Answer:
[tex]\frac{-8 +2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
When working with surds we need to take note of the roots present there.
To expand this equation we can do it the following way noting that √3 X √3 = 3
Expanding (1-√3)(⅓+√3)
1 X 1/3 = 1/3
1 X √3 = √3
-√3 X 1/3 =-√3/3
√3 X √3 = 3
hence, expanding the equation, we have
1/3 + √3 -√3/3 + 3
We can simply group the like terms and add them up.
[1/3 +3] +[√3-√3/3]
10/3 + [tex]\frac{2\sqrt{3} }{3}[/tex]
= [tex]\frac{-8 +2\sqrt{3} }{3}[/tex]
The volume of a cube is 3,375 cubic inches. What is the measure of each side of the cube?
Answer:
l=w=h=15
Step-by-step explanation:
Volume of a cube= l*w*h
where l=w=h
[tex]l = {}^{3} \sqrt{ v} \: \: \: l = {}^{3} \sqrt{3375} = 15 [/tex]
15*15*15=3375
Hope this helps ;) ❤❤❤
The measure of each side of the cube will be 15 inches.
What is volume?The Volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. Volume is defined as the space occupied by an object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the cube or Cuboid
The cube has all the sides equal means that the length, width, and height of the cube will be the same. Let's suppose the length, width, and height of the cube is a.
The volume of a cube will be given by the formula:-
Volume = side³ = a³
a³ = 3375
a = ∛3375
a = ∛( 15 x 15 x 15 )
a = 15 cubic inches.
Therefore, the measure of each side of the cube will be 15 inches.
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The force of gravity on Mars is different than on Earth. The function of the same situation on Mars would be represented by the parabolic function shown below. On which planet would the ball go the highest? On which planet would the ball take the longest to return to the ground? Explain your reasoning.
Answer:
If thrown up with the same speed, the ball will go highest in Mars, and also it would take the ball longest to reach the maximum and as well to return to the ground.
Step-by-step explanation:
Keep in mind that the gravity on Mars; surface is less (about just 38%) of the acceleration of gravity on Earth's surface. Then when we use the kinematic formulas:
[tex]v=v_0+a\,*\,t\\y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2[/tex]
the acceleration (which by the way is a negative number since acts opposite the initial velocity and displacement when we throw an object up on either planet.
Therefore, throwing the ball straight up makes the time for when the object stops going up and starts coming down (at the maximum height the object gets) the following:
[tex]v=v_0+a\,*\,t\\0=v_0-g\,*\,t\\t=\frac{v_0}{t}[/tex]
When we use this to replace the 't" in the displacement formula, we et:
[tex]y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2\\y-y_0=v_0\,(\frac{v_0}{g} )-\frac{g}{2} \,(\frac{v_0}{g} )^2\\y-y_0=\frac{1}{2} \frac{v_0^2}{g}[/tex]
This tells us that the smaller the value of "g", the highest the ball will go (g is in the denominator so a small value makes the quotient larger)
And we can also answer the question about time, since given the same initial velocity [tex]v_0[/tex] , the smaller the value of "g", the larger the value for the time to reach the maximum, and similarly to reach the ground when coming back down, since the acceleration is smaller (will take longer in Mars to cover the same distance)
Which is an equation of a line that has a slope of -1/3 and passes through the point (-5, 2)?
Answer:
y= -⅓x +⅓
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.
This form is also known as the point-slope form.
Since the slope is given to be -⅓, m= -⅓.
y= -⅓x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -5, y=2,
2= -⅓(-5) +c
[tex]2 = \frac{5}{3} + c \\ c = 2 - \frac{5}{3} \\ c = \frac{1}{3} [/tex]
Thus, the equation of the line is y= -⅓x +⅓.
Max’s car holds 18 gallons of gasoline. Driving on the highway, the car uses approximately 2 gallons per hour. Let h represent the number of hours Max has been riding on the highway. Write an expression that shows how many gallons of gasoline Max has left after driving h hours. Then find that number after Max drives 3.5 hours on the highway.
Answer:
y=18 gallons
Step-by-step explanation:
You can multiply how many hours he's been driving by the 2 gallons and subtract it from 18
Answer:
11 gallons
18=-2h h=3.5
Step-by-step explanation:
-2(3.5)=18
18-7=11, he has 11 gallons of gas left
3/8+1/8-1/6+1/4=? What is the answer? please!!!
Answer:
.58 repeating 3
Step-by-step explanation:
7/12=.58 repeating 3
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5)
B = {1,3,5,7)
How many elements are in A'n B?
Step-by-step explanation:
First,
(A intersect B) = {1,2,4,5} intersect {1,3,5,7}
= {1,5}
Now,
A'n B = (A) - (A intersect B)
= {1,2,4,5} - {1,5}
= {2,4}
compare your answers from parts A and B. What connections can you make between the size and number of squares in part A and the prime factors in part B?
Answer:
In part A, 6 squares made up of 4 units represented an area of 24.
In part B, the prime factorization of 24 gave 24 = 2 ∙ 2 · 2 · 3, which is equal to 4 · 6.
The factor that is a perfect square, in this case 4, determines the size of squares needed for the visual model, and other factor, 6, determines the number of squares of that size.
Step-by-step explanation:
Steve's scores on 6 of his tests were 92, 78, 86, 92, 95, and 91. If he took a seventh test and raised the mean of his scores by exactly 1 point, what was the score on the seventh test? Show your work.
Answer:
96
Step-by-step explanation:
First we need to know the mean of the Steve's scores on 6 of his tests. Given the six scores as 92, 78, 86, 92, 95, and 91.
Mean = sum of the scores/Total test taken
Mean = 92+78+86+92+95+ 91/6
Mean = 534/6
Mean = 89
If he took the seventh test and the mean score is raised by 1 them the new mean will be expressed as;
New mean = 92+78+86+92+95+ 91+x/7 = 89+1
Where x is the new score. Note that of a new score is added, the total year taken will also change to 7
To get x;
92+78+86+92+95+ 91+x/7 = 89+1
92+78+86+92+95+ 91+x/7 = 90
534+x/7 = 90
Cross multiply
533+x = 90×7
533+x = 630
x = 630-534
x = 96
Hence the score of the seventh test is 96
How to 2-(-5)+1 simplified
Answer:
8
Step-by-step explanation:
We can simplify this expression by solving it.
[tex]2-(-5)+1[/tex]
Subtracting a negative is the same as adding a positive:
[tex]2+5+1[/tex]
And addition here shows that [tex]2+5+1=8[/tex].
Hope this helped!
Answer:
8Step-by-step explanation:
[tex]2-\left(-5\right)+1\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a\\\\-\left(-5\right)=+5\\\\=2+5+1\\\\2+5=7\\\\= 7+1 \\\\=8[/tex]
Find the indicated angle measures. pls help i’m dyin lol
Answer:
utv = 24° wtx=113°
Step-by-step explanation:
I solved in the picture
hope this helps ^-^
Use the Counting Principle to find the probability. rolling a 4 on each of 4 number cubes
Answer:
Step-by-step explanation:
There is a 1/6 chance for the first cube
There is a 1/6 chance for the second cube
There is a 1/6 for the third cube
There is a 1/6 for the fourth cube.
=========
Probability for all events is (1/6)^4
P(all 1/6) = 1/1296 = 0.00077
Find the equation of the line passing through (0,5) with a slope of 2/3
Answer:
y= 2/3x +5
Step-by-step explanation:
(0,5) is the y intercept and the slope is 2/3 so we can use the y intercept form
y = mx+b where m is the slope and b is the y intercept
y= 2/3x +5
Answer:
y= 2/3x+5
Step-by-step explanation:
Okay, to write the equation of a line you need two values. The y intercept and the slope. The y intercept has an x coordinate of zero, and lucky us, the point you were given has an x coordinate of zero so that's done. You were also given the slope, so you don't have to calculate it. Anyways, the formula of a line is written in slope intercept form usually, so y=mx+b. Just fill in the gaps, m= the slope and b=the y intercept. The slope is 2/3, and the y intercept is 5. So, inserting in the variables you get y=2/3x+5.
Hope that helps!
I need to name the type of special pairs of angles shown. Please and thank you
Answer:
WXY is an obtuse angle, YXZ is an acute angle, and WXZ is a straight line.
Step-by-step explanation:
WXY is greater than 90 degrees, YXZ is lesss than 90 degrees, and WXZ is a straight 180 degree line.
The required name for a special type of pair of angles shown is supplementary angles.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
The figure, shown is pair of angles whose sum is equal to 180,
The by definitions of the angle where the sum is equal to 180° and adjacent angles are said to be supplymentary angles.
Thus, the required name for a special type of pair of angles shown is supplementary angles.
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Sinplify x+3x-36. 3x-36 3x²-36 4x-36 4x²-36
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{4x - 36}}}}[/tex]Step-by-step explanation:
[tex] \sf{x + 3x - 36}[/tex]
Here, we have to collect like terms.
_________________________________
▪️What do you mean by like terms ?
⇒Like terms are those which have the same base. While adding or subtracting like terms, we should add or subtract the coefficients of like terms.
_________________________________
Let's add the like terms :
Answer : 4x - 36
Hope I helped!
Best regards!
Plz write all the steps
Answer:
Step-by-step explanation:
See attachment
4. Write these fractions in the simplest form.
6
_
9
Answer:
Given fraction is 6/9 .
→What does fractions in simplest form means?
Fractions are said to be in simplest form if the HCF of numerator and denominator is equal to 1 .→ How to convert?
We will find the HCF of numerator and denominator and we will divide the numerator and denominator by that number.Now HCF of 6 and 9 is 3.
→ 6/9 = 6÷3/9÷3 = 2/3.
Hence the required answer is 2/3.
Answer:
[tex]\Large \boxed{\displaystyle \frac{2}{3}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6}{9}[/tex]
Factor out 3 from the numerator and denominator.
[tex]\displaystyle \frac{3(2)}{3(3)}[/tex]
Cancel the common factors.
[tex]\displaystyle \frac{2}{3}[/tex]
The vertices of triangle PQR are listed below.
P(-5, 3), Q(-13, -3), R(-5, -9)
What is the perimeter of triangle PQR?
A.
32 units
B.
51 units
C.
22 units
D.
48 units
Answer:
A. 32 units
Step-by-step explanation:
First, we need to find all of the side lengths of triangle using distance formula:
[tex]Distance = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]Now, we can calculate length of PQ, QR and PR sides by using their vertices and above formula:
[tex]PQ=\sqrt{(-13-(-5))^2+(-3-3)^2} =\sqrt{8^2+6^2}=10[/tex] [tex]QR=\sqrt{(-5-(-13))^2+(-9-(-3))^2} =\sqrt{8^2+6^2}=10[/tex] [tex]PR=\sqrt{(-5-(-5))^2+(-9-3)^2} =\sqrt{0^2+12^2}=12[/tex]For perimeter we add up the length of all of its sides:
[tex]Perimeter = PQ +QR + PR=10+10+12=32[/tex]19. A game is played by rolling a group of at least 3 dice. The highest two numeric results are removed
from the table. If any 6s remain on the table the player wins. If only 3 dice are rolled then the
probability of winning is 1/216. As the number of dice used increases without bound what does the
probability of a winning roll approach?
Answer: Approaches to 1.
Step-by-step explanation:
If there are only 3 dice used, then the only chance that the player has to win is when the 3 dice have the same outcome, 6.
The probability will be:
p = (1/6)^3 = 1/216.
Now, if we add one more dice, we still need at least 3 sixes to win, but the other dice can have any other value. so now the probabilities are:
dice 1---- outcome = 6, prob = 1/6.
dice 2---- outcome = 6, prob = 1/6.
dice 3---- outcome = 6, prob = 1/6.
dice 4---- outcome = any number, prob = 1.
The probability for this arrangement is still:
p = 1/216.
But now we have permutations!.
The dice that can be any number has 4 possible positions, so the actual probability will be:
P = 4*p = 4/216.
Now remember that if we have N elements, the total number of combinations of K elements ( N ≥ K) is:
[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]
if we add other dice, then we will have 5 dices, and 2 of them that can not be 6 that can take any position, then the number of combinations will be:
[tex]C(5, 2) = \frac{5!}{(5 - 2)!2!} = \frac{5*4}{2} = 10[/tex]
Then the probability will be:
P = 10*p = 10/216.
So we can start to see a pattern here, if we have N dices, we still only need 3 of them to be strictly 6, then we have (N - 3) dices that can be any number.
Then the probabilty of winning if you have N dices is:
P = C(N, N - 3)*p = C(N, N - 3)*(1/216)
Then as N increases, we will see that the probability tends to 1, (it actually grows larger than that, but remember that the probability is a number between 0 and 1, so the maximum is 1)
Why? well... if you roll a lot of dice, suppose 1000 of them, is really likely to have at least 3 sixes in there, so as the number of dice increases, also does the probability.
Explain how to use the distributive property to find an expression that is equivalent to 20+10
Answer: 2(10+5)
Step-by-step explanation: half of 20 is 10. half of 10 is five and i put them both in parentheses. outside the parenthesis i placed 2 so it is multiplied to the inner set of numbers.
Factorise:
( a²- 1) ( b²- 1) + 4ab
pls give a detailed explanation
pls answer it......
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed{ a^2 b^2 + -a^2 + -b^2 + 1 + 4ab}[/tex]
Let's simplify step-by-step.
[tex]( a^2 - 1 ) ( b^2 -1) + 4ab[/tex]
Distribute:
[tex]=( a^2) (b^2) + (a^2) (-1) + ( -1) (b^2) + (-1) (-1) + 4ab[/tex]
[tex]= a^2 b^2 + -a^2 + -b^2 + 1 + 4ab[/tex]
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Have a great day/night!
❀*May*❀
Answer:
a²b² - a² - b² + 4ab + 1
Step-by-step explanation:
( a²- 1) ( b²- 1) + 4ab
(a²b² - a² - b² + 1) + 4ab
a²b² - a² - b² + 4ab + 1
The second side of a triangular deck is 6 feet longer than the shortest side, and the third side is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 72 feet, what are the length of the three sides?
Answer:
let the shortest side be 'x' ft
length of second side = x + 6 ft
length of third side = 2(x+6) - 6 ft
perimeter of triangle = 72 feet
shortest side + second side + third side = 72 ft
x + x + 6 + 2(x+6) - 6 = 72
4x + 12 = 72
x = 15
length of shortest side = 15 ft
length of second side = 15 + 6 = 21 ft
length of third side = 2(15 + 6) - 6 = 36 ft
which statement is true regarding the graphed functions?
This is because the red and blue lines cross at (0,-2). We don't really need to worry about the y coordinate here. For this problem, all we care about is the x coordinate, which is x = 0.
When x = 0, the outputs of each function f(x) and g(x) are both the same value. So that's why we can say f(0) = g(0). It's the same as saying f(x) = g(x) has the solution x = 0.
What is the remainder when f(x) = x^2 + 14x − 8 is divided by (x − 5)? 103 88 87 72
Answer:
The answer is 87Step-by-step explanation:
f(x) = x² + 14x - 5
To find the reminder when f(x) is divided by x - 5 , substitute the value of x into the above formula
That's
x - 5 = 0
x = 5
So we have
f(5) = 5² + 14(5) - 8
f(5) = 25 + 70 - 8
f(5) = 95 - 8
We have the final answer as
87Hope this helps you
Answer: 87
Step-by-step explanation: took the test hope this helps :)
Anne is 26 years older than her daughter, and the sum of their ages is at least 48. Which of the following inequalities, when solved, will give the possible ages of Anne's daughter?
Answer:
A = 26 + D
A + D = 48
use substitution
(26 + D) + D = 48
26 + 2D = 48
2D = 22
D = 11 years old
find the inequality that will result in the daughter being 11
Answer:
at least means greater than or equal to
Step-by-step explanation:
therefore
Question 13 options:
2x + 26 ≥ 48 ----------->this is the correct answer
x + 26 > 48
x + 26 ≥ 48
2x + 26 > 48
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.5 inches, and standard deviation of 7.3 inches.
A) What is the probability that a randomly chosen child has a height of less than 52.85 inches?
B) What is the probability that a randomly chosen child has a height of more than 46.8 inches?
Answer:
A) 0.46452
B) 0.82064
Step-by-step explanation:
We solve for question A and B using z score formula
z = (x - μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
A) What is the probability that a randomly chosen child has a height of less than 52.85 inches?
x = 52.85 inches, μ = 53.5 inches, σ = 7.3 inches
z = (x - μ)/σ
= 52.85 - 53.5 / 7.3
= -0.08904
Using the z table to find the probability of the z score above.
P(x<52.85) = 0.46452
Therefore, the probability that a randomly chosen child has a height of less than 52.85 inches is 0.46452
B) What is the probability that a randomly chosen child has a height of more than 46.8 inches?
x = 46.8 inches, μ = 53.5 inches, σ = 7.3 inches
z = (x - μ)/σ
= 46.8 - 53.5 / 7.3
= -0.91781
Using the z table to find the probability of the z score above.
P(x<46.8) = 0.17936
P(x>46.8) = 1 - P(x<46.8)
= 1 - 0.17936
= 0.82064
Therefore, the probability that a randomly chosen child has a height of more than 46.8 inches is 0.82064
If the measures of two angles add up to 180°, then the angles are supplementary.
Part of a regression output is provided below. Some of the information has been omitted.
Source of variation SS df MS F
Regression 3177.17 2 1588.6
Residual 17 17.717
Total 3478.36 19
The SS(Residual) is?
Answer:
301.189
Step-by-step explanation:
Given the table :
Source of Variation - - SS - - - df - - - MS - - - - F
Regression - - - - - -3177.17 - - -2 - - 1588.6
Residual - - - - - - - - ______ --17 - - -17.717
Total - - - - - - - - - - 3478.36 - - 19
Calculate the SSR, Sum of Square residual
The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR) and Degree of Freedom RESIDUAL (DFR) are related by the formular :
MSR = SSR / DFR
Hence,
SSR = MSR × DFR
Fr the table ;
MSR = 17.717 ; DFR = 17
SSR = (17.717 × 17)
SSR = 301.189
A map of a park says its scale is 1 to 100 What do you think that means? Type your answer here
1cm:100m
Step-by-step explanation:
It means for every 1 cm in the map 100 m will be represented correspondingly..
Hence.. 2 cm:200m and so on..
Simplify each expression.
1) 7x - 9x
2) -2x - 7+ 8x - 10
3) 3 - 10x - 3-6x
4) 2m - 6+ m + 1
5) 10m - 8m
6) x - 4+x-5
7 4x + 5x
8) -x + 3 + 7x + 5
Answer:
1) -2x
2) 6x - 17
3) -16x
4) 3m - 5
5) 2m
6) 2x - 9
7) 9x
8) 6x + 8
Step-by-step explanation:
1) = x(7-9) = x(2) = 2x
2) x(-2+8) - 7 - 10 = x(6) - 17 = 6x - 17
3) x(-10-6) + 3 - 3 = x(-16) + 0 = 16x
4) m(2+1) - 6 + 1 = 3m - 5
5) m(10-8) = m(2) = 2m
6) x(1+1) - 5 - 4 = 2x - 9
7) x(4+5) = x(9) = 9x
8) x(7-1) + 3 + 5 = 6x + 8
A diver descended 20 feet in 5 seconds. What is the average rate per second that he traveled? Explain how you can use integer tiles to solve the problem and find the answer. Pls help
Answer:
The diver is moving down, so he moved −20 feet. Start with 20 negative tiles and separate them into 5 equal groups. There are 4 negative tiles in each group, so he traveled at a rate of −4 feet per second.
Step-by-step explanation:
Answer:
4 feet per second
Step-by-step explanation:
We can create a proportion:
[tex]\frac{20}{5} = \frac{x}{1}[/tex]
Cross multiply:
[tex]20\cdot1=20\\\\20\div5=4[/tex]
So he's travelling at a rate of 4 feet per second.
Hope this helped!