Step-by-step explanation:
[tex] \sqrt{15} = 3.872983346 = 3.88[/tex]
Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using this relationship, what is the value of each function composition?
(h o k) (3)=
(k o h)(-4b) =
Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
Sarah bought a TV for £250
Three years later she sold it for £180
Work out her percentage loss
Answer:
36%
Step-by-step explanation:
Step-by-step explanation:
Loss percentage= loss/cost× 100%
250-180=70
70/180=0.3888
0.3888×100%=39%
a line through (4,2) with slope 1/2
Answer:
Step-by-step explanation:
Use the formula P=MX+B
❗️‼️❗️❗️‼️‼️‼️❗️‼️
What’s the area help please and please attach work
Answer:
106
Step-by-step explanation:
5 x 2 = 10
7 + 5 = 12
8 x 12 = 96
96 + 10 = 106 :)
A. State whether each figure is a polygon
Write the following equation in the general form Ax + By + C = 0.
y - x - 1 = 0
2x - 3y + 6 = 0
2x - 3y - 6 = 0
-2x + 3y - 6 = 0
Answer:
C. -2x +3y-6=0
this is the answer
simplify the following 4√28÷3√7
[tex]\displaystyle\bf 4\sqrt{28} :3\sqrt{7} =4\sqrt{4} \cdot \sqrt{7} :3\sqrt{7} =4\cdot2:3=\boxed{\frac{8}{3} }[/tex]
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Answer:
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
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.
If [tex]|Z| > 2[/tex], the value of X is considered to be unusual.
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.
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
Sample of 3
This means that [tex]n = 3, s = \frac{15}{\sqrt{3}}[/tex]
Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
We have to find the z-score.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}[/tex]
[tex]Z = 1.73[/tex]
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
Rewrite |3x+5|<or equals to 1 without absolute
value sign
Answer:
remember how the absolute value works:
|x| = x if x ≥ 0
|x| = -x if x < 0
Then we can rewrite:
|x| ≤ a
as:
-a ≤ x ≤ a
Now let's apply this to our case:
|3x + 5| ≤ 1
we can rewrite this as:
-1 ≤ 3x + 5 ≤ 1
We could solve this for x now, first subtracting 5 in the 3 sides:
-1 - 5 ≤ 3x + 5 - 5 ≤ 1 - 5
-6 ≤ 3x ≤ -4
now dividing by 3 in the 3 sides:
-6/3 ≤ 3x/3 ≤ -4/3
-2 ≤ x ≤ -(4/3)
So we rewrote the inequality without the absolute value part.
Carly withdraws $18 from her bank account. Which number line represents this amount?
Find the cost of eight apples at 50c each, three oranges at 35c each and 5 kg of bananas at
$2.69 per kilogram. show your working.
Answer:
1850 cents or $18.50
Step-by-step explanation:
50*8=400
3*35=105
5*269=1345 ($2.69 can be converted to 269 cents)
400+105+1345=1850
drink sales for an afternoon at the school carnival were recorded in the table. What is the experimental probability that the next drink is a small cocoa
Answer:
Not enough data
Step-by-step explanation:
Which values are NOT in the domain of the function?
f(x)
x +4
x2 – 25
O
A) x = -4,4
B) 2 = -5,4
C) x = -4,5
OD) X = -5,5
Given:
The function is:
[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]
To find:
The values that are NOT in the domain of the given function.
Solution:
We have,
[tex]f(x)=\dfrac{x+4}{x^2-25}[/tex]
This function is a rational function and it is defined for all real values of x except the values for which the denominator is equal to 0.
Equate the denominator and 0.
[tex]x^2-25=0[/tex]
[tex]x^2=25[/tex]
Taking square root on both sides, we get
[tex]x=\pm \sqrt{25}[/tex]
[tex]x=\pm 5[/tex]
So, the values [tex]x=-5,5[/tex] are not in the domain of the given function.
Therefore, the correct option is D.
calculus help needed!
Answer:
No
Not continous at x = 6
Step-by-step explanation:
When x = 6
G(6) = 1/(6 - 6) = 1/0
Dividing by 0 creates a discontinuity
What’s the value of the expression below
Answer:
8
Step-by-step explanation:
When multiplying numbers with the same base
the exponents are added
1/4 + 1/4 + 1/4 + 1/4 = 1
8¹ = 8
The vertices of ABC are A (5,5), B (-3,-1) and C (1,-3). Explain how would you verify that ABC is a right triangle.
Answer:
For that you should prove Ac²=Ab²+Bc²
Step-by-step explanation:
Use distance formula for finding each distance Ac,Ab and BC and prove "Ac²=Ab²+Bc²" as true
Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V r2h
-
Write the formula to calculate the height, h.
Step-by-step explanation:
V should be written as (1/3) pi r^2 h
V = (1/3) pi r^2 h multiply by 3
3V = pi r^2 h Divide by pi
3V/ pi = r^2 h Divide by r^2
3V / (pi *r^2 ) = h
Robert and Chris can skate 4 miles in 18 minutes. How far can they ride in 45 minutes?
Answer: Robert and Chris can skate 10 miles in 45 minutes.
Step-by-step explanation:
Let's start by finding the unit rate.
[tex]\frac{4}{18} =\frac{2}{9} \\\frac{18}{18} =1[/tex]
Robert and Chris can skate [tex]\frac{2}{9}[/tex] of a mile in 1 minute. Now we can multiply both by 45 to see how far the can go in 45 minutes.
[tex](\frac{2}{9}) (\frac{45}{1} )\\\frac{(2)(45)}{(9)(1)} \\\frac{90}{9} \\10[/tex]
45x1=45
The can skate 10 miles in 45 minutes.
Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.7 feet and a standard deviation of 0.4 feet. A sample of 74 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 2.5 feet. Round your answer to 4 decimal places, if necessary.
Answer:
0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.
Step-by-step explanation:
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.
Mean of 2.7 feet and a standard deviation of 0.4 feet.
This means that [tex]\mu = 2.7, \sigma = 0.4[/tex]
Find the probability that an individual man’s step length is less than 2.5 feet.
This is the p-value of Z when X = 2.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 2.7}{0.4}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085
0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.
ANSWER ALL QUESTIONS
1. In a class of 28 pupils, 13 have pencils, 9 have erasers and 9 have neither pencils nor erasers. How
many pupils have both pencils and erasers?
2. A universal set, U consists of prime numbers with P and Q as subsets of U. If P and Q are given by
P = {n: 3(n + 1) = 2(n + 10)}, and Q = {n: 7<n<31}, list the elements of P n Q.
1. 3
29-9=19
13+9=22
22-19=3
I don't know number 2, sorry.
if you help me with this i will mark you brainly-est but you gotta tell me how to because i don't know how ? \
Answer:
1/6
Step-by-step explanation:
Rhianna has 3/6 or 1/2 of a box of pencils
When she divides 3/6 among three people, you get 1/6
Each friend gets 1/6 of a box
Solve the system x-2y+2z=9 y+2z=5 z=3
Enter the answer as an ordered triple, (X,Y,Z)
The last equation says z = 3, so that in the second equation we get
y + 2z = y + 6 = 5 ==> y = -1
and in turn, the first equation tells us
x - 2y + 2z = x + 2 + 6 = x + 8 = 9 ==> x = 1
So the solution to the system is (x, y, z) = (1, -1, 3).
David has available 240 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?
Answer:
Below in bold.
Step-by-step explanation:
Perimeter = 2*width + 2*length
So
240 = 2w + 2l
120 = w + l
l = 120 - w
(a) Area = w*l
Substituting for l:
A = w(120 - w)
A = 120w - w^2
(b)
Finding the derivative:
A = 120w - w^2
A' = 120 - 2w
For a maximum area A' = 0, so:
120 - 2w = 0
2w = 120
w = 60 yards for maximum area.
(c)
Maximum area
= 120*60 - 60^2
= 3600 yd^2.
Write down the equation of the function whose graph is shown.
will mark brainliest
Answer:
y = 1(x - 5)² + 3
Step-by-step explanation:
The general formula of a quadratic equation is written as;
y = a(x − h)² + k
Where (h, k) are the x and y coordinates at the vertex.
Our vertex coordinate is (5, 3)
Thus;
y = a(x - 5)² + 3
Now,we are given another coordinate as (8, 12)
Thus;
12 = a(8 - 5)² + 3
12 = 9a + 3
9a = 12 - 3
9a = 9
a = 9/9
a = 1
Thus,the equation is;
y = 1(x - 5)² + 3
given 12 consecutive integers in how many ways can three of these integers be selected to give a sum which divides by 4?
There are [tex]55[/tex] ways of these integers be selected to give a sum.
Given that:
It has [tex]12[/tex] consecutive integers .
Now,
Definition of consecutive integers :
" Consecutive integers are the integers that follow in the fixed sequence .
Consecutive integers is represented by [tex]n,n+1,n+2,n+3,....[/tex] where [tex]n[/tex] is an integer."
By given :
we have [tex]12[/tex] consecutive integers .
Thus,[tex]n=1[/tex] and substitute the equation is,
[tex]1,(n+1),(1+2),(1+3),(1+4),(1+5),(1+6),(1+7),(1+8),(1+9),(1+10),(1+11)\\\\\implies 1,2,3,4,5,6,7,8,9,10,11,12[/tex]
Now,
Split all the integers into 4 equal parts,
Part 1: Those integers are divisible by [tex]4[/tex] and the remainder be 0.
Then,
[tex]a=0(mod 4)[/tex]
Part 2: Those integer producing the remainder [tex]1[/tex] when it is divisible by [tex]4[/tex].
Then,
[tex]a=1(mod 4)[/tex]
Part 3: Those integer producing the remainder [tex]2[/tex] when it is divisible by[tex]4[/tex].
Then,
[tex]a=2(mod 4)[/tex]
Part 4: Those integer producing the remainder [tex]3[/tex] when it is divisible by[tex]4[/tex].
Then,
[tex]a=3(mod4)[/tex]
Since, three of these integers be selected to give a sum which divides by [tex]4[/tex] is,
In any 12 consecutive integers there are [tex]12\div4[/tex]
i.e. exactly 3 numbers of each category of mod4 namely ,
[tex]0(mod4), 1(mod4), 2(mod4), 3(mod4)[/tex]
Thus, the total combinations of above [tex]5[/tex] categories of sets of [tex]3[/tex] integers are
All the 3 numbers are [tex]0(mod4)[/tex][tex]3C_1=3(1)=3[/tex]
One number be [tex]0(mod4)[/tex] and other two numbers are [tex]2(mod4)[/tex][tex]3C_1*3C_2=3(1)*3=9[/tex]
One number [tex]0(mod4)[/tex] and other numbers [tex]1(mod4)[/tex] & [tex]3(mod4)[/tex][tex]3C_1*3C_1*3C_1=3*3*3=27[/tex]
Two numbers be [tex]1(mod4)[/tex] and one number be [tex]2(mod4)[/tex][tex]3C2 * 3C1 = 3*3 = 9[/tex]
One number be [tex]2(mod4)[/tex] and two numbers be [tex]3(mod4)[/tex][tex]3C1 * 3C2 = 3*3 = 9[/tex]
Thus, sum of the total ways be [tex]12[/tex] consecutive integers of three integers is divisible by 4 is,
[tex]3+9+27+9+9=55[/tex]
Hence, it has [tex]55[/tex] ways.
For more information,
https://brainly.com/question/24144187
Tom worked the following hours last week but he needs to complete his timesheet in decimals
Answer:
Monday: 7.25
Tuesday: 6.75
Wednesday: 5.2
Thursday: 6.1
can anyone ps answer this? it's urgent!
Answer:
9:125
Step-by-step explanation:
To write a ratio correctly, you need the same units for both numbers.
Let's convert liters into milliliters.
1 L = 1000 mL
Ratio of 72 mL to 1000 mL =
= 72:1000
Divide both numbers by their GCF, 8.
= 9:125
How many different license plates are possible if digits and letter can be repeated if the configuration is 3 letters, 2 digits, 2 letters?
Answer:
1,188,137,600 possible combinations
Step-by-step explanation:
The first three and last two digits can be any letter while the middle two digits can be any number.
26*26*26*10*10*26*26=1,188,137,600
The student council has 30 male members and 25 female members. What is the ratio of male student council members to female?
Suppose the mean height for men is 70 inches with a standard deviation of 2
inches. What percentage of men are between 68 and 74 inches tall? Enter
the value of the percentage without the percent sign.
Answer:
81.85.
Step-by-step explanation:
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.
Suppose the mean height for men is 70 inches with a standard deviation of 2 inches.
This means that [tex]\mu = 70, \sigma = 2[/tex]
What percentage of men are between 68 and 74 inches tall?
The proportion is the p-value of Z when X = 74 subtracted by the p-value of Z when X = 68.
X = 74
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74 - 70}{2}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
X = 68
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68 - 70}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.9772 - 0.1587 = 0.8185
0.8185*100% = 81.85%.
Thus the percentage is 81.85%, and the answer is 81.85.