Given:
The expression is
[tex](7-\sqrt{7})(-6+\sqrt{7})[/tex]
To find:
The product of the radical expression.
Solution:
We have,
[tex](7-\sqrt{7})(-6+\sqrt{7})[/tex]
Using distributive propertry, we get
[tex]=(7)(-6)+(7)(\sqrt{7})+(-\sqrt{7})(-6)+(-\sqrt{7})(\sqrt{7})[/tex]
[tex]=-42+7\sqrt{7}+6\sqrt{7}-7[/tex]
On combining like term, we get
[tex]=(-42+7)+(7\sqrt{7}+6\sqrt{7})[/tex]
[tex]=-49+13\sqrt{7}[/tex]
Therefore, the product of the given radical expression is [tex]-49+13\sqrt{7}[/tex].
How do I do this -16x =-160
Answer:
you have to put -160 over -16 then divide and your answer will be 10
so x=10. I hope this helps :)
Shannon, Oscar, and Ella contribute the same amount to their father’s gift. Their older sister Moriah contributes $12. How much does Oscar contribute if the total for the gift is $36? Write and solve an equation.
Answer:
Amount contributed by Oscar = $8
Step-by-step explanation:
Given that:
Amount spent on gift = $36
Amount contributed by Moriah = $12
Let,
x be the amount contributed by each of them.
Thus,
Gift total = Contribution of all
36 = x+x+x+12
36 = 3x+12
3x+12 = 36
3x=36-12
3x=24
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{24}{3}\\x=8[/tex]
Hence,
Amount contributed by Oscar = $8
34) Which equation is equivalent to: 3r=78+14 ?
A. −3r=−78+14
B. 3r−14=78
C. 3r=78−14
D. −3r=78−14
The dimensions of a cylindrical water tank are shown below.
18 yd
o
58,320 yd
3,240 yd
60 yd
O
19,440 yd
15,270 yd3
Which of the following is the best estimate of the volume of
this water tank?
Need help on this one, can someone please answer this?
Answer:
quadrant 3
Step-by-step explanation:
The general manager, marketing director, and 3 other employees of Company A are hosting a visit by the vice president and 2 other employees of Company B. The eight people line up in a random order to take a photo. Every way of lining up the people is equally likely.
(a) What is the probability that the general manager is next to the vice president?
(b) What is the probability that the marketing director is in the leftmost position?
(c) Determine whether the two events are independent. Prove your answer by showing that one of the conditions for independence is either true or false.
Solution :
Let the three places be 1, 2, 3, 4, 5, 6, 7, 8
a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2
= 14
[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]
Therefore the required probability is
[tex]$=\frac{14}{8!}$[/tex]
= [tex]$\frac{14}{40320} = 0.000347$[/tex]
b). The probability that the marketing director to be placed in the leftmost position is
[tex]$=\frac{7!}{8!}$[/tex]
[tex]$=\frac{1}{8} = 0.125$[/tex]
c). The two events are not independent because
[tex]$P(A \cap B) \neq P(A) \times P(B)$[/tex]
[tex]$\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$[/tex]
where A is the case a and B is the case b.
(a) The possibility of the general manager is next to the vice president is [tex]\frac{1}{4}[/tex].
(b) The possibility of the marketing director is in the leftmost position is [tex]\frac{1}{8}[/tex].
(c) So, the two events are dependent on each other.
Probability:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.
Total people in company A and company B is [tex]=8[/tex]
Overall ways in which these [tex]8[/tex] people can be lined up[tex]=8![/tex]
[tex]=40320[/tex]
(a) The probability that the general manager is next to the vice president is[tex]=P(A)[/tex]
Now, we can combine the general manager and vice president as one, then the total people in both the company will become [tex]7[/tex].
by arranging these [tex]7[/tex] people in one line [tex]=7![/tex]
[tex]=5040[/tex]
Again, combine the general manager and vice president in one line[tex]=2![/tex]
[tex]=2[/tex]
Therefore, [tex]P(A)=\frac{5040\times 2}{40320}[/tex]
[tex]=\frac{10080}{40320}[/tex]
[tex]P(A)=\frac{1}{4}[/tex]
(b) The probability that the marketing director is in the leftmost position is[tex]=P(B)[/tex]
Now, fixing the position of marketing director in the leftmost.
arranging the [tex]7[/tex] other people in [tex]7![/tex] ways [tex]=5040[/tex]
Therefore,[tex]P(B)=\frac{5040}{40320}[/tex]
[tex]=\frac{1}{8}[/tex]
[tex]P(B)=\frac{1}{8}[/tex]
(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.
Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest [tex]7[/tex] people, we have to fix the position of one person that causes the repetition of probability.
So, the two events are dependent on each other.
Learn more about the topic of Probability: https://brainly.com/question/26959834
Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3,100. Assume that the standard deviation is $1,400.
Required:
a. What is the z-score for a backyard structure costing $2300?
b. What is the z-score for a backyard structure costing $4900?
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.
Answer:
a) The z-score for a backyard structure costing $2300 is -0.57.
b) The z-score for a backyard structure costing $4900 is 1.29
c) A backyard structure costing $2300 costs 0.57 standard deviations below the mean, while a backyard structure costing $4900 costs 1.29 standard deviations above the mean. Since both are within 2 standard deviations of the mean, none is an outlier.
d) Since this combination costs more than 2 standard deviations from the mean, yes, it should be considered an outlier.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
If the z-score is more than two standard deviations from the mean(lesser than -2 or more than 2), the score X is considered an outlier.
In this question, we have that:
[tex]\mu = 3100, \sigma = 1400[/tex]
a. What is the z-score for a backyard structure costing $2300?
We have to find Z when [tex]X = 2300[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2300 - 3100}{1400}[/tex]
[tex]Z = -0.57[/tex]
The z-score for a backyard structure costing $2300 is -0.57.
b. What is the z-score for a backyard structure costing $4900?
We have to find Z when [tex]X = 2300[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4900 - 3100}{1400}[/tex]
[tex]Z = 1.29[/tex]
The z-score for a backyard structure costing $4900 is 1.29
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
A backyard structure costing $2300 costs 0.57 standard deviations below the mean, while a backyard structure costing $4900 costs 1.29 standard deviations above the mean. Since both are within 2 standard deviations of the mean, none is an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier?
We have to find the z-score when X = 13000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13000 - 3100}{1400}[/tex]
[tex]Z = 7.07[/tex]
Since this combination costs more than 2 standard deviations from the mean, yes, it should be considered an outlier.
please help me guys lol?
Answer:
Hey
Step-by-step explanation:
Write the fraction in simplest form
[tex] - \frac{29}{18} [/tex]
EXPLANATION[tex] \frac{8}{9} - \frac{5}{2} [/tex]
Find the difference between 8/9 and 5/-2
[tex] \frac{8}{9} - \frac{5}{2} [/tex]
[tex] \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} [/tex]
[tex] \frac{16}{18} - \frac{45}{18} [/tex]
[tex] \frac{16 - 45}{18} [/tex]
[tex] \frac{ - 29}{18} [/tex]
[tex] - \frac{29}{18} [/tex]
I will mark you Brainly-est pls! I need this done by tomorrow :) it’s 55 points btw
Answer:
Step-by-step explanation:
9. 1.6f + 0.4j - 13
11. -6y + 13
13. -1/2j + 15
Someone help me quick
Answer: x > - 18
Step-by-step explanation:
solve the question below, please
Answer:
carios has greater angle
Step-by-step explanation:
hope this helps
Consider this quadratic expression.
x² – 10x + c + 11 – c
What value of c is needed to complete the square for this expression?
A. 10
B. 20
C. 25
D. 100
Answer:
c = 25Step-by-step explanation:
Given this quadratic expression.
x² – 10x + c = 0
We are to find the value c that will make the expression a perfect square'
Using the completing the square method
Add the square of the half of coefficient of x
Coefficient of x = -10
Half of -10 = 1/2(-10) = -5
Square of -5 = (-5)^2 = 25
Hence the value of c to complete the expression is 25
Simplify the following expression (2x^2y^5)^3
Answer:
The correct answer is,
[tex] {8x}^{6y {}^{5} } [/tex]
Only answer if you're sure its correct!
Answer:
im sure its D.)
Step-by-step explanation:
Is 3/2 less than greater than equal than 1
Answer:
greater than
Step-by-step explanation:
2/2 = 1
3/2 = 1 1/2
The sum of four times a number and fifteen is forty-seven. Find the number.
Answer:
8 is the number
Step-by-step explanation:
I don't know why it took me so long to figure it out, 4 x 8 = 32 32 + 15 = 47
It probably took me a really long time because I am tired, and I am not using a calculator.
1. Line L passes through point (-1, 2) and (-3,-2) on a coordinate plane. Line
M passes through the points (1.1) and (-1, W). For what value of W will make
line L and line M parallel.
Answer:
Slope of a line passing through ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2} , y_{2}[/tex]) is given by:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Now,
Slope of line L, (m) = [tex]\frac{-3-(-1)}{-2-2}[/tex] = 0.5
Slope of line M, (n) = [tex]\frac{-1-1}{W-1}[/tex] = [tex]\frac{-2}{W-1}[/tex]
If the lines L and M are parallel to each other,
m = n
or, 0.5 = [tex]\frac{-2}{W-1}[/tex]
or, 0.5 (W - 1) = -2
or, W - 1 = -4
or, W = -3
Therefore the required value of W is -3.
If three pounds of bananas cost $4.50 find the cost of 10 pounds of bananas
Answer:
45
Step-by-step explanation:
4.50 × 10 =45!
.
.
.
.
.
.?
.
.
.
.
.
Answer:
$15
Step-by-step explanation:
$4.50 time 3 = $13.50 (9 lbs)
$4.50 divided by 3 = $1.50 (1 lb)
$1.50 plus $13.50 = $15
PLEASE ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I PROMISE ILL MARK BRAINLEIST PLEASE I AM BEGGING YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Stephanie swims 4/5 of a mile in 5/6 of an hour.
Enter the number of miles Stephanie swims in 1 hour.
Hi.. U should do like this
4/5 mile in 50 min
X mile in 60 min
X=5/4 mile
Answer:
5 milesss
:)))
subtract -3n^2 from -7n^2
Answer: 4n^2
Step-by-step explanation: -3n^2 - (-7n^2) = -3n^2 + 7n^2= 4n^2. When adding and subtracting the exponents stay the same only the coefficients are subtracted or added
write an equivalent expression for the following using distributive property A(9b+13)
apply distributive property AKA (A • 9b)+(A • 13)
9Ab + 13A
I hope this helps :)
Mr. Toshiro manages a company that supplies a variety of domestic and imported nuts to supermarkets. He received as order for 120 bags of cashews , 310 bags of walnuts, and 60 bags of Brazil nuts. The price per bag for each type are $29, $18, and $21, respectively. Represent the number of bags ordered and the cost as vectors.
Answer: Total cost would be 10,320
Step-by-step explanation: Hope this helps
Hal is going over the credit scores he received from the three major credit bureaus. He Experian score is 711, his
Equifax score is 736, and his TransUnion score is 736. What is the mode of Hal's credit scores? (Round to the nearest
whole point, if applicable.)
736
b 728
723
d There is no mode in this group
a
С.
Please select the best answer from the choices provided
A
B
ОООО
C
D
Mark this and retum
Save and Exit
Next
Submit
Answer:
A
Step-by-step explanation:
It is letter A I got 100!
Answer:
A
Step-by-step explanation:
EDGE 2021
Given that P(B|A)=0.75 and P(A)=0.47, what is P(B AND A)? Round to three decimal places.
Answer:
0.627
Step-by-step explanation:
ILL GIVE U BRAINLIST!!
Connor is working two summer jobs, making $8 per hour walking dogs and making $12 per hour landscaping. In a given week, he can work a maximum of 15 total hours and must earn no less than $160. If Connor worked 12 hours walking dogs, determine the maximum number of whole hours landscaping that he can work and still meet his requirements. If there are no possible solutions, submit an empty answer.
Answer:
[tex]\mathrm{No\: solutions}[/tex]
Step-by-step explanation:
Since Connor has worked 12 hours walking dogs, he's earned [tex]12\cdot 8 = \$96[/tex] from walking dogs. He still needs to earn [tex]\$160-\$96=\$64[/tex]. As stated in the problem, he makes $12 an hour landscaping, therefore the minimum number of whole hours he must work to fulfill his requirements is [tex]\lceil{ \frac{64}{12} \rceil = 6\: \mathrm{hours}[/tex]. However, the problem states he can only work a maximum of 15 hours. He would have to work [tex]12+6=18[/tex] to fulfill his requirements and therefore he will not be able to meet his requirements with the restrictions given.
Pls help extra points and mark brainlist easy reading
Answer: It's the third one down
Step-by-step explanation:
Item 7
The ratio of the weight of an object on Jupiter to its weight on Earth is 8:5, meaning that an object that weighs 8 pounds on Jupiter weighs only 5 pounds on Earth. In the first box provided, write an equation that represents the relationship between the weight on Jupiter j and the weight on Earth e and on the second line, write its reciprocal.
Answer:8,5 recirpoal is 5,8
Step-by-step explanation:
Write an equation in the first box (use x as your variable). Then, solve (in second box).
Answer: 3.2x = 48
Step-by-step explanation: So that means x = 15.
Solve.
How much pure acid is in 860 milliliters of a 18% solution?
The answer is ____ ml.
Answer:
The answer is 154.8 ml
Step-by-step explanation:
In this question, the amount of pure acid is 18% of the total solution, that is, 18% of 860 milliliters. So
0.18*860 = 154.8 ml
The answer is 154.8 ml
HELPPPPP!!!
Will give brainliest
For which pair of points can you use this number line to find the distance?
4
2 3
5 6
-2 -1 0 1
7 8
(-4, 1) and (7,4)
(-4, 1) and (-4,7)
(-1, 4) and (4,7)
O (-4, -1) and (-4,-7)
Answer:
[tex](-4, 1) \: and \: (-4,7)[/tex]
Step-by-step explanation:
[tex]the \: shortest \: distance \: between \: two \: points \: can \: be \: used \: here \to \\ were : d = \sqrt{ (x_{2} -x_{1} ) {}^{2} + (y_{2} -y_{1} ) {}^{2} } \\checking \: for \: the \: pair \to \: (-4, 1) \: and \: (-4,7) \\ d = \sqrt{ (( - 4)-( - 4)) {}^{2} + (7 -1 ) {}^{2} } \\ d = \sqrt{ (- 4 + 4) {}^{2} + (6) {}^{2} } \\ d = \sqrt{ (0) {}^{2} + (6) {}^{2} } \\ d = \sqrt{ (6) {}^{2} } \\ \underline{ \boxed{d = 6}}[/tex]