Answer:
[tex]\frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \\\\=\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \times \frac{5 \ - \ \sqrt2 }{5 \ - \ \sqrt2 } \\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{5 \sqrt3 \ + \ 5\sqrt 2 \ - \ \sqrt{ 3\times 2 } \ - \ \sqrt{2 \times 2}}{(5)^2 \ - \ (\sqrt2)^2}\\\\= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{25 - 2}\\\\[/tex]
[tex]= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]
How to find the inverse of this matrix
[tex]\left[\begin{array}{ccc}1&0\\0&3\\\end{array}\right][/tex]
Answer:
Here we have the matrix:
[tex]M = \left[\begin{array}{ccc}1&0\\0&3\end{array}\right][/tex]
And we want to find its inverse.
The inverse of a 2x2 matrix A is:
(1/det(A))*adj(A)
where det(A) is the determinant of the matrix.
Such that for a matrix:
[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right][/tex]
The determinant is:
det(A) = a₁₁*a₂₂ - a₁₂*a₂₁
in the case of our matrix M, the determinant is:
det(M) = 1*3 - 0*0 = 3
and adj(A) is a transposition along the diagonal, and for the other elements, we just change its sign.
Then for our matrix A we would have:
[tex]adj(A) = \left[\begin{array}{ccc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex]
Then for our matrix M, we have:
[tex]adj(M) = \left[\begin{array}{ccc}3&-0\\-0&1\end{array}\right][/tex]
Then the inverse of the matrix M is:
[tex]M^{-1} = \frac{1}{det(M)} *adj(M) = \frac{1}{3}\left[\begin{array}{ccc}3&0\\0&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1/3\end{array}\right][/tex]
(7/8*9)*3/4*(9/3*5)=
Answer:
2835/32 or 88 19/32Step-by-step explanation:
(7/8 × 9) × 3/4 × (9/3 × 5)= 63/8 × 3/4 × (3 × 5)= 63/8 × 3/4 × 15= 2835/32 or 88 19/32[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
[tex]88 \frac{19}{32} [/tex]
If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a
Answer:
Step-by-step explanation:
[tex](a^2-1)x^2+(a-1)x+a^2-4a+3=0\\\\Calculate\ and\ identify\ the\ polynomials\\\\\Longleftrightarrow\ a^2x^2-x^2+ax-x+a^2-4a+3=0\\\\\Longleftrightarrow\ a^2x^2+ax+a^2-4a+3=x^2+x+0\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}a^2&=&1\\a&=&1\\a^2-4a+3&=&0\\\end{array} \right.\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}(a-1)(a+1)&=&0\\a-1&=&0\\(a-1)(a-3)&=&0\\\end{array} \right.\\\\\\We\ must\ exclude\ a=-1\ and\ a=3\ (not\ solution)\\\Longrightarrow\ a=1\\[/tex]
51.Tandin Dorji was married to five women. First woman had three
daughters and five sons and the youngest wife had two sons. Two
of the remaining wives had one son each. If the ratio of children of
5th wife was 1:3 with the children of other wives. How many
children does Tandin have
Answer:
Tandin has 16 children.
Step-by-step explanation:
Total of children:
3+5 = 8(first woman)
2(youngest wife)
1 + 1 = 2(two of the remaining wives)
So
8 + 2 + 2 = 12
If the ratio of children of 5th wife was 1:3 with the children of other wives.
Thus the 5th wife has 12/3 = 4 children.
How many children does Tandin have?
12 + 4 = 16
Tandin has 16 children.
Question 8 plz show ALL STEPS
Answer:
Substitute the functions and the value of the functions.
Step-by-step explanation:
Doing all will be long, so i'll present a and d
Here,(no a)
f(x)=3x-1, g(x)=x^2+2
Now,
f(g(x))=f(x^2+2)=3(x^2+2)-1=3x^2+6-1=3x^2+5
g(f(x))=g(3x-1)=(3x-1)^2+2=9x^2-6x+1+2=9x^2-6x+3
Here, (no d)
f(x)=x^2-9, g(x)=√(x+4)
Now,
f(g(x))=f(√(x+4))=(√(x+4))^2-9=x+4-9=x-5
g(f(x))=g(x^2-9)=√(x^2-9+4)=√(x^2-5)
Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)
Answer:
A)
[tex]k=0[/tex]
B)
[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]
C)
[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]
A)
Given that h(1) = 20, we want to find k.
h(1) = 20 means that h(x) = 20 when x = 1. Substitute:
[tex]\displaystyle (20) = 20e^{k(1)}[/tex]
Simplify:
[tex]1= e^k[/tex]
Anything raised to zero (except for zero) is one. Therefore:
[tex]k=0[/tex]
B)
Given that h(1) = 40, we want to find 2k + 1.
Likewise, this means that h(x) = 40 when x = 1. Substitute:
[tex]\displaystyle (40) = 20e^{k(1)}[/tex]
Simplify:
[tex]\displaystyle 2 = e^{k}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]
By definition, ln(e) = 1. Hence:
[tex]\displaystyle k = \ln 2[/tex]
Therefore:
[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]
C)
Given that h(1) = 10, we want to find k - 3.
Again, this meas that h(x) = 10 when x = 1. Substitute:
[tex]\displaystyle (10) = 20e^{k(1)}[/tex]
Simplfy:
[tex]\displaystyle \frac{1}{2} = e^k[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]
Therefore:
[tex]\displaystyle k = \ln \frac{1}{2}[/tex]
Therefore:
[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]
when 18 is subtracted from six times a certain number the result is 96 what is the number
Let the number be x
ATQ
[tex]\\ \sf\twoheadrightarrow 6x-18=96[/tex]
[tex]\\ \sf\twoheadrightarrow 6x=96+18[/tex]
[tex]\\ \sf\twoheadrightarrow 6x=112[/tex]
[tex]\\ \sf\twoheadrightarrow x=\dfrac{112}{6}[/tex]
[tex]\\ \sf\twoheadrightarrow x=7[/tex]
Given: 3x+11=y, solve for x if y = 29
answer is 6
Step-by-step explanation:
3x+11=y
y=29
3x+11=29
3x=29-11
3x=18
x=18÷3
x=6
Answer:6
Step-by-step explanation:
3x+11=29
3x=29-11
3x=18
X=18/3
X=6
One book is 4cm thick, find out how many such books can be placed in a space of 53cm.
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
Instructions: Given the following constraints, find the maximum and minimum values for
z
.
Constraints: 2−≤124+2≥0+2≤6 2x−y≤12 4x+2y≥0 x+2y≤6
Optimization Equation: =2+5
z
=
2
x
+
5
y
Maximum Value of
z
:
Minimum Value of
z
:
Answer:
z(max) = 16
z(min) = -24
Step-by-step explanation:
2x - y = 12 multiply by 2
4x - 2y = 24 (1)
4x + 2y = 0 add equations
8x = 24
x = 3
4(3) + 2y = 0
y = -6
so (3, -6) is a common point on these two lines
z = 2(3) + 5(-6) = -24
4x - 2y = 24 (1)
x + 2y = 6 add equations
5x = 30
x = 6
6 + 2y = 6
y = 0
so (6, 0) is a common point on these two lines
z = 2(6) + 5(0) = 12
4x + 2y = 0 multiply by -1
-4x - 2y = 0
x + 2y = 6 add equations
-3x = 6
x = -2
-2 + 2y = 6
y = 4
so (-2, 4) is a common point on these two lines
z = 2(-2) + 5(4) = 16
The 4th of an AP is 15 and the 9th term is 35. find the 15th term
Consecutive terms in this sequence are separated by a constant c, so if the 4th term is 15, then the next terms would be
5th: 15 + c
6th: (15 + c) + c = 15 + 2c
7th: (15 + 2c) + c = 15 + 3c
and so on. More generally, since any given number in the sequence depends on the number that came before it, we can write the n-th term in terms of the 4th term,
n-th: 15 + (n - 4) c
Then the 9th term in the sequence is
15 + (9 - 4) c = 35
and solving for c gives
15 + 5c = 35 ==> 5c = 20 ==> c = 4
Then the 15th term would be
15 + (15 - 4)×4 = 15 + 11×4 = 15 + 44 = 59
Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ [tex]\frac{1}{\sqrt{x^{2} +y^{2} } }[/tex]dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4[tex]\leq x^{2} +y^{2} \leq 9[/tex]
It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]
help giving brainilest, heart, and 5 stars
Answer:
4 = 6
5 = -17
Step-by-step explanation:
4. a² - b / b² - c
a² = 2² = 4
b = -2
4 - (-2) = 4 + 2 = 6
6 / b² - c = 6/4 - 3 = 6/1 = 6
4 = 6
5. -3x² + 2xy + 7
-3x² = -3 * -2² = -3 * 4 = -12
2xy = 2 * -2 * 3 = -4 * 3 = -12
-12 + -12 + 7 = -24 + 7 = -17
5 = -17
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Instructions: Find the measure of the indicated angle to the nearest degree.
Answer:
? = 13.6
Step-by-step explanation:
Let the unknown angle be y
so
tan y= p/b
tan y =8/33
y = tan‐¹(8/33)
y = 13.62699486
y = 13.6
Dividing integers
7. (-154) ➗ (-14) =
11. (-40) ➗10=
15. 90 ➗ (-15)=
16. 108 ➗ (-9)=
17. (-48) ➗ (-6)=
18. (-105) ➗ 7=
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.
here,
7. (-154) ➗ (-14) =11
11. (-40) ➗10=-4
15. 90 ➗ (-15)=-6
16. 108 ➗ (-9)=-12
17. (-48) ➗ (-6)=8
18. (-105) ➗ 7=-15
hope it helps you......
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. The article "Properties of Waste Silk Shod Fiber/Cellulose Green Composite Films" (. of Composite Materials, 2012: 123-127) reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value?
Complete Question
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.)
t=8.169
P-value= ?
Answer:
a) [tex]P-value=0[/tex]
b) Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=10[/tex]
Mean [tex]\=x= 51.3[/tex]
Standard deviation [tex]\sigma=1.2[/tex]
Significance level is taken as [tex]\alpha=0.05[/tex]
t test statistics
[tex]t=8.169[/tex]
Therefore
[tex]P-Value=P(t>8.169)[/tex]
Critical point
[tex]t_{\alpha,df}[/tex]
[tex]\alpha=0.05[/tex]
[tex]df=10-1=>9[/tex]
Therefore
P-value from T distribution table
[tex]P-value=0[/tex]
Conclusion
[tex]P-value (0)< \alpha(0.05)[/tex]
We Reject the Null Hypothesis [tex]H_0[/tex]
Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
If f(x) is an exponential function where f(-1.5) 26 and
f(5.5) = 7, then find the value of f(10), to the nearest hundredth.
Answer:
[tex]f(10) = 1147.25[/tex]
Step-by-step explanation:
Given
[tex]f(-1.5) = 26[/tex]
[tex]f(5.5) = 7[/tex]
Required
f(10)
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
[tex]f(-1.5) = 26[/tex] impleies that:
[tex]26 = ab^{-1.5}[/tex] --- (1)
[tex]f(5.5) = 7[/tex] implies that
[tex]7 = ab^{5.5}[/tex] --- (2)
Divide (2) by (1)
[tex]26/7 = ab^{-1.5}/ab^{5.5}[/tex]
[tex]3.71429 = b^{-1.5+5.5}[/tex]
[tex]3.71429 = b^{4}[/tex]
Take 4th root
[tex]b = 1.39[/tex]
Substitute [tex]b = 1.39[/tex] in [tex]26 = ab^{-1.5}[/tex]
[tex]26 = a * 1.39^{-1.5}[/tex]
[tex]26 = a * 0.6102[/tex]
Solve for (a)
[tex]a = 26/0.6102[/tex]
[tex]a = 42.61[/tex]
f(10) is calculated as:
[tex]f(10) = ab^{10}[/tex]
[tex]f(10) = 42.61 * 1.39^{10}[/tex]
[tex]f(10) = 1147.25[/tex]
Can someone help me? I am struggling and I would be so happy if any of you helped me. Thank you for your help!
Answer:
Mean = 52
Standard Deviation = 13.64
Step-by-step explanation:
mean = 260/5
= 52
Standard Deviation = [tex]\sqrt{\frac{930}{5} }[/tex] = 13.64
I wasn't sure about my answer so used the Gauthmath app
(PLEASE HELP ITS THE LAST QUESTION)
Find the measure of angle L.
A) 21.6°
B) 43.8°
C) 33.4°
D) 21.9°
Answer:
A
Step-by-step explanation:
lemme meh knw if it was helpful..
A car which was advertised for sale for 95000, was ultimately sold for 83600. Find the percent reduction in the price?
Answer: 12%
Step-by-step explanation:
95,000-83,600=11,400
(11,400/95000)(100) = 12%
The percentage reduction in the price of the car is 12%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Original price of car=95000 and Selling price=83600
Thus the reduction in price= 95000-83600
=11400
Thus percentage reduction in the price of the car is
= 11400/95000 × 100
=12%
Hence, The percentage reduction in the price of the car is 12%
Learn more about percentages here:
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Is the ratio 4:1 equivalent to the ratio 12:9
Answer:
No
Step-by-step explanation:
4:1
Multiply each side by 3
4*3 : 1*3
12: 3
This is not equal to 12:9
Answer:
no
Step-by-step explanation:
12 : 9
4 : 3 ≠ 4 : 1
What is the base and height of parallelogram S?
Gieo đồng thời hai con xúc xắc. Tìm xác suất để nhận được:Tổng số chấm là 8.
Answer:
what is this sy man i dnt get it
Step-by-step explanation:
5765865876+5737555586=
Answer:
5765865876+5737555586=11503421462
True or False. A rational number can be expressed as the quotient a/b where b ≠ 0
Answer:
true. A rational number can be expressed as the quotient a/b where b ≠ 0
Fill in the blanks.
(3b^3)^2 = _b^_
We can seperate (3b³) into two different parts, the constant and the variable.
The constant (3) and the variable (b) can both be squared and multiplied to get the correct answer, so:
3² = 9
(b³)² = [tex]b^{6}[/tex]
So, [tex](3b^{3})^{2} = 9b^{6}[/tex]
Mindy cheers at 16 regular season football games each year. She cheers for a total of 58.35 minutes each game. If her teams make the playoffs, she will cheer at each game for 59.15 minutes. How many total minutes will mindy cheer if she cheers at all regular season games and two playoff games?
Answer:
1051.9 minutes
Step-by-step explanation:
16 games at 58.35 minutes =
16* 58.35 =933.6 minutes
2 playoffs at 59.15
2 * 59.15 = 118.3 minutes
Add them together
933.6+118.3 =1051.9 minutes
Answer:
the answer is 1051.9 minutes
Step-by-step explanation:
[tex]\sf{}[/tex]
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. The correct probability tree looks like
Answer:
The probability tree is;
0.95 [tex](+)[/tex]
[tex](S)[/tex]
0.1 0.05 [tex](-)[/tex]
[ P ]
0.9 0.15 [tex](+)[/tex]
[tex](S_{no})[/tex]
0.85 [tex](-)[/tex]
Step-by-step explanation:
Given the data in the question;
10% of the rugby team members use steroids
so Probability of using steroid; P( use steroid ) = 10% = 0.10
Probability of not using steroid; P( no steroid use ) = 1 - 0.10 = 0.90
Since the test show positive for an athlete who uses steroids, 95% of the time.
Probability of using steroids and testing positive = 95% = 0.95
Probability of using steroids and testing Negative = 1 - 0.95 = 0.05
Also from the test, 15% of all steroid-free individuals also test positive.
so
Probability of not using steroids and testing positive = 15% = 0.15
Probability of not using steroids and testing negative = 1 - 0.15 = 0.85
To set up the probability tree, Let;
[tex](S)[/tex] represent steroid use
[tex](S_{no})[/tex] represent no steroid use
[tex](+)[/tex] represent test positive
[tex](-)[/tex] represent test negative
so we have;
0.95 [tex](+)[/tex]
[tex](S)[/tex]
0.1 0.05 [tex](-)[/tex]
[ P ]
0.9 0.15 [tex](+)[/tex]
[tex](S_{no})[/tex]
0.85 [tex](-)[/tex]
Find the final amount of money in an account if $7, 200 is deposited at 2.5 % interest compounded
quarterly (every 3 months) and the money is left for 9 years.
The final amount is $
Round answer to 2 decimal places
The final amount is $7,615.27
A = P(1 + r/n)^t
Where,
A = Final amount
P = principal = $7, 200
r = interest rate = 2.5% = 0.025
n = number of periods = 4
t = time = 9 years
A = P(1 + r/n)^t
= 7,200(1 + 0.025/4)^9
= 7,200(1 + 0.00625)^9
= 7,200(1.00625)^9
= 7,200(1.0576769512798)
= 7,615.2740492152
Approximately,
A = $7,615.27
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