x<3
Step-by-step explanation:
–2(5 – 4x) < 6x – 4
(–10 + 8x) < 6x – 4
8x –6x < –4 + 10
2x < 6
x < 3
Simplify (5√3 − 2√5) the whole square
Answer:
95 - 20[tex]\sqrt{15}[/tex]
Step-by-step explanation:
(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²
= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )
each term in the second factor is multiplied by each term in the first factor, that is
5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis
= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms
= 95 - 20[tex]\sqrt{15}[/tex]
Answer:
95 - 20√15
Step-by-step explanation:
I assume the expression is (5√3 − 2√5)^2 (?).
(5√3 − 2√5)*(5√3 − 2√5)
25√3^2 - 20√15 + 4√5^2
25*3 - 20√15 +4*5
75 - 20√15 +20
95 - 20√15
If the ratio of the measures of corresponding sides of two similar is 4:9, then the ratio of their perimeter is
Answer:
4 : 9
Step-by-step explanation:
ratio of corresponding sides and ratio of perimeter are equal
then ratio of perimeter = 4 : 9
what is the volume of the prism pls help
The volume of the rectangular prism is 8 1 / 8 units³
Volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
volume of a rectangular prism = base area × height
volume of a rectangular prism = 16 1 / 4 × 1 / 2
volume of a rectangular prism = 65 / 4 × 1 / 2
volume of a rectangular prism = 65 / 8
volume of a rectangular prism = 8 1 / 8 units³
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Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
The correct answer is 8.5 in.
What is Heron's formula in math?Heron's formula, formula credited to Heron of Alexandria for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.we know that
The formula of area of triangle is equal to
[tex]A = \frac{1}{2} (b) (h)[/tex]
We have
b = BC = 6 in
h = AD = x in
substitute
[tex]A = \frac{1}{2} (6) (x)[/tex]
[tex]A = 3x^{2} in^{2} ..................(1)[/tex]
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let a,b,c be the lengths of the sides of a triangle.
The area is given by:-
[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex] where p is half the perimeter
[tex]p = \frac{a +b+ c}{2}[/tex]
a = 9 in , b= 9 in, c = 6 in
[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]
Find the area
[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]
[tex]A = \sqrt{12 (3)(3)(6)}[/tex]
[tex]A = \sqrt{648}[/tex]
[tex]A = 25.46 in^{2}[/tex]
Substitute the value of the area in the equation 1 and solve for x
[tex]A = 3x in^{2}[/tex]
25.46 = 3x
x = 25.46/3
x = 8.5 in
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The complete question is -
HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 8 in.
B. 11.3 in.
C. 8.5 in.
D. 6.2 in.
plss help!!
1. Abigail is 8 years older than Cynthia. Twenty years ago Abigail was three times as old as Cynthia. How old is each now?
2. Three years ago Tom was twice as old as Jean. And in two years the sum of their ages will be 28 years. Find their present ages.
3. Bill is 5 years older than Sue is, and the sum of their ages is 67 years. How old is Bill and Sue?
4. The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digits, and the tens digit equals to the sum of the other two. Find the number.
5. The units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.
Answer:
1. a = 32, c = 24
Step-by-step explanation:
a = c+8
a-20 = 3(c-20)
(c+8)-20 = 3c-60
c = 24
a = 24+8
a = 32
2. t = 15, j = 9
t-3 = 2(j-3)
t-3 = 2j-6
t = 2j-3
t + 2 + j + 2 = 28
(2j-3)+ 2 + j + 2 = 28
3j + 1 = 28
3j = 27
j = 9
t-3 = 2(9-3)
t-3 = 2(6)
t-3=12
t = 15
3. b=36, s=31
b = s + 5
b+s = 67
(s+5)+s = 67
2s+5 = 67
2s = 62
s = 31
b = 31+5
b = 36
4. 231
h + t + u = 6
(with h=hundreds digit, t=tens digit, u=units digit)
h = 2u
t = h+u
t = (2u) + u
(2u) + (2u +u) + u = 6
6u = 6
u = 1
h = 2
t = 3
the number is 231
5. 48
u = 2t
the 2-digit number is 10t+u
2(10t+u) = 10u+t+12
2(10t + 2t) = 10(2t) + t + 12
20t + 4t = 20t + t + 12
24t = 21t + 12
3t = 12
t = 4
u = 2*4
u = 8
the number is 48
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
2. What is the domain and range of the
graph shown?
-8-64
10-
8-
B
4+
2-
4+
6+
do do t
-10
2 4 6 8 10 12
Answer:
domain: x ≥ 0range: y ≥ 0Step-by-step explanation:
The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.
DomainThe domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).
RangeThe range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).
A pattern has 77 yellow triangles to every 33 green triangles. What is the ratios of green triangles to yellow triangles?
What are the x-intercepts of the function y = 22 -x - 120? Check all that apply. O (-120. 0) O (-11.466, 0) O (-10.466, 0) O (0, -120) (10.466, 0) O (11.466, 0)
The x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)
How to determine the x-intercept?The function is given as:
y = 2x^2 - x - 120
Set the function to 0
2x^2 - x - 120 = 0
Factor out 2
2(x^2 - 0.5x - 60) = 0
Divide by 2
x^2 - 0.5x - 60 = 0
Expand the function
x^2 + 7.5x - 8x - 60 = 0
Factorize the function
(x + 7.5)(x - 8) = 0
Split
x + 7.5 = 0 and x - 8 = 0
Solve for x
x = -7.5 and x = 8
Hence, the x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)
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Solve this recurrence relation together with the initial condition given. an = 2an−1 for n ≥ 1, a0 = 3
The solution of the recurrence relation is [tex]a_n=3.2^n[/tex]
For given question,
We have been given a recurrence relation [tex]a_n = 2a_{n-1}[/tex] for n ≥ 1
and an initial condition [tex]a_0=3[/tex]
Let [tex]a_n[/tex] = m², [tex]a_{n-1}[/tex] = m and [tex]a_{n-2}[/tex] = 1
So from given recurrence relation we get an characteristic equation,
⇒ m² = 2m
⇒ m² - 2m = 0 .........( Subtract 2m from each side)
⇒ m(m - 2) = 0 .........(Factorize)
⇒ m = 0 or m - 2 = 0
⇒ m = 0 or m = 2
We know that the solution of the recurrence relation is then of the form
[tex]a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n[/tex] where [tex]m_1,m_2[/tex] are the roots of the characteristic equation.
Let, [tex]m_1[/tex] = 0 and [tex]m_2[/tex] = 2
From above roots,
[tex]\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n[/tex]
For n = 0,
[tex]\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2[/tex]
But [tex]a_0=3[/tex]
This means [tex]\alpha_2=3[/tex]
so, the solution of the recurrence relation would be [tex]a_n=3.2^n[/tex]
Therefore, the solution of the recurrence relation is [tex]a_n=3.2^n[/tex]
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60% of UCLA is girls. What perrcentage are boys
.
Answer:
40%
Step-by-step explanation:
Percent must be equal to 100, so if 60 are girls, then 40% must be boys.
Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
False, Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
What animals evolved during Cambrian period?
Animals include, from left: Dinomischus, Ottoia, Halucinoginia, Wiwaxia, Trilobites, Archeocyathans, Microdictyon, Canadia, and Pikia. Two larger Anomolocarus are seen in the distant background.When did animals evolve in the Cambrian?
The Cambrian explosion happened more than 500 million years ago. It was when most of the major animal groups started to appear in the fossil record, a time of rapid expansion of different forms of life on Earth.What long lived group of arthropods went extinct at the end of the Permian?
The trilobites, a group of extinct arthropods, as well as the closely related eurypterids, first appeared in the Permian. The Paleozoic Era saw the extinction of rugose and tabulate corals.Learn more about Cambrian animals evolved.
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The complete question is -
True or false . Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
A triangle has vertices at (4, 4), (-6, 2) and (2, 0).
a. Find the coordinates of the mid-points of eachside
b. Find the lengths of the sides of the triangle
formed by joining the mid-points.
each side.
Answer:
A. (-1, 3) (3, 2) (-2, 1)
B. [tex]\sqrt{17}[/tex] [tex]\sqrt{5}[/tex] [tex]\sqrt{26}[/tex]
Step-by-step explanation:
The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].
MIDPOINTS
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)
Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].
DISTANCE
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]
a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.
(4-6)/2=-1 (4+2)/2=3
Repeat for other sides.
(2-6)/2=-2 (2+0)/2=1
(2+4)/2=3 (4+0)/2=2
Coordinates of midpoints are (-1,3), (-2,1), (3,2)
b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.
sqrt((-1+2)^2 + (3-1)^2)
Sqrt(5)
Repeat.
Sqrt(17)
Sqrt(26)
The lengths of the inner triangle are as follows:
(-1,3), (-2,1) = Sqrt(5)
(-1,3), (3,2) = Sqrt(17)
(-2,1), (3,2) = Sqrt(26)
For 8-10, Find the area of the polygon.
Please help!
Which of these r-values represents the weakest correlation?
A. 0.2
B. 0.3
C. 0.4
D. 0.1
Answer: 0.1
Step-by-step explanation:
The smaller the absolute value of the correlation coefficient, the weaker the correlation.
Find the arc length if the measure of the central angle is 80° and the radius
is 8 inches.
Answer:
[tex]\frac{32\pi }{9}[/tex] or [tex]11.17[/tex]
Step-by-step explanation:
The formula for arc length is [tex]2\pi r( \frac{x}{360} )[/tex] where "r" stands for radius and "x" stands for your angle[tex]2\pi 8(\frac{80}{360} )[/tex]
[tex]=16\pi (\frac{80}{360} )[/tex]
[tex]=16\pi (\frac{2}{9})[/tex]
[tex]=\frac{32\pi }{9}[/tex]
In a model of a construction project, 1 yard is represented as 0.25 inch. What would be the actual area of a garden in square yards, if it is represented by 20 square inches in the model?
15-point question. Pls help
Answer:
3/8
Step-by-step explanation:
There are 8 equal slices so each slice is 1/8th of the whole pizza
1/8+1/8=2/8 he ate right away
2/8+1/8 for what he ate before going to sleep
2/8+1/8=3/8
what is 8 square root of 6. answered as a square root ?
The value of 8√6 as a square root is √384
Surd expressionSurd are written as the square root of prime numbers. Given the expression below;
8√6
This is can be written as;
8√6 = √(8 * 8 * 6)
8√6 = √64 * 6
8√6 = √384
Therefore the value of 8√6 as a square root is √384
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Simplify.
Rewrite the expression in the form y^n.
(y^2)^3 =
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
So there is an exponent identity that states: [tex](x^b)^a = x^{a*b}[/tex] which means this question becomes: [tex](y^2)^3 = y^{2*3} = y^6[/tex].
Just so you completely understand why this works, it might help to express y^2, as what it truly represents: [tex]y^2=y*y[/tex]. So using this definition we can substitute it into the equation so it becomes: [tex](y*y)^3[/tex]. Now let's use the definition of exponents like we just did with the y, to redefine this in terms of multiplication: [tex](y*y)^3 = (y * y) * (y * y) * (y * y)[/tex]. We can just multiply all these out, and we get: [tex]y * y * y * y * y * y =y^6[/tex].
To make it a bit more general when we have the exponent: [tex]x^b[/tex] it can be expressed as: [tex](x*x*x...\text{ b amount of times})[/tex] now when we raise it to the power of a. we get: [tex](x * x * x...\text{ b amount of times})^a[/tex] which can further be rewritten using the definition of an exponent to become the equation: [tex](x*x*x\text... \text{ b amount of times}) * (x * x * x...\text{ b amount of times})...\text{ a amount of times}[/tex] which just simplifies to: [tex]x*x*x*x...\text{ a times b amount of times}[/tex]. Hopefully this makes the identity a bit more understandable
Model the situation with the sum of polynomials. Simplify their sun.
A rectangular picture frame has the dimensions shown in the figure. Write a polynomial that represents the perimeter of the frame.
Answer:
16x-2
Step-by-step explanation:
Perimeter is 2w+2l
so we plug it in
2(3x+1) + 2(5x-2)
now we distribute
6x+2 + 10x -4
now we add like terms
6x+10x+2-4
16x-2
Calculate x for each of the following right angled triangles.
Give your answer as a simplified surd (or integer).
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
(a) x = 6.5 cm (b) x = 10 cm(c) x = 7 cm(d) x = 7.9 cmStep-by-step explanation:
To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..
Formula :(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2
(h)^2 = (p)^2 + (b)^2
therefore,(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (√12)^2 + (√30)^2
→ x^2 = 12 + 30
→ x^2 = 42
→ x = √42
→ x = 6.480...
→ x = 6.5 cm. (approx)
___________________________(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√300)^2 = (x)^2 + (√200)^2
→ 300 = x^2 + 200
→ x^2 = 300 – 200
→ x^2 = 100
→ x = √100
→ x= 10 cm.
___________________________(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√66)^2 = (x)^2 + (√17)^2
→ 66 = x^2 + 17
→ x^2 = 66 – 17
→ x^2 = 49
→ x = √49
→ x = 7 cm.
___________________________(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (2√3)^2 + (5√12)^2
→ x^2 = 12 + 50
→ x^2 = 62
→ x = √62
→ x = 7.874...
→ x = 7.9 cm. (approx)
___________________________Hope it helps you!!Jaun rides the bus to school each day he always arrives at his bus stop on time but his bus is late 80% of the time
The correct probability that Juan's bus is going to be late every week next week is 20 percent.
How to solve for the probabilityWe have the total number in the stimulation on to be from 0 to 9
On the fact that it would be late, the number ranges from 2 to 9
Hence the fact that it would be late would be
2/10
= 0.2
0.2 is also the same as 20 percent.
Complete questionJuan rides the bus to school each day. He always arrives at his bus stop on time, but his bus is late 80% of the time. Juan runs a simulation to model this using a random number generator. He assigns these digits to the possible outcomes for each day of the week:
• Let 0 and 1 = bus is on time
• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is late
The table shows the results of the simulation.
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Rewrite the function by completing the square. x2 + 4x = 0 (x + )2 =
When the completing the square is applied, the rewritten function is (x + 2)^2 = 4
How to complete the square?The equation is given as:
x^2 + 4x = 0
The above equation is a quadratic equation and the coefficient of x in the above equation is 4.
So, we have:
k = 4
Divide the variable k by 2
k/2 = 4/2
k/2 = 2
Square the above result
(k/2)^2 = 4
Next, we add 4 to both sides of x^2 + 4x = 0
x^2 + 4x + 4 = 4
Expand the equation by expressing 4x as 2x + 2x
This gives
x^2 + 2x + 2x + 4 = 4
Factorize the above equation
x(x + 2) + 2(x + 2) = 4
Factor out x + 2 from the above equation
(x + 2)(x + 2) = 4
Rewrite the equation as a perfect square of (x + 2)
(x + 2)^2 = 4
Hence, the rewritten function after completing the square is (x + 2)^2 = 4
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Theresa needs twice as many feet of wood as samuel how many pieces of wood does teresa need?
Using addition or multiplication, Teresa has twice a number of wood as Samuel.
According to the question,
Teresa needs twice as many feet of wood as Samuel in order to find the number of pieces of wood Teresa need only if we add the number Teresa has by itself or multiply it by 2.
Hence, we need to do only multiply it by 2
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How does the figure help verify the triangle inequality theorem?
The line is drawn from a length of 15, two lines constructing a triangle and intersecting the arc from a length of the lines 7, 4
A.
by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third
B.
by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third
C.
by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the third
D.
by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
Option D. The triangle inequality theorem is verified by by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.
How to make this proofFrom the given picture we can see the length of the sides. These are 7, 4 and 15.
The length of the two sides cannot join due to the fact that they are less than 15.
4 + 7 < 15
11< 15
Hence the answer is D.
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by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
Simplify (9y²-x² )÷ (xy+3y²)
Step-by-step explanation:
[tex] \cfrac{(9y²-x² )}{ (xy+3y²)}[/tex][tex] \cfrac{3 {}^{2} (y) {}^{2} - x}{3(y {})^{2} + xy } [/tex][tex]3 {}^{2 - 1} y {}^{2 - 2 - 1} - x {}^{2 - 1} [/tex][tex]3 y { }^{ - 1} - x[/tex][tex] \cfrac{3}{y} - x[/tex]Therefore,the answer is [tex] \cfrac{3}{y} - x[/tex].
[Some of the steps I didn't show,try by yourself,to find!]An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 5.7 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
The p-value from the hypothesis test is 0.142 i.e., greater than the given significance level of 0.05. So, the null hypothesis is not rejected. The z-score for the given sample is 1.471.
What is the decision rule for the p-value approach to hypothesis testing?The decision rule based on p-value states,
If p > α (significance level), then the null hypothesis is not rejectedIf p < α (significance level), then the null hypothesis is rejected in favor of the alternative hypothesis.Calculation:Since it is given that the valve would produce a mean pressure of 5.4 pounds/square inch. I.e., μ = 5.4 p/si
So, Defining the hypothesis:
Null hypothesis H0: μ = 5.4
Alternative hypothesis Ha: μ ≠ 5.4
It is given that,
The valve was tested on 24 engines. I.e., Sample size n = 24
The sample mean X = 5.7
Standard deviation σ = 1.0 and
The significance level = 0.05
Since the population distribution is approximately normal,
the test statistic is calculated as follows:
z = (X - μ)/(σ/[tex]\sqrt{n}[/tex])
On substituting the value,
z = (5.7 - 5.4)/(1.0/[tex]\sqrt{24}[/tex])
= (0.3)/0.204
= 1.471
Fron this z-score, the p-value is calculated as 0.142.
Since, the value of p > 0.05 (significance level), the null hypothesis is not rejected.
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Someone help me please
Answer:
x=15
Step-by-step explanation:
Use the Pythagorean Theorem: a^2+b^2=c^2
1. a = 20, b = x, c = 25
2. 20^2+b^2= 25^2
3. Expand: 400+b^2= 625
4. Subtract + Simplify: b^2= 625-400
5. Fully Solve: b^2 = 225 -> Square root of b^2 = Square root of 225
6. Last Step: Simplify: b = 15.
Here is a similar problem for you to solve, put your answer in the comments.
a= 12, b=5, c=?
Solve for c using the Pythagorean theorem.
what’s ten times ten