the inverse of the function and then determine whether the inverse is a function.
y=x^2+4
Ennifer owes $185 to a credit card company. She makes a $12 purchase with the card and then pays $70 on the account. what us her current balance
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
Joe’s weekly pay increased from $80 to $100. What is the percent increase in Joe’s weekly pay?
10%
40%
25%
20%
What is the distance between points (-23. 17) and (-3, -4)
"Suppose X ~ N(2, 3).
What value of x has a z-score of −0.74? (Enter an exact number as an integer, fraction, or decimal.)"
Thanks so much for any and all help. I have no idea what I'm doing. :P
The value of x with a z-score of -0.74 is -0.22.
Explanation:To find the value of x that has a z-score of -0.74, we can use the formula:
x = mean + (z-score * standard deviation)
Given that the mean (mean) is 2 and the standard deviation (standard deviation) is 3, we can substitute these values into the formula:
x = 2 + (-0.74 * 3)
Simplifying the equation, we get:
x = 2 - 2.22
x = -0.22
Therefore, the value of x that has a z-score of -0.74 is -0.22.
Learn more about Value of x with z-score here:https://brainly.com/question/35654641
#SPJ11
Simplify i12
-1
-i
i
1
Answer:
[tex]i^{12}=1[/tex]
Last option is correct.
Step-by-step explanation:
We have to simplify the expression [tex]i^{12}[/tex]
We can rewrite this expression using the properties [tex](a^m)^n=a^{mn}[/tex]
[tex](i^4)^{3}[/tex]
Now, we know that [tex]i^4=1[/tex]
Hence, we have
[tex](1)^{3}[/tex]
On simplifying, we get
[tex]1[/tex]
Thus, the simplified form is 1.
Last option is correct.
Answer:
it's 1
Step-by-step explanation:
3333% of college students say they use credit cards because of the rewards program. you randomly select 10 college students and ask each to name the reason he or she uses credit cards. find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. if convenient, use technology to find the probabilities.
a. at r = 2
P = [10! / (10 – 2)! 2!] * 0.33^2 * 0.67^(10 – 2)
P = 0.1989 ~ 0.20 (answer)
b. We deduct the values of P when r = 0, r = 1, r = 2 from 1 to get all values when r > 2
at r = 0
P = [10! / (10 – 0)! 0!] * 0.33^0 * 0.67^(10 – 0)
P = 0.0182
at r = 1
P = [10! / (10 – 1)! 1!] * 0.33^1 * 0.67^(10 – 1)
P = 0.0898
so for r > 2, the probability is:
P = 1 – (0.1989 + 0.0182 + 0.0898)
P = 0.6931 (answer)
c. at r = 3
P = [10! / (10 – 3)! 3!] * 0.33^3 * 0.67^(10 – 3)
P = 0.2614
at r = 4
P = [10! / (10 – 4)! 4!] * 0.33^4 * 0.67^(10 – 4)
P = 0.2253
at r = 5
P = [10! / (10 – 5)! 5!] * 0.33^5 * 0.67^(10 – 5)
P = 0.1332
So when r is between 2 and 5 inclusive, the probability is:
P = 0.1989+ 0.2614 + 0.2253 + 0.1332
P = 0.8188 (answer)
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.
Read more:
https://brainly.com/question/24505821
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.
Describe which of the two points lies on the graph of the line
2x+2y=6
A,-4,5
B,6-3
Sarah's grade point average is 2.4. based on the frequency distribution of grouped scores in the table below, what is the percentile rank of sarah's grade point average?
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.
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
Learn more on percentages :https://brainly.com/question/24304697
#SPJ6
A. use the zero product
the diagonals of a parallelogram are congruent and are perpendicular bisectors of each other. the parallelogram is which type of quadrilaterals?
A. square
B. rectangle
C. trapezoid
D. kite
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.
9(x + 3) = 108 what does 9x equal and i need major help on how to do this in genral
rewrite the equation in the form y= k/x
xy= -45
x= 15/y
2xy=9
what are the answers and how do i solve them?
The time t (in minutes) for a small plane to climb to an altitude of h feet is given by t = 50 log10 (18000/(18000-h)) where 18000 feet is the plane's absolute ceiling. a. Determine the domain of the function appropriate for the context of the problem. b. Graph the function and identify any asymptotes. c. As the plane approaches its absolute ceiling, what can be said about the time required to further increase its altitude. d. Find the amount of time it will take for the plane to climb to an altitude of 4000 feet.
The domain of the function is restricted to the altitude of the plane, and the plane cannot exceed its absolute ceiling. The graph of the function will have a vertical asymptote at the absolute ceiling. As the plane approaches its absolute ceiling, the time required to further increase its altitude increases significantly. To find the time it will take for the plane to climb to a specific altitude, substitute the altitude into the equation and solve for time.
Explanation:a. The domain of the function is determined by the restrictions given in the problem. In this case, the domain represents the altitude of the plane. Since the plane's absolute ceiling is 18,000 feet, the altitude cannot exceed 18,000 feet. Therefore, the domain is 0 ≤ h ≤ 18,000.
b. To graph the function, we can plot points by substituting different values of h into the function and calculating the corresponding values of t. This will result in a smooth curve. Asymptotes occur when the function approaches certain values of h or t. In this case, the function has a vertical asymptote at h = 18,000, because the plane cannot climb beyond its absolute ceiling.
c. As the plane approaches its absolute ceiling of 18,000 feet, the time required to further increase its altitude increases significantly. This is because the logarithmic function in the equation has a slower growth rate as h approaches its limit.
d. To find the time it will take for the plane to climb to an altitude of 4000 feet, we can substitute h = 4000 into the equation t = 50 log10 (18000/(18000-h)) and solve for t.
Is 120% equal to less than or greater than 1
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.
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
Simplify open parentheses x to the 2 ninths power close parentheses to the 3 eighths power
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.
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.
Which relationship between sample size and sampling error is correct?
y/6-3=-11
What does y equal?
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:
What is the greatest perfect square that is a factor of 980?
Answer:
The greatest perfect square that is a factor of 980 is 196.
Step-by-step explanation:
To find : What is the greatest perfect square that is a factor of 980?
Solution :
First we factor the number 980.
[tex]980=2\times 2 \times 5\times 7\times 7[/tex]
[tex]980=2^2\times 7^2\times 5[/tex]
[tex]980=(2\times 7)^2\times 5[/tex]
[tex]980=(14)^2\times 5[/tex]
[tex]980=196\times 5[/tex]
This clearly means that 196 is the required factor.
Therefore, The greatest perfect square that is a factor of 980 is 196.
We have that The Greatest perfect square of 980 is
x= 196
From the question we are told that
The greatest perfect square that is a factor of 980
Generally
Greatest perfect square
Where a perfect square is a number that is written to given the product of two identical Numbers
Therefore
Greatest perfect square of 980 is
x= 196
Where
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
Therefore
The Greatest perfect square of 980 is
x= 196
For more information on this visit
https://brainly.com/question/23366835?referrer=searchResults