which of the following product? assume y>0 3 square root(y^2 square root 4+ square root 8y)
Answers
Answer:
[tex]6y^2\sqrt{10}+12\sqrt{5y}[/tex]
Step-by-step explanation:
Use the distributive property and the rules for forming and simplifying square roots.
(√a)(√b) = √(ab)
√(a²b) = a√b
__
[tex]3\sqrt{10}\cdot(y^2\sqrt{4}+\sqrt{8y})=(3\sqrt{10})(2y^2) +(3\sqrt{10})(\sqrt{8y})\\\\=6y^2\sqrt{10}+3\sqrt{80y}\\\\=6y^2\sqrt{10}+3\sqrt{(4^2)(5y)}\\\\=\boxed{6y^2\sqrt{10}+12\sqrt{5y}}\qquad\text{matches the first choice}[/tex]
Answer:
a
Step-by-step explanation:
Related Questions
What is the equation of the graphed line in standard form? y = 2x + 6 12x+y=6 12x−y=−6 −2x+y=6
Answers
Answer:
THe standard form of equation for a line is -2x+y=6
Step-by-step explanation:
THe standard equation has a form of Ax+ By=C, where A, B and C are constants.
12x-y=-6 is not a standard form of a line equation, because the value near you is negative, but should be positive. It would be this form if we would change it a little bit to the form:
-12x=y=6
The average age of 15 students is 16 years. If teacher’s age is included the average increases
by 1. Find teacher’s age
Answers
31
because 15 +16 :31
[tex]. = y1 = \times [/tex]
What the correct answer fast
Answers
Answer:
[tex] s = 5.8 [/tex]
Step-by-step Explanation:
Given:
∆RST,
m < T = 17°
t = RS = 5
m < S = 20°
s = RT = ?
Apply the Law of Sines to find s
[tex] \frac{s}{sin(S)} = \frac{t}{sin(T)} [/tex]
[tex] \frac{s}{sin(20)} = \frac{5}{sin(17)} [/tex]
Multiply both sides by sin(20) to make s the subject of formula.
[tex] \frac{s}{sin(20)}*sin(20) = \frac{5}{sin(17)}*sin(20) [/tex]
[tex] s = \frac{5*sin(20)}{sin(17)} [/tex]
[tex] s = 5.8 [/tex] (to nearest tenth)
Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio.
Answers
This question is incomplete
Complete Question
Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio. A quadrilateral is broken into a triangle and rectangle. The triangle has a base of 20 feet and a height of 6 feet. The rectangle has a base of 20 feet and a height of 12 feet. How many total stone tiles will Mr. Connor need for the patio?
Answer:
300 tiles
Step-by-step explanation:
From the above question, we know that the patio is a combination of a triangle and a rectangle.
Step 1
Find the area of the shape
a) Area of the Triangle = 1/2 × Base × Height
Base = 20 feet
Height = 6 feet
Area = 1/2 × 20 × 6
Area = 60 square feet
b) Area of the rectangle
= Length × Breadth.
The rectangle has a
Base = Breadth = 20 feet
Height = Length = 12 feet
Area = 20 × 12 = 240 square feet.
Total Area of the patio
= Area of Triangle + Area of square
= 60 square feet + 240 square feet
= 300 square feet
Step 2
We are told that each stone tile = 1 square foot.
Hence, if the total area of the patio = 300 square feet, the number of stone tiles that would be used is
1 square foot = 1 stone tile
300 square feet = 300 stone tiles.
Therefore,the total stone tiles that Mr. Connor will need for the patio is 300 stone tiles.
Answer:
The answer is 300
Step-by-step explanation:
A large company is hosting a conference. So far, a total of 3,922 people have signed up, including 26 from united states. How many people from other countries have signed up?
Answers
Answer:
3,896 have signed up from other countries
Step-by-step explanation:
In this problem we are required to calculate the number of signups from other countries.
well, since we know the total sign ups to be 3,922
And also we know that 26 out of the total signed up from the USA
This means that the sign ups from other countries will be
3,922-26=3,896
The linear function f (x) and g(x) are represented on the graph where g(x) is a tranfomation of f(x) I need help with part A part B and Part C
Answers
Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) to the left or we can shift f(x) up to make it become g(x)
Part B
y = f(x + k) k > 0 moves it left
Using the point ( 2,8) for f(x) and ( 0,8) for g(x)
k is 2 units
g(x) = f(x+2)
y = f(x) + k k > 0 moves it up
Using the point ( 0,-2) for f(x) and ( 0,8) for g(x)
The difference between -2 and 8 is 10
k = 10
g(x) = f(x) + 10
Part C
for the shift to the left g(x) = f(x+2)
for the shift up g(x) = f(x) + 10
4(x − 7) = 0.3(x + 2) + 2.11
Answers
Step-by-step explanation:
[tex]4(x-7)=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3x+0.6+2.11\\\\Combine\\like\\terms\\\\4x+28=0.3x+2.71\\\\Subtract\\\\3.7x+28=2.71\\\\Subtract\\\\3.7x=-25.29\\\\Divide\\\\x=\tex{ about }6.83513514[/tex]
Hope it helps <3
Answer:
x = 83/10=8^3/10=8.3
Step-by-step explanation:
4(x − 7) = 0.3(x + 2) + 2.11
Use the distributive property to multiply 4 by x−7.
4x−28=0.3(x+2)+2.11
Use the distributive property to multiply 0.3 by x+2.
4x−28=0.3x+0.6+2.11
Add 0.6 and 2.11 to get 2.71.
4x−28=0.3x+2.71
Subtract 0.3x from both sides.
4x−28−0.3x=2.71
Combine 4x and −0.3x to get 3.7x.
3.7x−28=2.71
Add 28 to both sides.
3.7x=2.71+28
Add 2.71 and 28 to get 30.71.
3.7x=30.71
Divide both sides by 3.7.
x= 3071/370
Expand 3.7/30.71≈8.3 by multiplying both numerator and the denominator by 100.
x = 83/10
Two planes make a 1750 mile flight, one flying 75 miles per hour faster than the other. The quicker plane makes the trip 3 hours faster. How long did it take the slower plane to complete the flight?
Answers
Answer:
The slower plane is flying at 175 miles per hour and complete the trip in 10 hours
The faster plane is flying at 250 Miles per hour and complete the trip in 7 hours
Step-by-step explanation:
Let s= speed of the slower plane s+75= speed of the faster plane
The time it takes the slower plane to make the flight = 1750/s
The time it takes the faster plane to make the flight is=1750/(s+75)
The difference in these two times is 3 hours
1750/s - 1750/(s+7)=3
{(s+75) / (s+75) * (1750/s)} - {(s/s) * (1750/s+75)} =3
(1750s+131250 / s^2+75s) - (1750s/s^2+75s) =3
1750s+131,250-1750s / s^2+75d =3
131,250 / s^2+75s = 3
Cross product
131,250=3(s^2+75s)
131,250=3s^2+225s
43,750=s^2+75s
s^2+75s-43,750=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a=1
b=75
c= -43750
x= -b +or- √b^2-4ac / 2a
= -75 +or- √(75)^2 - (4)(1)(-43750) / (2)(1)
= -75 +or- √(5625) - (-175,000) / 2
= -75 +or- √180625) / 2
= -75 +or- 425 / 2
x= -75 + 425/2 OR -75- 425/2
=350/2 OR -500/2
x=175 OR -250
We will ignore the negative sign because the planes are not flying Backward
The slower plane is flying at 175 miles per hour and complete the trip in 1750/175= 10 hours
The faster plane is flying at 250 Miles per hour and complete the trip in 1750/250= 7 hours
Jennifer wants to see if the color of the testing room causes test anxiety. She asks 100 participants to come to a modified classroom, and as they walk in, she asks each person to choose either a testing cubicle painted bright red or a testing cubicle painted off white. On the basis of their choices, participants spend 20 minutes in one or the other cubicle solving challenging math problems. Then, they complete a survey asking them questions about how anxious they were during the math test. What's wrong with Jennifer's experiment?
Answers
Answer: Jennifer didn't randomly assign participants to the control and experimental group.
Step-by-step explanation: In the scenario discussed above, Jennifer failed to perform a random assignment of the participants who took part in the survey, that is the experimental group, those who receive the treatment and the control group, those who don't. Random assignment is required in other to address the issue of bias in our experiment. She was supposed to perform a random assignment of the participants to the two groups instead of asking them to make a choice.
Sales of a popular toy were about 20 million in 2000 and growing about 5% each year. At this growth rate, the function f(x) = 20(1.05)^x gives the annual number of toys sold in million in the xth year after 2000. Using this model, in about what year will the annual sales surpass 37 million?
Answers
===========================
Work Shown:
Plug in f(x) = 37. Solve for x. Use logarithms.
f(x) = 20(1.05)^x
37 = 20(1.05)^x
20(1.05)^x = 37
1.05^x = 37/20
1.05^x = 1.85
log( 1.05^x ) = log( 1.85 )
x*log( 1.05 ) = log( 1.85 )
x = log( 1.85 )/log( 1.05 )
x = 12.6088044498867
Round up to the nearest whole number to get x = 13.
In the year 2013, sales exceed 37 million.
A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.
Answers
Answer:
The height of the cylinder is 4 x units.
The area of the cylinder’s base is One-fourthπx2 square units
Step-by-step explanation:
Formula for volume of the cylinder:
V = r² π h
Volume of the cylinder=
πx^3
Diameter=x
Radius (r)=diameter/2
=x/2
V = r² π h
πx^3=(x/2)^2πh
πx^3=(x^2/4)πh
Divide both sides by π
x^3=(x^2/4)h
Make h the subject of the formula
h=x^3÷x^2/4
=x^3×4 / x^2
=4x^3 / x^2
=4*x*x*x / x*x
h=4x
Area of the base:
B = r² π
Recall, r=x/2
B=(x/2)^2 * π
=(x^2/4)π
=πx^2/4
=1/4(πx^2)
The area of the cylinder’s base is One-fourthπx2 square units.
Answer:
B & E
Step-by-step explanation:
Edge 2020
The amount that two groups of students spent on snacks in one day is shown in the dot plots below. Which statements about the measures of center are true? Select three choices. The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B. The mode for Group A is less than the mode for Group B. The median for Group A is 2. The median for Group B is 3.
Answers
Answer:
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Step-by-step explanation:
First, we can find the measures of center for each group.
Group A
Mode: 1
Median: (1 + 2) / 2 = 3 / 2 = 1.5
Mean: (1 * 5 + 2 * 4 + 3) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6
Group B
Mode: 3
Median: 92 + 3) / 2 = 5 / 2 = 2.5
Mean: (1 * 3 + 2 * 2 + 3 * 4 + 5) / 10 = (3 + 4 + 12 + 5) / 10 = 24 / 10 = 2.4
From here, we can see that...
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Hope this helps!
Answer:
ABC
Step-by-step explanation:
Please answer this in two minutes
Answers
Answer: 9.9
Step-by-step explanation:
SINE RULE:
7/sin(31) = q / sin(47)
Therefore q = 7 / sin(31) * sin(47)
which equals: 9.9 to the nearest tenth.
Answer:
q = 9.9
Step-by-step explanation:
We can use the rule of sines
sin R sin Q
------------- = ------------
PQ PR
sin 31 sin 47
------------- = ------------
7 q
Using cross products
q sin 31 = 7 sin 47
Divide by sin 31
q = 7 sin 47 / sin 31
q =9.939995043
To the nearest tenth
q = 9.9
Solve for x. (x+2)/3+(2x-4)/4=3
Answers
Answer:
x=4
Step-by-step explanation:
First you need to factor the equation. You can do this by multiplying the numbers by eachother so they have a denominatior of 12.
You would come out to have this...
((x+2)*4)/12 + ((2x-4)*3)/4=3
At this point you can combine the numerators over the common denominator.
((x+2)*4+(2x-4)*3)/12=3
You can now rewrite the equation into factored form.
5x-2/6=3
Multiply both sides of the equation by 6.
5x-2=18
move the terms not containing x to the right
5x=20
and divide by 5
x=4
Select all the correct answers. Which statements are correct interpretations of the logarithmic function f(x) = 7 log2 x, with respect to the context? The password is weakest if it uses a single symbol for all 7 characters. The strength of the password increases with a decrease in the number of symbols. The password is stronger with an increase in the number of symbols. The password is strongest if a single symbol is used for all 7 characters. There are 2 possible symbol options per character to produce a password of strength of 7 bits. There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Answers
Answer:
The password is weakest if it uses a single symbol for all 7 characters.
The strength of password increases with an increase in the number of symbols.
There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Step-by-step explanation:
The password strength is determined by the usage of symbols and upper case and lower case letters along with a numeric character. The strength of password increases when different symbols are used. It is considered as weak password if only single symbol is used for all the 7 characters. The strong passwords are not easy to break and decode.
Answer:
The three correct options are:
The password is weakest if it uses a single symbol for all 7 characters.
The password is stronger with an increase in the number of symbols.
There are 2 possible symbol options per character to produce a password of strength of 7 bits.
If b = 1/2x −1/y, then what is an expression for 2/b in terms of x and y?
Answers
Answer:
2/xy
Step-by-step explanation:
you have to do the math but im not very sure on this
I need the answer in degrees
Answers
Answer:
x = 69°Step-by-step explanation:
Angles at a point add up to 360°
To find x add up all the angles and equate them to 360°
That's
168 + 123 + x = 360
291 + x = 360
x = 360 - 291
x = 69°
Hope this helps you
Answer:
x = 69
Step-by-step explanation:
The sum of a circle is 360 degrees
x+ 168+123 = 360
Combine like terms
x +291 = 360
Subtract 291 from each side
x+291-291 = 360-291
x =69
Agrid shows the positions of a subway stop and your house. The
subway stop is located at (-7,8) and your house is located at (6,4).
What is the distance, to the nearest unit, between your house and
the subway stop?
Answers
Answer: about 13u
Step-by-step explanation:
Distance can be calculated as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(6-(-7))^2+(4-8)^2}\\\\\\\sqrt{(13)^2+(-4)^2}\\\\\\\sqrt{185}\\\\13[/tex]
Hope it helps <3
Solve by the quadratic formula: 3x^2 - 4x + 1 = 0
Answers
Answer:
x = 1/3 and x = 1.
Step-by-step explanation:
3x^2 - 4x + 1 = 0
(3x - 1)(x - 1) = 0
The solutions are when either 3x - 1 = 0 or x - 1 = 0.
3x - 1 = 0
3x = 1
x = 1/3
x - 1 = 0
x = 1
So, x = 1/3 and x = 1.
Hope this helps!
The product of ages of a man 5 years ago and
5 years hence is 600, find his present age.
Answers
Answer:
25
Step-by-step explanation:
let his age be x, then
5 years ago his age was x - 5 and in 5 years will be x + 5 , thus
(x - 5)(x + 5) = 600 ← expand factors using FOIL
x² - 25 = 600 ( add 25 to both sides )
x² = 625 ( take the square root of both sides )
x = [tex]\sqrt{625}[/tex] = 25
Answer:
[tex]\boxed{Age \ of \ man = 25 \ years}[/tex]
Step-by-step explanation:
Let the age be x
Then, the given condition is:
(x-5)(x+5) = 600 [ x-5 for age 5 years ago and x+5 for age 5 years after ]
Using Formula [tex](a+b)(a-b) = a^2-b^2[/tex]
[tex]x^2-25 = 600[/tex]
Adding 25 to both sides
[tex]x^2 = 600+25[/tex]
[tex]x^2 = 625[/tex]
Taking sqrt on both sides
[tex]x = 25[/tex] years
At Camp Sunshine, 4 kids went home sick. Of the remaining campers, 18 kids went hiking and the other 41 kids spent the day swimming. How many kids started the day at Camp Sunshine?
Answers
Answer:
63 kids
Step-by-step explanation:
We can add up the number of students who went home sick, hiked, and swam to find the total amount of people.
[tex]4+18+41 = 63[/tex]
Therefore, 63 kids started their day at Camp Sunshine.
I get that feeling I oversimplified this one, let me know if I did. I'm not sure if this is right.
Answer:
63 kids
Step-by-step explanation:
We know that there are some kids who went home sick, some went hiking and some went swimming.
The total number of kids that started the day at Camp Sunshine can be found by adding the number who went home sick, went hiking and went swimming.
sick + hiking + swimming
4 went home sick, 18 went hiking and 41 went swimming.
4+ 18 + 41
Add the numbers together
22+ 41
63
63 kids started the day at Camp Sunshine.
Jackson is running a 10-mile race. He runs 1 mile every 8 minutes. Jackson's distance from this finish line after x minutes is represented by the function x+8y=80
Answers
Answer:
Jackson's distance from the finish line after x minutes will be given as;
since from the statements we know that x represents the number of minutes he had run, for us to be able to calculate his distance from the finish line we simply solve the problem mathematically as follows;
x=80-8y
Step-by-step explanation:
from the initial representation we have x+8y=80,
from the preliminary statement we know x to be the number of minutes from the start of the race to the current point Jackson.
so we assume that y in the equation represents the number of distance covered by the x minutes in miles.
that is how we end up with ;
x=80-8y.
A college student team won 20% of the games it played this year. If the team won 11 games, how many games did it play?
Answers
Answer:
55 games
Step-by-step explanation:
What we have to figure out is the total amount of games they played the whole year. We know they won 20% of their games, which equates to 11 games won in total. In order to find the total amount of games we will need to set up the equation [tex]g = 11/20[/tex]%. We solve this accordingly: [tex]g = (11/20) *100[/tex]; [tex]g = (.55)*100[/tex]; [tex]g = 55[/tex].
John needs to find out the probability that he will sell all his cars by the end of the
year. He takes a sample of the customers that come in to see if they will buy a car.
How many customers should he sample to get an accurate probability?
a) 3 customers
b) 10 customers
c) 100 customers
d) 1000 customers
Answers
Answer:
c) 100
Step-by-step explanation:
This is the best choice because the number is not too low or too high. He will get an accurate probability.
Find the perimeter of parallelogram AFCB.
A. 14
B. 12
C. 28
D. 24
Answers
Answer:
C.28
Step-by-step explanation:
It gives you 2 sides.
One of them is 8.
The other one is 12 but the 12 is divided by 2 which is 6.
Since it is a parallelogram there is the same measurements on the opposite sides.
So finally you get 6+6+8+8= 28
The perimeter of parallelogram AFCB is C. 28
How do you calculate a perimeter?
With the purpose to discover the perimeter or distance around the rectangle, we want to add up all four side lengths. this can be performed efficiently by using truly including the duration and the width, after which multiplying this sum by means of when you consider that there are of every facet length.
What is perimeter for instance?The Perimeter is the gap around the item. for instance, your own home has a fenced backyard. the perimeter is the length of the fence. If the yard is 50 toes × 50 feet your fence is 2 hundred feet long.
Learn more about Perimeter here https://brainly.com/question/397857
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There are 30 names in a hat. If two names are picked without repalcement, which expression shows the probability that Jack and Jill will be picked?
Answers
Step-by-step explanation:
The probability that either Jack or Jill will be selected on the first draw is 2/30.
The probability that the other person will be selected on the second draw is 1/29.
The probability of both events is (2/30) (1/29), which simplifies to 1/435.
The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table. A 2-column table has 4 rows. The first column is labeled Eye Color with entries brown, green, blue, hazel. The second column is labeled Number of People with entries 20, 6, 17, 7. What is the probability that a person chosen at random from this group has brown or green eyes? StartFraction 3 Over 25 EndFraction StartFraction 7 Over 25 EndFraction StartFraction 13 Over 25 EndFraction StartFraction 17 Over 25 EndFraction
Answers
Answer:
13/25
Step-by-step explanation:
The total number of people is 20 + 6 + 17 + 7 = 50.
Of these, the number that have brown or green eyes is 20 + 6 = 26.
So the probability is 26/50, which reduces to 13/25.
The probability that a person chosen at random from this group has brown or green eyes is; 13/25
How to find the probability?From the given data values, we can deduce that;
Total number of people = 20 + 6 + 17 + 7 = 50.
Now, the total number of people that have brown or green eyes is;
Total(brown or green eyes) = 20 + 6 = 26.
Thus, the probability that a person chosen at random from this group has brown or green eyes is;
P(brown or green eyes) = 26/50 = 13/25.
Read more about Probability at; https://brainly.com/question/251701
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What is the equation of a circle with center (0, 5) and radius 8
Answers
Answer:
See below.
Step-by-step explanation:
Recall that the equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We know the center is (0,5) and the radius is 8. Plug in the numbers:
[tex](x-(0))^2+(y-(5))^2=(8)^2[/tex]
We can remove the parentheses on the left. Therefore, the equation will be:
[tex]x^2+(y-5)^2=64[/tex]
Answer:
( x) ^2 + ( y-5) ^2 = 64
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-0) ^2 + ( y-5) ^2 = 8^2
( x) ^2 + ( y-5) ^2 = 64
2 concentric circles have radii 2cm and 3cm respectively, calculate the ratio of their areas
Answers
Answer:For the first circle the radius is 2cm and for the second circle the radius is 3cm,by taking the ratio of their areas:
πr^2:πR^2
π cancels out and we are left with only r^2:R^2
r=2cm and R=3cm
Therefore r^2:R^2=2^2:3^2
=4:9
The answer is 4:9
Step-by-step explanation:
Solve the proportion for X.
5/2.5=
X/2
1
4
5.5
6.25
Answers
Answer:
[tex]\large \boxed{X = 4}[/tex]
Step-by-step explanation:
5/2.5 = X/2
To solve a proportion, use the following equation:
(numerator * opposite denominator) = (numerator * opposite denominator)
Substitute in given numbers
(5 * 2) = (X * 2.5)
Multiply to simplify
10 = 2.5X
Divide both sides of this equation by 2.5
[tex]\large \boxed{X = 4}[/tex]
Hope this helps :)