Answer:
[tex]\sqrt{8}+\sqrt{9}[/tex]
Step-by-step explanation:
By definition, the conjugate of a binomial is when you switch the operator (either + or -) in between the terms. For example, the conjugate of [tex]a+b\sqrt{c}=a-b\sqrt{c}[/tex] as we are just changing the addition symbol (+) to a subtraction symbol (-).
Therefore, the conjugate of [tex]\sqrt{8}-\sqrt{9}[/tex] occurs when we change the subtraction symbol to an additional symbol, hence the answer is [tex]\boxed{\sqrt{8}+\sqrt{9}}[/tex]
Determine the type of quadrilateral given the following coordinates. Show and explain all steps to prove your answer. A(2, 3) B(-1, 4) C(0, 2) D(-3, 3)
Answer:
The quadrilateral is a parallelogram
Step-by-step explanation:
If you plot the points on the graph it resembles the shape of a parallelogram. It prove this you need to check if the lengths are correct. The slope between point A and point B is 1/3 and the slope between point C and point D is also 1.3. The slope between point B and D is 1/2 and the slope between point A and point C is also 1/2
hope this helps
The quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
What is a parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal in length. The opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.
For the given situation,
The coordinates are A(2, 3) B(-1, 4) C(0, 2) D(-3, 3).
The graph below shows these points on the coordinates and the points ABDC forms the parallelogram.
This can be proved by finding the distance between these points.
The formula of distance between two points is
[tex]AB=\sqrt{(x2-x1)^{2}+ (y2-y1)^{2}}[/tex]
Distance AB is
⇒ [tex]AB=\sqrt{(-1-2)^{2}+ (4-3)^{2}}[/tex]
⇒ [tex]AB=\sqrt{(-3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]AB=\sqrt{9+ 1}[/tex]
⇒ [tex]AB=\sqrt{10}[/tex]
Distance BD is
⇒ [tex]BD=\sqrt{(-3+1)^{2}+ (3-4)^{2}}[/tex]
⇒ [tex]BD=\sqrt{(-2)^{2}+ (-1)^{2}}[/tex]
⇒ [tex]BD=\sqrt{4+ 1}[/tex]
⇒ [tex]BD=\sqrt{5}[/tex]
Distance DC is
⇒ [tex]DC=\sqrt{(0+3)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]DC=\sqrt{(3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]DC=\sqrt{9+ 1}[/tex]
⇒ [tex]DC=\sqrt{10}[/tex]
Distance CA is
⇒ [tex]CA=\sqrt{(2-0)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]CA=\sqrt{(2)^{2}+ (1)^{2}}[/tex]
⇒ [tex]CA=\sqrt{4+ 1}[/tex]
⇒ [tex]CA=\sqrt{5}[/tex]
Thus the lengths of the opposite sides are equal, the given points forms the parallelogram.
Hence we can conclude that the quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
Learn more about parallelogram here
https://brainly.com/question/16056863
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The test statistic of z=2.08 is obtained when testing the claim that p≠0.611. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of α=0.01, should we reject H0 or should we fail to reject H0?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
When the two-tailed were testing then:
Null and alternative hypothesis:
[tex]H_0 : p = 0.611\\\\H_a : p \neq 0.611[/tex]
Testing the statistics:
[tex]\to z = 2.08\\\\P-value = 0.0375\\\\\alpha = 0.01\\\\0.0375> 0.01\\\\P-value < \alpha\\\\[/tex]
therefore, it fails to reject the null hypothesis.
1. What kind of special angle pair do the 2
angles make? (corresponding,
supplementary, or vertical)
Answer:
supplementary angle is whose is mesure is 180
Determine how many days t will the two isotopes have the same activity
Answer:
t = 1 ... one day
Step-by-step explanation:
3 x [tex]10^{18}[/tex] * [tex](.5)^{t}[/tex] = 6 x [tex]10^{18}[/tex] * [tex](.5)^{2t}[/tex]
3 x [tex]10^{18}[/tex] = [tex](.5)^{2t}[/tex] / [tex](.5)^{t}[/tex]
6 x [tex]10^{18}[/tex]
1/2 = [tex].5^{t}[/tex]
ln( 1/2) = t ln( [tex].5[/tex] )
t = ln( .5)/ln( [tex].5[/tex] )
t = 1
Put an 'X' in 35% of the rectangles. A 'Y' in 25% of the rectangles and a 'Z' in 15%. Show in detail how you determine how rectangles to mark.
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Answer:
X X X X X X XY Y Y Y YZ Z ZStep-by-step explanation:
There are 20 rectangles, so 35% of them is ...
0.35 × 20 = 7 . . . . will be marked with X
25% of them is ...
0.25 × 20 = 5 . . . . will be marked with Y
15% of them is ...
0.15 × 20 = 3 . . . . will be marked with Z
_____
Additional comment
The total number of markings is 7+5+3 = 15, which is fewer than the number of rectangles. Consequently, it is not necessary to put more than one mark in any given rectangle, unless you just want to .
A set of triplets weighted 4lb 3oz , 3 lb 9oz and 4 lb 5 oz . What is the total weight of all three babies ?
Answer:
12 lb 1 oz
Step-by-step explanation:
Add the amounts together
4lb 3oz ,
3 lb 9oz
4 lb 5 oz
-------------------
11 lb 17 oz
But 16 oz is 1 lb so subtract 16 oz and add 1 lb
11 lb 17 oz
+1lb - 16 oz
--------------------
12 lb 1 oz
You have been provided with the following logic
expression:
(X+Y) (X+Y')= X
Prove the logic expression in the above scenario
using a Truth table. Show all steps.
If X and Y are Boolean variables, then X + Y represents disjunction (OR) and XY represents conjunction (AND), and X' denotes the negation (NOT). So X + Y = 1 if either X = 1 or Y = 1, and XY = 1 only if both X = 1 or Y = 1.
Now,
(X + Y) (X + Y') = XX + YX + XY' + YY'
… = X + X (Y + Y') + 0
… = X + X
… = X
or in table form,
[tex]\begin{array}{c|cccc}X&1&1&0&0\\Y&1&0&1&0\\Y'&0&1&0&1\\X+Y&1&1&1&0\\X+Y'&1&1&0&1\\(X+Y)(X+Y')&1&1&0&0\end{array}[/tex]
write your answer in simplest radical form
Answer:
y = 2
Step-by-step explanation:
y = √2 × √2 = 2
It's a 45-45-90 triangle
Question A volleyball team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $10, deluxe for $4, and regular for $2. The total number of tickets sold was 208, and the total amount of money from raffle tickets was $714. If 78 more regular tickets were sold than deluxe tickets, how many premium tickets were sold?
Answer:
24 premium tickets were sold.
Step-by-step explanation:
Let :
Deluxe ticket = x
Regular tickets = x + 78
Premium tickets = y
x + (x + 78) + y = 208
4x + 2(x+78) + 10y = 714
2x + y = 208 - 78
4x + 2x + 156 + 10y = 714
2x + y = 130 - - - - - (1)
6x + 10y = 558 - - - - (2)
Now we can solve the simultaneous equation using elimination method :
From (1)
y = 130 - 2x
Put y = 130 - 2x in (2)
6x + 10(130 - 2x) = 558
6x + 1300 - 20x = 558
- 14x = 558 - 1300
-14x = - 742
x = 742 / 14
x = 53
Put x = 53 in y = 130 - 2x
y = 130 - 2(53)
y = 130 - 106
y = 24
Please help. I don't understand how to solve for number 17, 19, and 21. Please show how you solved each problem
(17) From the plot, you see that
Pr[$15,500 ≤ x ≤ $18,500] = 99.7%
We can split up the probability on the left at the mean, so that
Pr[$15,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $18,500] = 99.7%
Any normal distribution is symmetric about its mean, so the two probabilities here are the same. The one on the left is what you want to compute. So you have
2 × Pr[$15,500 ≤ x ≤ $17,000] = 99.7%
==> Pr[$15,500 ≤ x ≤ $17,000] = 49.85%
(19) The mean of a normal distribution is also the median, so half the distribution lies to either side of the mean. Mathematically, we write
Pr[x ≥ $17,000] = 50%
The plot shows that
Pr[$16,500 ≤ x ≤ $17,500] = 68%
and by using the same reasoning as in (17), we have
Pr[$16,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $17,500] = 68%
2 × Pr[$17,000 ≤ x ≤ $17,500] = 68%
Pr[$17,000 ≤ x ≤ $17,500] = 34%
Now
Pr[x ≥ $17,000] = 50%
Pr[$17,000 ≤ x ≤ $17,500] + Pr[x ≥ $17,500] = 50%
34% + Pr[x ≥ $17,500] = 50%
==> Pr[x ≥ $17,500] = 16%
(21) From the plot,
Pr[$16,000 ≤ x ≤ $18,000] = 95%
This means (by definition of complement) that
Pr[x ≤ $16,000 or x ≥ $18,000] = 100% - 95% = 5%
and by symmetry,
Pr[x ≤ $16,000 or x ≥ $18,000] = 5%
Pr[x ≤ $16,000] + Pr[x ≥ $18,000] = 5%
2 × Pr[x ≤ $16,000] = 5%
==> Pr[x ≤ $16,000] = 2.5%
The slope of a line is −6. What is the slope of any line parallel to this line?
Answer:
-6
Step-by-step explanation:
Parallel lines have the same slope
If a line has a slope of -6, all lines parallel to this will have a slope of -6
please help!!!
find x
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Answer:
x = (17/2)√2
Step-by-step explanation:
The ratios of sides of an isosceles right triangle are ...
1 : 1 : √2
In this problem, that is identical to ...
x : x : 17
That is, ...
[tex]x=\dfrac{17}{\sqrt{2}}=\boxed{\dfrac{17}{2}\sqrt{2}}\qquad\text{after rationalizing the denominator}[/tex]
The sum of Ivy's and Audrey's ages is 27. Nine years ago, Ivy was
twice as old as Audrey. How old is each now?
Answer:
Ivy is 15 years old and Audrey is 12 years old.
Step-by-step explanation:
Let Ivy's age be [tex]i[/tex] and Audrey's age be [tex]a[/tex].
Since the sum of their ages is 27, we can write the equation [tex]i+a=27[/tex].
Next, we'll write a second equation from the fact that 9 years ago Ivy was twice as old as Audrey. Nine years ago, Ivy and Audrey's ages were [tex]i-9[/tex] and [tex]a-9[/tex], respectively. Therefore, we have [tex]i-9=2(a-9)[/tex]
Let's isolate [tex]i[/tex] by adding 9 to both sides:
[tex]i=2(a-9)+9[/tex]
Distribute:
[tex]i=2a-18+9,\\i=2a-9[/tex]
Now substitute [tex]i=2a-9[/tex] into our first equation:
[tex]2a-9+a=27,\\3a-9=27, \\3a=36, \\a=\boxed{12}[/tex]
Therefore, Ivy's age must be:
[tex]i+12=27,\\i=27-12=\boxed{15}[/tex]
Thus, Ivy must be 15 years old and Audrey must be 12 years old.
The
equation of the line in the graph is y= Blank x+ blank
Answer:
y = mx + b
Step-by-step explanation:
This is the basic equation for a line where m is the slope and b is the y intercept.
What function is represented by the graph? Of(x)=-2|x|+1 Of(x)=-1/2|x|+1 Of(x)=-2|x+1| Of(x)=-1/2|x+1|
Answer:
f(x)= -2[x+1]
this is the answer of the question
The duration of shoppers' time in Browse Wrld's new retail outlets is normally distributed with a mean of 27.8 minutes and a standard deviation of 11.4 minutes. How long must a visit be to put a shopper in the longest 10 percent
Answer:
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
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 27.8 minutes and a standard deviation of 11.4 minutes.
This means that [tex]\mu = 27.8, \sigma = 11.4[/tex]
How long must a visit be to put a shopper in the longest 10 percent?
The 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 27.8}{11.4}[/tex]
[tex]X - 27.8 = 1.28*11.4[/tex]
[tex]X = 42.39[/tex]
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
What is the slope of the line that goes through (-1, – 7) and (3, 9)?
Answer:
4
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 9 - -7)/( 3 - -1)
= (9+7)/(3+1)
=16/4
= 4
Identify the errors made in finding the inverse of
y = x2 + 12x
x= y2 + 12x
y2 = x -12
y2 = -11x
y= V-11x, for x 20
Describe the three errors
Answer:
x = y² + 12x
y² = x - 12
y² = -11x.
Step-by-step explanation:
We need to find the inverse of the given function , which is ,
[tex]\rm\implies y = x^2 + 12x [/tex]
Step 1 : Interchange x and y :-
[tex]\rm\implies x = y^2 + 12y [/tex]
But according to the steps given in the Question , in very first step in 12x , x is not replaced by y . After which , the steps go wrong in the question .
The 3 errors :-
x = y² + 12x y² = x - 12 y² = -11x.You want to buy a house that has a purchase price of $180,000 you plan to make a down payment of 10% of the purchase price and then while the rest what is the dollar value of the down payment?
Step-by-step explanation:
=10% of $180000
= 10*$180000/100
=$180
In the following scenario for a hypothesis test for a population? mean, decide whether the? z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known. Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably mildly skewed. The sample size is 70.
Choose the correct answer below.
a. The z-test is not an appropriate method, because the sample size is too small to be useful.
b. The z-test is an appropriate method, because the sample contains no outliers.
c. The z-test is an appropriate method, because the sample size is sufficiently large that the skewness of the variable does not matter.
d. The Z-test is not an appropriate method, because the sample is not a large sample and the data are highly skewed.
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Step-by-step explanation:
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Find any relative extrema of the function. List each extremum along with the x-value at which it occurs. Identify intervals over which the function is
increasing and over which it is decreasing. Then sketch a graph of the function.
f(x) = -x^3+ 9x?
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Answer:
relative minimum -6√3 at x = -√3relative maximum 6√3 at x = √3decreasing on x < -√3 and x > √3increasing on -√3 < x < √3see below for a graphStep-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
__
Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
Q is equidistant from the sides of TSR. Find the value of x.
T
(2x + 240°
30°
S
R
Lets do
[tex]\\ \sf\longmapsto 2x + 24 = 30 \\ \\ \sf\longmapsto 2x = 30 - 24 \\ \\ \sf\longmapsto 2x = 6 \\ \\ \sf\longmapsto x = \frac{6}{2} \\ \\ \sf\longmapsto x = 3[/tex]
Find the inverse relationship of the function y=2x+5
Answer:
y=x-5/2
Step-by-step explanation:
Swap y and x
x=2y+5
since a function has to be in the form y=mx+c
take 5 to the other side in order to remain with 2y then divide both sides by 2
x-5/2=y
y=x-5/2
Answer:
Duke is a very good team and
Solve for:
∫_(-1)^1 x^3+1/2 dx
Answer:
[tex]\int _{\left(-1\right)}^1\frac{x^3+1}{2}dx[/tex]
[tex]=\frac{1}{2}\cdot \int _{\left(-1\right)}^1x^3+1dx \Leftarrow(take \: constant\: out)[/tex]
[tex]=\frac{1}{2}\left(\int _{\left(-1\right)}^1x^3dx+\int _{\left(-1\right)}^11dx\right) \Longleftarrow (Sum\:Rule)[/tex]
[tex]\int _{\left(-1\right)}^1x^3dx=0[/tex]
[tex]\int _{\left(-1\right)}^11dx=2[/tex]
[tex]=\frac{1}{2}\left(0+2\right)[/tex]
[tex]=1[/tex]
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Answer:
yes
Step-by-step explanation:
grehrehshbrenjt5rahtrere
Refer to the picture above
Answer:
3.14
Step-by-step explanation:
First find the circumference of the circle:
[tex]2\pi r[/tex] = Circumference.
[tex]2 * \pi * 6[/tex] = [tex]12\pi[/tex]
Find the ratio of the angle in relation to the entire circle:
[tex]30^o[/tex] is what we have. So:
[tex]\frac{30^o}{360^o} = \frac{1}{12}[/tex]
Use the ratio and multiply the circumference to find the length:
[tex]12\pi * \frac{1}{12}[/tex] = [tex]\pi[/tex]
Round answer to the hundredth:
[tex]\pi = 3.14[/tex]
Devaughn is 10 years older than Sydney. The sum of their ages is 104. What is Sydney's age?
I
Answer:
Sydney's age = 42
Step-by-step explanation:
104 divided by 2 = 52
52 - 10 = 42
I am sorry if this is wrong. But this is what I learned at my school.
Camille is attending a fundraiser. She pays for her admission and buys raffle tickets for $5dollar each. If she buys 10 raffle tickets, then she would spend a total of $135 at the fundraiser.
The number S of dollars Camille spends at the fundraiser is a function of r, the number of raffle tickets she buys.
Write the function's formula.
Answer:
50r + a = 135
Admission cost was $85
Step-by-step explanation:
We are missing a crucial amount of information here. It is how much she spent on her admission. We can create an equation symbolizing this problem.
5r + a = 135
We know that she purchases 10 tickets so we can substitute that in r and solve for a.
50 + a = 135
a = 85
Best of Luck!
